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vector-toc-level-3"> <a class="vector-toc-link" href="#Reflections"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Reflections</span> </div> </a> <ul id="toc-Reflections-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Refractions" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Refractions"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.3</span> <span>Refractions</span> </div> </a> <ul id="toc-Refractions-sublist" class="vector-toc-list"> <li id="toc-Lenses" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Lenses"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.3.1</span> <span>Lenses</span> </div> </a> <ul id="toc-Lenses-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Physical_optics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Physical_optics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Physical optics</span> </div> </a> <ul id="toc-Physical_optics-sublist" class="vector-toc-list"> <li id="toc-Modelling_and_design_of_optical_systems_using_physical_optics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Modelling_and_design_of_optical_systems_using_physical_optics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Modelling and design of optical systems using physical optics</span> </div> </a> <ul id="toc-Modelling_and_design_of_optical_systems_using_physical_optics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Superposition_and_interference" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Superposition_and_interference"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>Superposition and interference</span> </div> </a> <ul id="toc-Superposition_and_interference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diffraction_and_optical_resolution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Diffraction_and_optical_resolution"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.3</span> <span>Diffraction and optical resolution</span> </div> </a> <ul id="toc-Diffraction_and_optical_resolution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dispersion_and_scattering" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Dispersion_and_scattering"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.4</span> <span>Dispersion and scattering</span> </div> </a> <ul id="toc-Dispersion_and_scattering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polarisation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Polarisation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.5</span> <span>Polarisation</span> </div> </a> <ul id="toc-Polarisation-sublist" class="vector-toc-list"> <li id="toc-Changing_polarisation" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Changing_polarisation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.5.1</span> <span>Changing polarisation</span> </div> </a> <ul id="toc-Changing_polarisation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Natural_light" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Natural_light"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.5.2</span> <span>Natural light</span> </div> </a> <ul id="toc-Natural_light-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Modern_optics" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Modern_optics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Modern optics</span> </div> </a> <button aria-controls="toc-Modern_optics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Modern optics subsection</span> </button> <ul id="toc-Modern_optics-sublist" class="vector-toc-list"> <li id="toc-Lasers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lasers"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Lasers</span> </div> </a> <ul id="toc-Lasers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kapitsa–Dirac_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kapitsa–Dirac_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Kapitsa–Dirac effect</span> </div> </a> <ul id="toc-Kapitsa–Dirac_effect-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Human_eye" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Human_eye"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Human eye</span> </div> </a> <ul id="toc-Human_eye-sublist" class="vector-toc-list"> <li id="toc-Visual_effects" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Visual_effects"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Visual effects</span> </div> </a> <ul id="toc-Visual_effects-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optical_instruments" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Optical_instruments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2</span> <span>Optical instruments</span> </div> </a> <ul id="toc-Optical_instruments-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Photography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Photography"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Photography</span> </div> </a> <ul id="toc-Photography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Atmospheric_optics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Atmospheric_optics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Atmospheric optics</span> </div> </a> <ul id="toc-Atmospheric_optics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Works_cited" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Works_cited"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Works cited</span> </div> </a> <ul id="toc-Works_cited-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Optics</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 112 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-112" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">112 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Optika" title="Optika – Afrikaans" lang="af" hreflang="af" data-title="Optika" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B5%D8%B1%D9%8A%D8%A7%D8%AA" title="بصريات – Arabic" lang="ar" hreflang="ar" data-title="بصريات" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%93ptica" title="Óptica – Asturian" lang="ast" hreflang="ast" data-title="Óptica" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Optika" title="Optika – Azerbaijani" lang="az" hreflang="az" data-title="Optika" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D9%88%D9%BE%D8%AA%DB%8C%DA%A9%D8%A7" title="اوپتیکا – South Azerbaijani" lang="azb" hreflang="azb" data-title="اوپتیکا" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%B2%E0%A7%8B%E0%A6%95%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="আলোকবিজ্ঞান – Bangla" lang="bn" hreflang="bn" data-title="আলোকবিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D1%8B%D0%BA%D0%B0" title="Оптыка – Belarusian" lang="be" hreflang="be" data-title="Оптыка" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D1%8B%D0%BA%D0%B0" title="Оптыка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Оптыка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Optika" title="Optika – Central Bikol" lang="bcl" hreflang="bcl" data-title="Optika" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Bulgarian" lang="bg" hreflang="bg" data-title="Оптика" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Optik" title="Optik – Bavarian" lang="bar" hreflang="bar" data-title="Optik" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A0%E0%BD%BC%E0%BD%91%E0%BC%8B%E0%BD%A2%E0%BD%B2%E0%BD%82%E0%BC%8B%E0%BD%94%E0%BC%8B" title="འོད་རིག་པ་ – Tibetan" lang="bo" hreflang="bo" data-title="འོད་རིག་པ་" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bs badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://bs.wikipedia.org/wiki/Optika" title="Optika – Bosnian" lang="bs" hreflang="bs" data-title="Optika" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%92ptica" title="Òptica – Catalan" lang="ca" hreflang="ca" data-title="Òptica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Chuvash" lang="cv" hreflang="cv" data-title="Оптика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Optika" title="Optika – Czech" lang="cs" hreflang="cs" data-title="Optika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Opteg" title="Opteg – Welsh" lang="cy" hreflang="cy" data-title="Opteg" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Optik" title="Optik – Danish" lang="da" hreflang="da" data-title="Optik" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Optik" title="Optik – German" lang="de" hreflang="de" data-title="Optik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Optika" title="Optika – Estonian" lang="et" hreflang="et" data-title="Optika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9F%CF%80%CF%84%CE%B9%CE%BA%CE%AE" title="Οπτική – Greek" lang="el" hreflang="el" data-title="Οπτική" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%93ptica" title="Óptica – Spanish" lang="es" hreflang="es" data-title="Óptica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Optiko" title="Optiko – Esperanto" lang="eo" hreflang="eo" data-title="Optiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/%C3%93tica" title="Ótica – Extremaduran" lang="ext" hreflang="ext" data-title="Ótica" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Optika" title="Optika – Basque" lang="eu" hreflang="eu" data-title="Optika" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D9%88%D8%B1%D8%B4%D9%86%D8%A7%D8%B3%DB%8C" title="نورشناسی – Persian" lang="fa" hreflang="fa" data-title="نورشناسی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Optique" title="Optique – French" lang="fr" hreflang="fr" data-title="Optique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Otiche" title="Otiche – Friulian" lang="fur" hreflang="fur" data-title="Otiche" data-language-autonym="Furlan" data-language-local-name="Friulian" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Optaic" title="Optaic – Irish" lang="ga" hreflang="ga" data-title="Optaic" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%93ptica" title="Óptica – Galician" lang="gl" hreflang="gl" data-title="Óptica" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B4%91%ED%95%99" title="광학 – Korean" lang="ko" hreflang="ko" data-title="광학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%95%D5%BA%D5%BF%D5%AB%D5%AF%D5%A1" title="Օպտիկա – Armenian" lang="hy" hreflang="hy" data-title="Օպտիկա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%95%E0%A4%BE%E0%A4%B6%E0%A4%BF%E0%A4%95%E0%A5%80" title="प्रकाशिकी – Hindi" lang="hi" hreflang="hi" data-title="प्रकाशिकी" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Optika" title="Optika – Croatian" lang="hr" hreflang="hr" data-title="Optika" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Optiko" title="Optiko – Ido" lang="io" hreflang="io" data-title="Optiko" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Optika" title="Optika – Indonesian" lang="id" hreflang="id" data-title="Optika" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Optica" title="Optica – Interlingua" lang="ia" hreflang="ia" data-title="Optica" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ezomkhanyizo" title="Ezomkhanyizo – Zulu" lang="zu" hreflang="zu" data-title="Ezomkhanyizo" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Lj%C3%B3sfr%C3%A6%C3%B0i" title="Ljósfræði – Icelandic" lang="is" hreflang="is" data-title="Ljósfræði" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ottica" title="Ottica – Italian" lang="it" hreflang="it" data-title="Ottica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%95%D7%A4%D7%98%D7%99%D7%A7%D7%94" title="אופטיקה – Hebrew" lang="he" hreflang="he" data-title="אופטיקה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Optika" title="Optika – Javanese" lang="jv" hreflang="jv" data-title="Optika" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A6%E0%B3%83%E0%B2%97%E0%B3%8D%E0%B2%B5%E0%B2%BF%E0%B2%9C%E0%B3%8D%E0%B2%9E%E0%B2%BE%E0%B2%A8" title="ದೃಗ್ವಿಜ್ಞಾನ – Kannada" lang="kn" hreflang="kn" data-title="ದೃಗ್ವಿಜ್ಞಾನ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9D%E1%83%9E%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="ოპტიკა – Georgian" lang="ka" hreflang="ka" data-title="ოპტიკა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Kazakh" lang="kk" hreflang="kk" data-title="Оптика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/%C3%92ptik" title="Òptik – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Òptik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Opt%C3%AEk" title="Optîk – Kurdish" lang="ku" hreflang="ku" data-title="Optîk" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Kyrgyz" lang="ky" hreflang="ky" data-title="Оптика" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Optica" title="Optica – Latin" lang="la" hreflang="la" data-title="Optica" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Optika" title="Optika – Latvian" lang="lv" hreflang="lv" data-title="Optika" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Optik" title="Optik – Luxembourgish" lang="lb" hreflang="lb" data-title="Optik" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Optika" title="Optika – Lithuanian" lang="lt" hreflang="lt" data-title="Optika" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Optika" title="Optika – Hungarian" lang="hu" hreflang="hu" data-title="Optika" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://mk.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Macedonian" lang="mk" hreflang="mk" data-title="Оптика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%95%E0%B4%BE%E0%B4%B6%E0%B4%B6%E0%B4%BE%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%82" title="പ്രകാശശാസ്ത്രം – Malayalam" lang="ml" hreflang="ml" data-title="പ്രകാശശാസ്ത്രം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Optik" title="Optik – Malay" lang="ms" hreflang="ms" data-title="Optik" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/%C3%93tica" title="Ótica – Mirandese" lang="mwl" hreflang="mwl" data-title="Ótica" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA" title="Оптик – Mongolian" lang="mn" hreflang="mn" data-title="Оптик" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%9C%E1%80%84%E1%80%BA%E1%80%B8%E1%80%97%E1%80%B1%E1%80%92" title="အလင်းဗေဒ – Burmese" lang="my" hreflang="my" data-title="အလင်းဗေဒ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Optika" title="Optika – Fijian" lang="fj" hreflang="fj" data-title="Optika" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijian" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Optica" title="Optica – Dutch" lang="nl" hreflang="nl" data-title="Optica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%85%E0%A4%AA%E0%A5%8D%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%8D%E0%A4%B8" title="अप्तिक्स – Newari" lang="new" hreflang="new" data-title="अप्तिक्स" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%85%89%E5%AD%A6" title="光学 – Japanese" lang="ja" hreflang="ja" data-title="光学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Optik" title="Optik – Northern Frisian" lang="frr" hreflang="frr" data-title="Optik" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Optikk" title="Optikk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Optikk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Optikk" title="Optikk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Optikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Optica" title="Optica – Occitan" lang="oc" hreflang="oc" data-title="Optica" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Optika" title="Optika – Uzbek" lang="uz" hreflang="uz" data-title="Optika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A9%8D%E0%A8%B0%E0%A8%95%E0%A8%BE%E0%A8%B8%E0%A8%BC_%E0%A8%B5%E0%A8%BF%E0%A8%97%E0%A8%BF%E0%A8%86%E0%A8%A8" title="ਪ੍ਰਕਾਸ਼ ਵਿਗਿਆਨ – Punjabi" lang="pa" hreflang="pa" data-title="ਪ੍ਰਕਾਸ਼ ਵਿਗਿਆਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF_%D9%86%D9%88%D8%B1_%D9%81%D8%B2%DB%8C%DA%A9" title="د نور فزیک – Pashto" lang="ps" hreflang="ps" data-title="د نور فزیک" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/%C3%92tica" title="Òtica – Piedmontese" lang="pms" hreflang="pms" data-title="Òtica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Optyka" title="Optyka – Polish" lang="pl" hreflang="pl" data-title="Optyka" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%93ptica" title="Óptica – Portuguese" lang="pt" hreflang="pt" data-title="Óptica" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Optic%C4%83" title="Optică – Romanian" lang="ro" hreflang="ro" data-title="Optică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D1%96%D0%BA%D0%B0" title="Оптіка – Rusyn" lang="rue" hreflang="rue" data-title="Оптіка" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Russian" lang="ru" hreflang="ru" data-title="Оптика" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%A2%E1%B1%9F%E1%B1%A8%E1%B1%A5%E1%B1%9F%E1%B1%9E_%E1%B1%A5%E1%B1%9F%E1%B1%AC%E1%B1%AE%E1%B1%A5" title="ᱢᱟᱨᱥᱟᱞ ᱥᱟᱬᱮᱥ – Santali" lang="sat" hreflang="sat" data-title="ᱢᱟᱨᱥᱟᱞ ᱥᱟᱬᱮᱥ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="Santali" class="interlanguage-link-target"><span>ᱥᱟᱱᱛᱟᱲᱤ</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Optik" title="Optik – Saterland Frisian" lang="stq" hreflang="stq" data-title="Optik" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Optika" title="Optika – Albanian" lang="sq" hreflang="sq" data-title="Optika" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/%C3%92ttica" title="Òttica – Sicilian" lang="scn" hreflang="scn" data-title="Òttica" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%9A%E0%B7%8F%E0%B7%81_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B7%80" title="ප්‍රකාශ විද්‍යාව – Sinhala" lang="si" hreflang="si" data-title="ප්‍රකාශ විද්‍යාව" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Optics" title="Optics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Optics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A8%D8%B5%D8%B1%D9%8A%D8%A7%D8%AA" title="بصريات – Sindhi" lang="sd" hreflang="sd" data-title="بصريات" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Optika_(odbor)" title="Optika (odbor) – Slovak" lang="sk" hreflang="sk" data-title="Optika (odbor)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Optika" title="Optika – Slovenian" lang="sl" hreflang="sl" data-title="Optika" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Araga" title="Araga – Somali" lang="so" hreflang="so" data-title="Araga" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%86%D9%BE%D8%AA%DB%8C%DA%A9" title="ئۆپتیک – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئۆپتیک" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Serbian" lang="sr" hreflang="sr" data-title="Оптика" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Optika" title="Optika – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Optika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Optiikka" title="Optiikka – Finnish" lang="fi" hreflang="fi" data-title="Optiikka" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Optik" title="Optik – Swedish" lang="sv" hreflang="sv" data-title="Optik" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Optika" title="Optika – Tagalog" lang="tl" hreflang="tl" data-title="Optika" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%92%E0%AE%B3%E0%AE%BF%E0%AE%AF%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="ஒளியியல் – Tamil" lang="ta" hreflang="ta" data-title="ஒளியியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Tasni%E1%BA%93%E1%B9%9Bi" title="Tasniẓṛi – Tachelhit" lang="shi" hreflang="shi" data-title="Tasniẓṛi" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-tt badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://tt.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Tatar" lang="tt" hreflang="tt" data-title="Оптика" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te badge-Q70893996 mw-list-item" title=""><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B0%BE%E0%B0%82%E0%B0%A4%E0%B0%BF_%E0%B0%B6%E0%B0%BE%E0%B0%B8%E0%B1%8D%E0%B0%A4%E0%B1%8D%E0%B0%B0%E0%B0%82" title="కాంతి శాస్త్రం – Telugu" lang="te" hreflang="te" data-title="కాంతి శాస్త్రం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%B1%E0%B8%A8%E0%B8%99%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="ทัศนศาสตร์ – Thai" lang="th" hreflang="th" data-title="ทัศนศาสตร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Tajik" lang="tg" hreflang="tg" data-title="Оптика" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Optik" title="Optik – Turkish" lang="tr" hreflang="tr" data-title="Optik" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Оптика – Ukrainian" lang="uk" hreflang="uk" data-title="Оптика" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B5%D8%B1%DB%8C%D8%A7%D8%AA" title="بصریات – Urdu" lang="ur" hreflang="ur" data-title="بصریات" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Optik" title="Optik – Veps" lang="vep" hreflang="vep" data-title="Optik" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Quang_h%E1%BB%8Dc" title="Quang học – Vietnamese" lang="vi" hreflang="vi" data-title="Quang học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Valgus%C3%B5oppus" title="Valgusõoppus – Võro" lang="vro" hreflang="vro" data-title="Valgusõoppus" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Optika" title="Optika – Waray" lang="war" hreflang="war" data-title="Optika" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Ngiste" title="Ngiste – Wolof" lang="wo" hreflang="wo" data-title="Ngiste" data-language-autonym="Wolof" data-language-local-name="Wolof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%85%89%E5%AD%A6" title="光学 – Wu" lang="wuu" hreflang="wuu" data-title="光学" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%A4%D7%98%D7%99%D7%A7" title="אפטיק – Yiddish" lang="yi" hreflang="yi" data-title="אפטיק" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%85%89%E5%AD%B8" title="光學 – Cantonese" lang="yue" hreflang="yue" data-title="光學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Opt%C4%97ka" title="Optėka – Samogitian" lang="sgs" hreflang="sgs" data-title="Optėka" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%85%89%E5%AD%A6" title="光学 – Chinese" lang="zh" hreflang="zh" data-title="光学" data-language-autonym="中文" data-language-local-name="Chinese" 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i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the branch of physics. For the book by Sir Isaac Newton, see <a href="/wiki/Opticks" title="Opticks">Opticks</a>. For other uses, see <a href="/wiki/Optics_(disambiguation)" class="mw-redirect mw-disambig" title="Optics (disambiguation)">Optics (disambiguation)</a>.</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:ANDY7187.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/ANDY7187.jpg/330px-ANDY7187.jpg" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/ANDY7187.jpg/500px-ANDY7187.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/ANDY7187.jpg/960px-ANDY7187.jpg 2x" data-file-width="4168" data-file-height="2779" /></a><figcaption>A researcher working on an optical system</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist 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src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Physics" title="Category:Physics">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:TopicTOC-Physics" title="Template:TopicTOC-Physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:TopicTOC-Physics" title="Template talk:TopicTOC-Physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:TopicTOC-Physics" title="Special:EditPage/Template:TopicTOC-Physics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Optics</b> is the branch of <a href="/wiki/Physics" title="Physics">physics</a> that studies the behaviour and properties of <a href="/wiki/Light" title="Light">light</a>, including its interactions with <a href="/wiki/Matter" title="Matter">matter</a> and the construction of <a href="/wiki/Optical_instruments" class="mw-redirect" title="Optical instruments">instruments</a> that use or <a href="/wiki/Photodetector" title="Photodetector">detect</a> it.<sup id="cite_ref-McGrawHill_1-0" class="reference"><a href="#cite_note-McGrawHill-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Optics usually describes the behaviour of <a href="/wiki/Visible_light" class="mw-redirect" title="Visible light">visible</a>, <a href="/wiki/Ultraviolet" title="Ultraviolet">ultraviolet</a>, and <a href="/wiki/Infrared" title="Infrared">infrared</a> light. Light is a type of <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>, and other forms of electromagnetic radiation such as <a href="/wiki/X-ray" title="X-ray">X-rays</a>, <a href="/wiki/Microwave" title="Microwave">microwaves</a>, and <a href="/wiki/Radio_wave" title="Radio wave">radio waves</a> exhibit similar properties.<sup id="cite_ref-McGrawHill_1-1" class="reference"><a href="#cite_note-McGrawHill-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Most optical phenomena can be accounted for by using the <a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">classical electromagnetic</a> description of light, however complete electromagnetic descriptions of light are often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, <a href="/wiki/Geometric_optics" class="mw-redirect" title="Geometric optics">geometric optics</a>, treats light as a collection of <a href="/wiki/Ray_(optics)" title="Ray (optics)">rays</a> that travel in straight lines and bend when they pass through or reflect from surfaces. <a href="/wiki/Physical_optics" title="Physical optics">Physical optics</a> is a more comprehensive model of light, which includes <a href="/wiki/Wave" title="Wave">wave</a> effects such as <a href="/wiki/Diffraction" title="Diffraction">diffraction</a> and <a href="/wiki/Interference_(optics)" class="mw-redirect" title="Interference (optics)">interference</a> that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation. </p><p>Some phenomena depend on light having both <a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">wave-like and particle-like properties</a>. Explanation of these effects requires <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>. When considering light's particle-like properties, the light is modelled as a collection of particles called "<a href="/wiki/Photon" title="Photon">photons</a>". <a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a> deals with the application of quantum mechanics to optical systems. </p><p>Optical science is relevant to and studied in many related disciplines including <a href="/wiki/Astronomy" title="Astronomy">astronomy</a>, various <a href="/wiki/Engineering" title="Engineering">engineering</a> fields, <a href="/wiki/Photography" title="Photography">photography</a>, and <a href="/wiki/Medicine" title="Medicine">medicine</a> (particularly <a href="/wiki/Ophthalmology" title="Ophthalmology">ophthalmology</a> and <a href="/wiki/Optometry" title="Optometry">optometry</a>, in which it is called physiological optics). Practical applications of optics are found in a variety of technologies and everyday objects, including <a href="/wiki/Mirror" title="Mirror">mirrors</a>, <a href="/wiki/Lens_(optics)" class="mw-redirect" title="Lens (optics)">lenses</a>, <a href="/wiki/Optical_telescope" title="Optical telescope">telescopes</a>, <a href="/wiki/Microscope" title="Microscope">microscopes</a>, <a href="/wiki/Laser" title="Laser">lasers</a>, and <a href="/wiki/Fibre_optics" class="mw-redirect" title="Fibre optics">fibre optics</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_optics" title="History of optics">History of optics</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Timeline_of_electromagnetism_and_classical_optics" title="Timeline of electromagnetism and classical optics">Timeline of electromagnetism and classical optics</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Nimrud_lens_British_Museum.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Nimrud_lens_British_Museum.jpg/250px-Nimrud_lens_British_Museum.jpg" decoding="async" width="220" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Nimrud_lens_British_Museum.jpg/330px-Nimrud_lens_British_Museum.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Nimrud_lens_British_Museum.jpg/500px-Nimrud_lens_British_Museum.jpg 2x" data-file-width="1040" data-file-height="926" /></a><figcaption>The Nimrud lens</figcaption></figure> <p>Optics began with the development of lenses by the <a href="/wiki/Ancient_Egypt" title="Ancient Egypt">ancient Egyptians</a> and <a href="/wiki/Mesopotamia" title="Mesopotamia">Mesopotamians</a>. The earliest known lenses, made from polished <a href="/wiki/Crystal" title="Crystal">crystal</a>, often <a href="/wiki/Quartz" title="Quartz">quartz</a>, date from as early as 2000 BC from <a href="/wiki/Crete" title="Crete">Crete</a> (Archaeological Museum of Heraclion, Greece). Lenses from <a href="/wiki/Rhodes" title="Rhodes">Rhodes</a> date around 700 BC, as do <a href="/wiki/Assyria" title="Assyria">Assyrian</a> lenses such as the <a href="/wiki/Nimrud_lens" title="Nimrud lens">Nimrud lens</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Ancient_Roman" class="mw-redirect" title="Ancient Roman">ancient Romans</a> and <a href="/wiki/Ancient_Greece" title="Ancient Greece">Greeks</a> filled glass spheres with water to make lenses. These practical developments were followed by the development of theories of light and vision by ancient <a href="/wiki/Greek_philosophy" class="mw-redirect" title="Greek philosophy">Greek</a> and <a href="/wiki/Indian_philosophy" title="Indian philosophy">Indian</a> philosophers, and the development of <a href="/wiki/Geometrical_optics" title="Geometrical optics">geometrical optics</a> in the <a href="/wiki/Greco-Roman_world" title="Greco-Roman world">Greco-Roman world</a>. The word <i>optics</i> comes from the <a href="/wiki/Ancient_Greek" title="Ancient Greek">ancient Greek</a> word <span title="Ancient Greek (to 1453)-language text"><span lang="grc">ὀπτική</span></span>, <span title="Ancient Greek (to 1453)-language romanization"><i lang="grc-Latn">optikē</i></span> <span class="gloss-quot">'</span><span class="gloss-text">appearance, look</span><span class="gloss-quot">'</span>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Greek philosophy on optics broke down into two opposing theories on how vision worked, the <a href="/wiki/Intromission_theory" class="mw-redirect" title="Intromission theory">intromission theory</a> and the <a href="/wiki/Emission_theory_(vision)" title="Emission theory (vision)">emission theory</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The intromission approach saw vision as coming from objects casting off copies of themselves (called eidola) that were captured by the eye. With many propagators including <a href="/wiki/Democritus" title="Democritus">Democritus</a>, <a href="/wiki/Epicurus" title="Epicurus">Epicurus</a>, <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> and their followers, this theory seems to have some contact with modern theories of what vision really is, but it remained only speculation lacking any experimental foundation. </p><p><a href="/wiki/Plato" title="Plato">Plato</a> first articulated the <a href="/wiki/Emission_theory_(vision)" title="Emission theory (vision)">emission theory</a>, the idea that <a href="/wiki/Visual_perception" title="Visual perception">visual perception</a> is accomplished by rays emitted by the eyes. He also commented on the <a href="/wiki/Parity_(physics)" title="Parity (physics)">parity</a> reversal of mirrors in <i><a href="/wiki/Timaeus_(dialogue)" title="Timaeus (dialogue)">Timaeus</a></i>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Some hundred years later, <a href="/wiki/Euclid" title="Euclid">Euclid</a> (4th–3rd century BC) wrote a treatise entitled <i><a href="/wiki/Euclid#Other_works" title="Euclid">Optics</a></i> where he linked vision to <a href="/wiki/Geometry" title="Geometry">geometry</a>, creating <i>geometrical optics</i>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> He based his work on Plato's emission theory wherein he described the mathematical rules of <a href="/wiki/Perspective_(graphical)" title="Perspective (graphical)">perspective</a> and described the effects of <a href="/wiki/Refraction" title="Refraction">refraction</a> qualitatively, although he questioned that a beam of light from the eye could instantaneously light up the stars every time someone blinked.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Euclid stated the principle of shortest trajectory of light, and considered multiple reflections on flat and spherical mirrors. <a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>, in his treatise <i><a href="/wiki/Ptolemy#Optics" title="Ptolemy">Optics</a></i>, held an extramission-intromission theory of vision: the rays (or flux) from the eye formed a cone, the vertex being within the eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer's intellect about the distance and orientation of surfaces. He summarized much of Euclid and went on to describe a way to measure the <a href="/wiki/Angle_of_refraction" class="mw-redirect" title="Angle of refraction">angle of refraction</a>, though he failed to notice the empirical relationship between it and the angle of incidence.<sup id="cite_ref-Ptolemy_8-0" class="reference"><a href="#cite_note-Ptolemy-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Plutarch" title="Plutarch">Plutarch</a> (1st–2nd century AD) described multiple reflections on spherical mirrors and discussed the creation of magnified and reduced images, both real and imaginary, including the case of <a href="/wiki/Chirality" title="Chirality">chirality</a> of the images. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ibn_Sahl_manuscript.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Ibn_Sahl_manuscript.jpg/250px-Ibn_Sahl_manuscript.jpg" decoding="async" width="170" height="245" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Ibn_Sahl_manuscript.jpg/330px-Ibn_Sahl_manuscript.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Ibn_Sahl_manuscript.jpg/500px-Ibn_Sahl_manuscript.jpg 2x" data-file-width="1012" data-file-height="1458" /></a><figcaption>Reproduction of a page of <a href="/wiki/Ibn_Sahl_(mathematician)" title="Ibn Sahl (mathematician)">Ibn Sahl</a>'s manuscript showing his knowledge of <a href="/wiki/Snell%27s_law" title="Snell's law">the law of refraction</a> </figcaption></figure> <p>During the <a href="/wiki/Middle_Ages" title="Middle Ages">Middle Ages</a>, Greek ideas about optics were resurrected and extended by writers in the <a href="/wiki/Muslim_world" title="Muslim world">Muslim world</a>. One of the earliest of these was <a href="/wiki/Al-Kindi" title="Al-Kindi">Al-Kindi</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 801</span>–873) who wrote on the merits of Aristotelian and Euclidean ideas of optics, favouring the emission theory since it could better quantify optical phenomena.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> In 984, the <a href="/wiki/Persia" class="mw-redirect" title="Persia">Persian</a> mathematician <a href="/wiki/Ibn_Sahl_(mathematician)" title="Ibn Sahl (mathematician)">Ibn Sahl</a> wrote the treatise "On burning mirrors and lenses", correctly describing a law of refraction equivalent to Snell's law.<sup id="cite_ref-j1_10-0" class="reference"><a href="#cite_note-j1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> He used this law to compute optimum shapes for lenses and <a href="/wiki/Curved_mirror" title="Curved mirror">curved mirrors</a>. In the early 11th century, <a href="/wiki/Ibn_al-Haytham" title="Ibn al-Haytham">Alhazen (Ibn al-Haytham)</a> wrote the <i><a href="/wiki/Book_of_Optics" title="Book of Optics">Book of Optics</a></i> (<i>Kitab al-manazir</i>) in which he explored reflection and refraction and proposed a new system for explaining vision and light based on observation and experiment.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> He rejected the "emission theory" of Ptolemaic optics with its rays being emitted by the eye, and instead put forward the idea that light reflected in all directions in straight lines from all points of the objects being viewed and then entered the eye, although he was unable to correctly explain how the eye captured the rays.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Alhazen's work was largely ignored in the Arabic world but it was anonymously translated into Latin around 1200 A.D. and further summarised and expanded on by the Polish monk <a href="/wiki/Witelo" class="mw-redirect" title="Witelo">Witelo</a><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> making it a standard text on optics in Europe for the next 400 years.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>In the 13th century in medieval Europe, English bishop <a href="/wiki/Robert_Grosseteste" title="Robert Grosseteste">Robert Grosseteste</a> wrote on a wide range of scientific topics, and discussed light from four different perspectives: an <a href="/wiki/Epistemology" title="Epistemology">epistemology</a> of light, a <a href="/wiki/Metaphysics" title="Metaphysics">metaphysics</a> or <a href="/wiki/Cosmogony" title="Cosmogony">cosmogony</a> of light, an <a href="/wiki/Etiology" title="Etiology">etiology</a> or physics of light, and a <a href="/wiki/Theology" title="Theology">theology</a> of light,<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> basing it on the works of Aristotle and Platonism. Grosseteste's most famous disciple, <a href="/wiki/Roger_Bacon" title="Roger Bacon">Roger Bacon</a>, wrote works citing a wide range of recently translated optical and philosophical works, including those of Alhazen, Aristotle, <a href="/wiki/Avicenna" title="Avicenna">Avicenna</a>, <a href="/wiki/Averroes" title="Averroes">Averroes</a>, Euclid, al-Kindi, Ptolemy, Tideus, and <a href="/wiki/Constantine_the_African" title="Constantine the African">Constantine the African</a>. Bacon was able to use parts of glass spheres as <a href="/wiki/Magnifying_glass" title="Magnifying glass">magnifying glasses</a> to demonstrate that light reflects from objects rather than being released from them. </p><p>The first wearable eyeglasses were invented in Italy around 1286.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> This was the start of the optical industry of grinding and polishing lenses for these "spectacles", first in Venice and Florence in the thirteenth century,<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> and later in the spectacle making centres in both the Netherlands and Germany.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Spectacle makers created improved types of lenses for the correction of vision based more on empirical knowledge gained from observing the effects of the lenses rather than using the rudimentary optical theory of the day (theory which for the most part could not even adequately explain how spectacles worked).<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEIlardi2007[httpsarchiveorgdetailsbub_gb_peIL7hVQUmwCpagen221_210]_20-0" class="reference"><a href="#cite_note-FOOTNOTEIlardi2007[httpsarchiveorgdetailsbub_gb_peIL7hVQUmwCpagen221_210]-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> This practical development, mastery, and experimentation with lenses led directly to the invention of the compound <a href="/wiki/Optical_microscope" title="Optical microscope">optical microscope</a> around 1595, and the <a href="/wiki/Refracting_telescope" title="Refracting telescope">refracting telescope</a> in 1608, both of which appeared in the spectacle making centres in the Netherlands.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-LZZginzib4C_page_55_22-0" class="reference"><a href="#cite_note-LZZginzib4C_page_55-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Kepler_-_Ad_Vitellionem_paralipomena_quibus_astronomiae_pars_optica_traditur,_1604_-_158093_F.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Kepler_-_Ad_Vitellionem_paralipomena_quibus_astronomiae_pars_optica_traditur%2C_1604_-_158093_F.jpg/250px-Kepler_-_Ad_Vitellionem_paralipomena_quibus_astronomiae_pars_optica_traditur%2C_1604_-_158093_F.jpg" decoding="async" width="220" height="283" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Kepler_-_Ad_Vitellionem_paralipomena_quibus_astronomiae_pars_optica_traditur%2C_1604_-_158093_F.jpg/330px-Kepler_-_Ad_Vitellionem_paralipomena_quibus_astronomiae_pars_optica_traditur%2C_1604_-_158093_F.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Kepler_-_Ad_Vitellionem_paralipomena_quibus_astronomiae_pars_optica_traditur%2C_1604_-_158093_F.jpg/500px-Kepler_-_Ad_Vitellionem_paralipomena_quibus_astronomiae_pars_optica_traditur%2C_1604_-_158093_F.jpg 2x" data-file-width="1084" data-file-height="1396" /></a><figcaption>The first treatise about optics by <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a>, <span title="Latin-language text"><i lang="la">Ad Vitellionem paralipomena quibus astronomiae pars optica traditur</i></span> (1604), generally recognized as the foundation of modern optics.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Opticks.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Opticks.jpg/170px-Opticks.jpg" decoding="async" width="170" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Opticks.jpg/255px-Opticks.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Opticks.jpg/340px-Opticks.jpg 2x" data-file-width="738" data-file-height="1000" /></a><figcaption>Cover of the first edition of Newton's <i>Opticks</i> (1704)</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Table_of_Opticks,_Cyclopaedia,_Volume_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg/250px-Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg" decoding="async" width="170" height="275" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg/330px-Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg/500px-Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg 2x" data-file-width="1789" data-file-height="2899" /></a><figcaption>Board with optical devices, 1728 Cyclopaedia</figcaption></figure> <p>In the early 17th century, <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> expanded on geometric optics in his writings, covering lenses, reflection by flat and curved mirrors, the principles of <a href="/wiki/Pinhole_camera" title="Pinhole camera">pinhole cameras</a>, inverse-square law governing the intensity of light, and the optical explanations of astronomical phenomena such as <a href="/wiki/Lunar_eclipse" title="Lunar eclipse">lunar</a> and <a href="/wiki/Solar_eclipse" title="Solar eclipse">solar eclipses</a> and astronomical <a href="/wiki/Parallax" title="Parallax">parallax</a>. He was also able to correctly deduce the role of the <a href="/wiki/Retina" title="Retina">retina</a> as the actual organ that recorded images, finally being able to scientifically quantify the effects of different types of lenses that spectacle makers had been observing over the previous 300 years.<sup id="cite_ref-FOOTNOTEIlardi2007[httpsarchiveorgdetailsbub_gb_peIL7hVQUmwCpagen255_244]_24-0" class="reference"><a href="#cite_note-FOOTNOTEIlardi2007[httpsarchiveorgdetailsbub_gb_peIL7hVQUmwCpagen255_244]-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> After the invention of the telescope, Kepler set out the theoretical basis on how they worked and described an improved version, known as the <i><a href="/wiki/Keplerian_telescope" class="mw-redirect" title="Keplerian telescope">Keplerian telescope</a></i>, using two convex lenses to produce higher magnification.<sup id="cite_ref-FOOTNOTECaspar1993[httpsarchiveorgdetailskepler00casppage192mode2up_192–202]_25-0" class="reference"><a href="#cite_note-FOOTNOTECaspar1993[httpsarchiveorgdetailskepler00casppage192mode2up_192–202]-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>Optical theory progressed in the mid-17th century with <a href="/wiki/The_World_(Descartes)#Cartesian_theory_on_light" class="mw-redirect" title="The World (Descartes)">treatises</a> written by philosopher <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a>, which explained a variety of optical phenomena including reflection and refraction by assuming that light was emitted by objects which produced it.<sup id="cite_ref-Sabra_26-0" class="reference"><a href="#cite_note-Sabra-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> This differed substantively from the ancient Greek emission theory. In the late 1660s and early 1670s, <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> expanded Descartes's ideas into a <a href="/wiki/Corpuscle_theory_of_light" class="mw-redirect" title="Corpuscle theory of light">corpuscle theory of light</a>, famously determining that white light was a mix of colours that can be separated into its component parts with a <a href="/wiki/Prism_(optics)" title="Prism (optics)">prism</a>. In 1690, <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a> proposed a wave theory for light based on suggestions that had been made by <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a> in 1664. Hooke himself publicly criticised Newton's theories of light and the feud between the two lasted until Hooke's death. In 1704, Newton published <i><a href="/wiki/Opticks" title="Opticks">Opticks</a></i> and, at the time, partly because of his success in other areas of physics, he was generally considered to be the victor in the debate over the nature of light.<sup id="cite_ref-Sabra_26-1" class="reference"><a href="#cite_note-Sabra-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>Newtonian optics was generally accepted until the early 19th century when <a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a> and <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">Augustin-Jean Fresnel</a> conducted experiments on the <a href="/wiki/Interference_(wave_propagation)" class="mw-redirect" title="Interference (wave propagation)">interference</a> of light that firmly established light's wave nature. Young's famous <a href="/wiki/Young%27s_interference_experiment" title="Young's interference experiment">double slit experiment</a> showed that light followed the <a href="/wiki/Superposition_principle" title="Superposition principle">superposition principle</a>, which is a wave-like property not predicted by Newton's corpuscle theory. This work led to a theory of diffraction for light and opened an entire area of study in physical optics.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Wave optics was successfully unified with <a href="/wiki/Electromagnetic_theory" class="mw-redirect" title="Electromagnetic theory">electromagnetic theory</a> by <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a> in the 1860s.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>The next development in optical theory came in 1899 when <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a> correctly modelled <a href="/wiki/Blackbody_radiation" class="mw-redirect" title="Blackbody radiation">blackbody radiation</a> by assuming that the exchange of energy between light and matter only occurred in discrete amounts he called <i>quanta</i>.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> In 1905, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> published the theory of the <a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a> that firmly established the quantization of light itself.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-AnnPhysik322132_31-0" class="reference"><a href="#cite_note-AnnPhysik322132-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> In 1913, <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a> showed that atoms could only emit discrete amounts of energy, thus explaining the discrete lines seen in <a href="/wiki/Emission_spectrum" title="Emission spectrum">emission</a> and <a href="/wiki/Absorption_spectrum" class="mw-redirect" title="Absorption spectrum">absorption spectra</a>.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> The understanding of the interaction between light and matter that followed from these developments not only formed the basis of quantum optics but also was crucial for the <a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">development</a> of quantum mechanics as a whole. The ultimate culmination, the theory of <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a>, explains all optics and electromagnetic processes in general as the result of the exchange of real and <a href="/wiki/Virtual_particles" class="mw-redirect" title="Virtual particles">virtual</a> photons.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> Quantum optics gained practical importance with the inventions of the <a href="/wiki/Maser" title="Maser">maser</a> in 1953 and of the laser in 1960.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>Following the work of <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> in <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, <a href="/wiki/George_Sudarshan" class="mw-redirect" title="George Sudarshan">George Sudarshan</a>, <a href="/wiki/Roy_J._Glauber" title="Roy J. Glauber">Roy J. Glauber</a>, and <a href="/wiki/Leonard_Mandel" title="Leonard Mandel">Leonard Mandel</a> applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistics</a> of light. </p> <div class="mw-heading mw-heading2"><h2 id="Classical_optics">Classical optics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=2" title="Edit section: Classical optics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Classical_Optics.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Classical_Optics.png/250px-Classical_Optics.png" decoding="async" width="250" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Classical_Optics.png/500px-Classical_Optics.png 1.5x" data-file-width="1551" data-file-height="1487" /></a><figcaption>Classical optics</figcaption></figure> <p>Classical optics is divided into two main branches: geometrical (or ray) optics and physical (or wave) optics. In geometrical optics, light is considered to travel in straight lines, while in physical optics, light is considered as an electromagnetic wave. </p><p>Geometrical optics can be viewed as an approximation of physical optics that applies when the wavelength of the light used is much smaller than the size of the optical elements in the system being modelled. </p> <div class="mw-heading mw-heading3"><h3 id="Geometrical_optics">Geometrical optics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=3" title="Edit section: Geometrical optics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Geometrical_optics" title="Geometrical optics">Geometrical optics</a></div> <figure class="mw-default-size mw-halign-right skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Reflection_and_refraction.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Reflection_and_refraction.svg/250px-Reflection_and_refraction.svg.png" decoding="async" width="250" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Reflection_and_refraction.svg/375px-Reflection_and_refraction.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Reflection_and_refraction.svg/500px-Reflection_and_refraction.svg.png 2x" data-file-width="641" data-file-height="355" /></a><figcaption>Geometry of reflection and refraction of light rays</figcaption></figure><p><i>Geometrical optics</i>, or <i>ray optics</i>, describes the <a href="/wiki/Wave_propagation" class="mw-redirect" title="Wave propagation">propagation</a> of light in terms of "rays" which travel in straight lines, and whose paths are governed by the laws of reflection and refraction at interfaces between different media.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> These laws were discovered empirically as far back as 984 AD<sup id="cite_ref-j1_10-1" class="reference"><a href="#cite_note-j1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and have been used in the design of optical components and instruments from then until the present day. They can be summarised as follows: </p><p>When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray. </p> <ul><li>The law of reflection says that the reflected ray lies in the plane of incidence, and the angle of reflection equals the angle of incidence.</li> <li>The law of refraction says that the refracted ray lies in the plane of incidence, and the sine of the angle of incidence divided by the sine of the angle of refraction is a constant: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sin {\theta _{1}}}{\sin {\theta _{2}}}}=n,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>n</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sin {\theta _{1}}}{\sin {\theta _{2}}}}=n,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1b9663c437379032c6b43a148857443d565bc14" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.364ex; height:5.843ex;" alt="{\displaystyle {\frac {\sin {\theta _{1}}}{\sin {\theta _{2}}}}=n,}" /></span> where <span class="texhtml"><i>n</i></span> is a constant for any two materials and a given colour of light. If the first material is air or vacuum, <span class="texhtml"><i>n</i></span> is the <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a> of the second material.</li></ul> <p>The laws of reflection and refraction can be derived from <a href="/wiki/Fermat%27s_principle" title="Fermat's principle">Fermat's principle</a> which states that <i>the path taken between two points by a ray of light is the path that can be traversed in the least time.</i><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Approximations">Approximations</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=4" title="Edit section: Approximations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Geometric optics is often simplified by making the <a href="/wiki/Paraxial_approximation" title="Paraxial approximation">paraxial approximation</a>, or "small angle approximation". The mathematical behaviour then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of <a href="/wiki/Gaussian_optics" title="Gaussian optics">Gaussian optics</a> and <i>paraxial <a href="/wiki/Ray_tracing_(physics)" title="Ray tracing (physics)">ray tracing</a></i>, which are used to find basic properties of optical systems, such as approximate <a href="/wiki/Image" title="Image">image</a> and object positions and <a href="/wiki/Magnification" title="Magnification">magnifications</a>.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Reflections">Reflections</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=5" title="Edit section: Reflections"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Reflection_(physics)" title="Reflection (physics)">Reflection (physics)</a></div> <figure class="skin-invert-image" typeof="mw:File/Frame"><a href="/wiki/File:Reflection_angles.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Reflection_angles.svg/170px-Reflection_angles.svg.png" decoding="async" width="170" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Reflection_angles.svg/255px-Reflection_angles.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Reflection_angles.svg/340px-Reflection_angles.svg.png 2x" data-file-width="170" data-file-height="204" /></a><figcaption>Diagram of specular reflection</figcaption></figure> <p>Reflections can be divided into two types: <a href="/wiki/Specular_reflection" title="Specular reflection">specular reflection</a> and <a href="/wiki/Diffuse_reflection" title="Diffuse reflection">diffuse reflection</a>. Specular reflection describes the gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for the production of reflected images that can be associated with an actual (<a href="/wiki/Real_image" title="Real image">real</a>) or extrapolated (<a href="/wiki/Virtual_image" title="Virtual image">virtual</a>) location in space. Diffuse reflection describes non-glossy materials, such as paper or rock. The reflections from these surfaces can only be described statistically, with the exact distribution of the reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by <a href="/wiki/Lambert%27s_cosine_law" title="Lambert's cosine law">Lambert's cosine law</a>, which describes surfaces that have equal <a href="/wiki/Luminance" title="Luminance">luminance</a> when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection. </p><p>In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with the <a href="/wiki/Surface_normal" class="mw-redirect" title="Surface normal">surface normal</a>, a line perpendicular to the surface at the point where the ray hits. The incident and reflected rays and the normal lie in a single plane, and the angle between the reflected ray and the surface normal is the same as that between the incident ray and the normal.<sup id="cite_ref-FOOTNOTEYoungFreedman20201109_38-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201109-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> This is known as the <a href="/wiki/Law_of_Reflection" class="mw-redirect" title="Law of Reflection">Law of Reflection</a>. </p><p>For <a href="/wiki/Plane_mirror" title="Plane mirror">flat mirrors</a>, the law of reflection implies that images of objects are upright and the same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. The law also implies that <a href="/wiki/Mirror_image" title="Mirror image">mirror images</a> are parity inverted, which we perceive as a left-right inversion. Images formed from reflection in two (or any even number of) mirrors are not parity inverted. <a href="/wiki/Corner_reflector" title="Corner reflector">Corner reflectors</a> produce reflected rays that travel back in the direction from which the incident rays came.<sup id="cite_ref-FOOTNOTEYoungFreedman20201112–1113_39-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201112–1113-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> This is called <a href="/wiki/Retroreflector" title="Retroreflector">retroreflection</a>. </p><p>Mirrors with curved surfaces can be modelled by ray tracing and using the law of reflection at each point on the surface. For <a href="/wiki/Parabolic_reflector" title="Parabolic reflector">mirrors with parabolic surfaces</a>, parallel rays incident on the mirror produce reflected rays that converge at a common <a href="/wiki/Focus_(optics)" title="Focus (optics)">focus</a>. Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing the focus to be smeared out in space. In particular, spherical mirrors exhibit <a href="/wiki/Spherical_aberration" title="Spherical aberration">spherical aberration</a>. Curved mirrors can form images with a magnification greater than or less than one, and the magnification can be negative, indicating that the image is inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen.<sup id="cite_ref-FOOTNOTEYoungFreedman20201142–1143,_1145_40-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201142–1143,_1145-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Refractions">Refractions</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=6" title="Edit section: Refractions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Refraction" title="Refraction">Refraction</a></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Snells_law.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Snells_law.svg/330px-Snells_law.svg.png" decoding="async" width="300" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Snells_law.svg/500px-Snells_law.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Snells_law.svg/600px-Snells_law.svg.png 2x" data-file-width="641" data-file-height="355" /></a><figcaption>Illustration of Snell's Law for the case <span class="texhtml"><i>n</i><sub>1</sub> < <i>n</i><sub>2</sub></span>, such as air/water interface</figcaption></figure> <p>Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an <a href="/wiki/Interface_(chemistry)" class="mw-redirect" title="Interface (chemistry)">interface</a> between a uniform medium with index of refraction <span class="texhtml"><i>n</i><sub>1</sub></span> and another medium with index of refraction <span class="texhtml"><i>n</i><sub>2</sub></span>. In such situations, <a href="/wiki/Snell%27s_Law" class="mw-redirect" title="Snell's Law">Snell's Law</a> describes the resulting deflection of the light ray: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6b2a5ea2d5d1fdf92e3b13e58bd3f91a48236ff" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.545ex; height:2.509ex;" alt="{\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}}" /></span> </p><p>where <span class="texhtml"><i>θ</i><sub>1</sub></span> and <span class="texhtml"><i>θ</i><sub>2</sub></span> are the angles between the normal (to the interface) and the incident and refracted waves, respectively.<sup id="cite_ref-FOOTNOTEYoungFreedman20201109_38-1" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201109-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>The index of refraction of a medium is related to the speed, <span class="texhtml"><i>v</i></span>, of light in that medium by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=c/v,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>v</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=c/v,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c9381a601b21040164107c883db52740835d3df" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.437ex; height:2.843ex;" alt="{\displaystyle n=c/v,}" /></span> where <span class="texhtml"><i>c</i></span> is the <a href="/wiki/Speed_of_light_in_vacuum" class="mw-redirect" title="Speed of light in vacuum">speed of light in vacuum</a>. </p><p>Snell's Law can be used to predict the deflection of light rays as they pass through linear media as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. In most materials, the index of refraction varies with the frequency of the light, known as <a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">dispersion</a>. Taking this into account, Snell's Law can be used to predict how a prism will disperse light into a spectrum.<sup id="cite_ref-FOOTNOTEYoungFreedman20201116_41-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201116-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton. </p><p>Some media have an index of refraction which varies gradually with position and, therefore, light rays in the medium are curved. This effect is responsible for <a href="/wiki/Mirage" title="Mirage">mirages</a> seen on hot days: a change in index of refraction air with height causes light rays to bend, creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Optical materials with varying indexes of refraction are called gradient-index (GRIN) materials. Such materials are used to make <a href="/wiki/Gradient-index_optics" title="Gradient-index optics">gradient-index optics</a>.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>For light rays travelling from a material with a high index of refraction to a material with a low index of refraction, Snell's law predicts that there is no <span class="texhtml"><i>θ</i><sub>2</sub></span> when <span class="texhtml"><i>θ</i><sub>1</sub></span> is large. In this case, no transmission occurs; all the light is reflected. This phenomenon is called <a href="/wiki/Total_internal_reflection" title="Total internal reflection">total internal reflection</a> and allows for fibre optics technology. As light travels down an optical fibre, it undergoes total internal reflection allowing for essentially no light to be lost over the length of the cable.<sup id="cite_ref-FOOTNOTEYoungFreedman20201113–1115_43-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201113–1115-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Lenses">Lenses</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=7" title="Edit section: Lenses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Lens_(optics)" class="mw-redirect" title="Lens (optics)">Lens (optics)</a></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Lens3b.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Lens3b.svg/360px-Lens3b.svg.png" decoding="async" width="360" height="257" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Lens3b.svg/540px-Lens3b.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/Lens3b.svg/720px-Lens3b.svg.png 2x" data-file-width="362" data-file-height="258" /></a><figcaption>A ray tracing diagram for a converging lens</figcaption></figure> <p>A device that produces converging or diverging light rays due to refraction is known as a <i>lens</i>. Lenses are characterized by their <a href="/wiki/Focal_length" title="Focal length">focal length</a>: a converging lens has positive focal length, while a diverging lens has negative focal length. Smaller focal length indicates that the lens has a stronger converging or diverging effect. The focal length of a simple lens in air is given by the <a href="/wiki/Lensmaker%27s_equation" class="mw-redirect" title="Lensmaker's equation">lensmaker's equation</a>.<sup id="cite_ref-FOOTNOTEHecht2017159_44-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017159-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p><p>Ray tracing can be used to show how images are formed by a lens. For a <a href="/wiki/Thin_lens" title="Thin lens">thin lens</a> in air, the location of the image is given by the simple equation </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}={\frac {1}{f}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>f</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}={\frac {1}{f}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cf466a3b4662f8e99a3168b9c58f46c4034b22a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.331ex; height:5.676ex;" alt="{\displaystyle {\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}={\frac {1}{f}},}" /></span> </p><p>where <span class="texhtml"><i>S</i><sub>1</sub></span> is the distance from the object to the lens, <span class="texhtml"><i>θ</i><sub>2</sub></span> is the distance from the lens to the image, and <span class="texhtml mvar" style="font-style:italic;">f</span> is the focal length of the lens. In the <a href="/wiki/Sign_convention" title="Sign convention">sign convention</a> used here, the object and image distances are positive if the object and image are on opposite sides of the lens.<sup id="cite_ref-FOOTNOTEHecht2017165_45-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017165-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Lens1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Lens1.svg/500px-Lens1.svg.png" decoding="async" width="360" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Lens1.svg/540px-Lens1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Lens1.svg/720px-Lens1.svg.png 2x" data-file-width="522" data-file-height="345" /></a><figcaption></figcaption></figure> <p>Incoming parallel rays are focused by a converging lens onto a spot one focal length from the lens, on the far side of the lens. This is called the rear focal point of the lens. Rays from an object at a finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. </p><p>With diverging lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at a spot one focal length in front of the lens. This is the lens's front focal point. Rays from an object at a finite distance are associated with a virtual image that is closer to the lens than the focal point, and on the same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens. As with mirrors, upright images produced by a single lens are virtual, while inverted images are real.<sup id="cite_ref-FOOTNOTEYoungFreedman20201157_46-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201157-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p>Lenses suffer from <a href="/wiki/Optical_aberration" title="Optical aberration">aberrations</a> that distort images. <i>Monochromatic aberrations</i> occur because the geometry of the lens does not perfectly direct rays from each object point to a single point on the image, while <a href="/wiki/Chromatic_aberration" title="Chromatic aberration">chromatic aberration</a> occurs because the index of refraction of the lens varies with the wavelength of the light.<sup id="cite_ref-FOOTNOTEYoungFreedman20201143,1163,1175_47-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201143,1163,1175-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Thin_lens_images.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Thin_lens_images.svg/500px-Thin_lens_images.svg.png" decoding="async" width="500" height="286" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Thin_lens_images.svg/750px-Thin_lens_images.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Thin_lens_images.svg/1000px-Thin_lens_images.svg.png 2x" data-file-width="512" data-file-height="293" /></a><figcaption>Images of black letters in a thin convex lens of focal length <span class="texhtml mvar" style="font-style:italic;">f</span> are shown in red. Selected rays are shown for letters <b>E</b>, <b>I</b> and <b>K</b> in blue, green and orange, respectively. Note that <b>E</b> (at <span class="texhtml">2<i>f</i></span>) has an equal-size, real and inverted image; <b>I</b> (at <span class="texhtml mvar" style="font-style:italic;">f</span>) has its image at infinity; and <b>K</b> (at <span class="texhtml"><i>f</i>/2</span>) has a double-size, virtual and upright image.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Physical_optics">Physical optics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=8" title="Edit section: Physical optics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Physical_optics" title="Physical optics">Physical optics</a></div> <p>In physical optics, light is considered to propagate as waves. This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics. The <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> waves in <a href="/wiki/Air" class="mw-redirect" title="Air">air</a> is approximately 3.0×10<sup>8</sup> m/s (exactly 299,792,458 m/s in <a href="/wiki/Vacuum" title="Vacuum">vacuum</a>). The <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> of visible light waves varies between 400 and 700 nm, but the term "light" is also often applied to infrared (0.7–300 μm) and ultraviolet radiation (10–400 nm). </p><p>The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Until the middle of the 19th century, most physicists believed in an "ethereal" medium in which the light disturbance propagated.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> The existence of electromagnetic waves was predicted in 1865 by <a href="/wiki/Electromagnetic_waves#Derivation_from_electromagnetic_theory" class="mw-redirect" title="Electromagnetic waves">Maxwell's equations</a>. These waves propagate at the speed of light and have varying electric and magnetic fields which are orthogonal to one another, and also to the direction of propagation of the waves.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> Light waves are now generally treated as electromagnetic waves except when <a class="mw-selflink-fragment" href="#Modern_optics">quantum mechanical effects</a> have to be considered. </p> <div class="mw-heading mw-heading4"><h4 id="Modelling_and_design_of_optical_systems_using_physical_optics">Modelling and design of optical systems using physical optics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=9" title="Edit section: Modelling and design of optical systems using physical optics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many simplified approximations are available for analysing and designing optical systems. Most of these use a single <a href="/wiki/Scalar_(physics)" title="Scalar (physics)">scalar</a> quantity to represent the electric field of the light wave, rather than using a <a href="/wiki/Euclidean_vector" title="Euclidean vector">vector</a> model with orthogonal electric and magnetic vectors.<sup id="cite_ref-Born_and_Wolf_50-0" class="reference"><a href="#cite_note-Born_and_Wolf-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Huygens%E2%80%93Fresnel_principle" title="Huygens–Fresnel principle">Huygens–Fresnel</a> equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygens' hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of <a href="/wiki/Superposition_principle" title="Superposition principle">superposition</a> of waves. The <a href="/wiki/Kirchhoff%27s_diffraction_formula" title="Kirchhoff's diffraction formula">Kirchhoff diffraction equation</a>, which is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens–Fresnel principle can be found in the articles on diffraction and <a href="/wiki/Fraunhofer_diffraction" title="Fraunhofer diffraction">Fraunhofer diffraction</a>. </p><p>More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with materials whose electric and magnetic properties affect the interaction of light with the material. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a dielectric material. A vector model must also be used to model polarised light. </p><p><a href="/wiki/Computer_simulation" title="Computer simulation">Numerical modeling</a> techniques such as the <a href="/wiki/Finite_element_method" title="Finite element method">finite element method</a>, the <a href="/wiki/Boundary_element_method" title="Boundary element method">boundary element method</a> and the <a href="/wiki/Transmission-line_matrix_method" title="Transmission-line matrix method">transmission-line matrix method</a> can be used to model the propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p><p>All of the results from geometrical optics can be recovered using the techniques of <a href="/wiki/Fourier_optics" title="Fourier optics">Fourier optics</a> which apply many of the same mathematical and analytical techniques used in <a href="/wiki/Acoustic_engineering" class="mw-redirect" title="Acoustic engineering">acoustic engineering</a> and <a href="/wiki/Signal_processing" title="Signal processing">signal processing</a>. </p><p><a href="/wiki/Gaussian_beam" title="Gaussian beam">Gaussian beam propagation</a> is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Superposition_and_interference">Superposition and interference</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=10" title="Edit section: Superposition and interference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Superposition_principle" title="Superposition principle">Superposition principle</a> and <a href="/wiki/Interference_(optics)" class="mw-redirect" title="Interference (optics)">Interference (optics)</a></div> <p>In the absence of <a href="/wiki/Nonlinear_optics" title="Nonlinear optics">nonlinear</a> effects, the superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances.<sup id="cite_ref-FOOTNOTEYoungFreedman20201187–1188_53-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201187–1188-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> This interaction of waves to produce a resulting pattern is generally termed "interference" and can result in a variety of outcomes. If two waves of the same wavelength and frequency are <i>in <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a></i>, both the wave crests and wave troughs align. This results in <a href="/wiki/Constructive_interference" class="mw-redirect" title="Constructive interference">constructive interference</a> and an increase in the amplitude of the wave, which for light is associated with a brightening of the waveform in that location. Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice versa. This results in <a href="/wiki/Destructive_interference" class="mw-redirect" title="Destructive interference">destructive interference</a> and a decrease in the amplitude of the wave, which for light is associated with a dimming of the waveform at that location. See below for an illustration of this effect.<sup id="cite_ref-FOOTNOTEYoungFreedman2020512,_1189_54-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman2020512,_1189-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <table> <tbody><tr> <td><b>combined<br /> waveform</b> </td> <td colspan="2" rowspan="3"><span class="mw-default-size skin-invert-image" typeof="mw:File"><a href="/wiki/File:Interference_of_two_waves.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Interference_of_two_waves.svg/365px-Interference_of_two_waves.svg.png" decoding="async" width="365" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Interference_of_two_waves.svg/548px-Interference_of_two_waves.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Interference_of_two_waves.svg/730px-Interference_of_two_waves.svg.png 2x" data-file-width="365" data-file-height="122" /></a></span> </td></tr> <tr> <td><b>wave 1</b> </td></tr> <tr> <td><b>wave 2</b> </td></tr> <tr> <td> </td> <td><b>Two waves in phase</b> </td> <td><b>Two waves 180° out <br />of phase</b> </td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Dieselrainbow.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Dieselrainbow.jpg/330px-Dieselrainbow.jpg" decoding="async" width="300" height="268" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Dieselrainbow.jpg/500px-Dieselrainbow.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Dieselrainbow.jpg/960px-Dieselrainbow.jpg 2x" data-file-width="976" data-file-height="871" /></a><figcaption>When oil or fuel is spilled, colourful patterns are formed by thin-film interference.</figcaption></figure> <p>Since the Huygens–Fresnel principle states that every point of a wavefront is associated with the production of a new disturbance, it is possible for a wavefront to interfere with itself constructively or destructively at different locations producing bright and dark fringes in regular and predictable patterns.<sup id="cite_ref-FOOTNOTEYoungFreedman20201191–1192_55-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201191–1192-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Interferometry" title="Interferometry">Interferometry</a> is the science of measuring these patterns, usually as a means of making precise determinations of distances or <a href="/wiki/Angular_resolution" title="Angular resolution">angular resolutions</a>.<sup id="cite_ref-interferometry_56-0" class="reference"><a href="#cite_note-interferometry-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Michelson_interferometer" title="Michelson interferometer">Michelson interferometer</a> was a famous instrument which used interference effects to accurately measure the speed of light.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p><p>The appearance of <a href="/wiki/Thin_film_optics" class="mw-redirect" title="Thin film optics">thin films and coatings</a> is directly affected by interference effects. <a href="/wiki/Antireflective_coating" class="mw-redirect" title="Antireflective coating">Antireflective coatings</a> use destructive interference to reduce the reflectivity of the surfaces they coat, and can be used to minimise glare and unwanted reflections. The simplest case is a single layer with a thickness of one-fourth the wavelength of incident light. The reflected wave from the top of the film and the reflected wave from the film/material interface are then exactly 180° out of phase, causing destructive interference. The waves are only exactly out of phase for one wavelength, which would typically be chosen to be near the centre of the visible spectrum, around 550 nm. More complex designs using multiple layers can achieve low reflectivity over a broad band, or extremely low reflectivity at a single wavelength. </p><p>Constructive interference in thin films can create a strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make <a href="/wiki/Dielectric_mirror" title="Dielectric mirror">dielectric mirrors</a>, <a href="/wiki/Interference_filter" title="Interference filter">interference filters</a>, <a href="/wiki/Heat_reflector" class="mw-redirect" title="Heat reflector">heat reflectors</a>, and filters for colour separation in <a href="/wiki/Colour_television" class="mw-redirect" title="Colour television">colour television</a> cameras. This interference effect is also what causes the colourful rainbow patterns seen in oil slicks.<sup id="cite_ref-FOOTNOTEYoungFreedman20201198–1200_58-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201198–1200-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Diffraction_and_optical_resolution">Diffraction and optical resolution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=11" title="Edit section: Diffraction and optical resolution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Diffraction" title="Diffraction">Diffraction</a> and <a href="/wiki/Optical_resolution" title="Optical resolution">Optical resolution</a></div> <figure class="mw-default-size mw-halign-right skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Double_slit_diffraction.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Double_slit_diffraction.svg/330px-Double_slit_diffraction.svg.png" decoding="async" width="300" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Double_slit_diffraction.svg/500px-Double_slit_diffraction.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Double_slit_diffraction.svg/600px-Double_slit_diffraction.svg.png 2x" data-file-width="500" data-file-height="265" /></a><figcaption>Diffraction on two slits separated by distance <span class="texhtml mvar" style="font-style:italic;">d</span>. The bright fringes occur along lines where black lines intersect with black lines and white lines intersect with white lines. These fringes are separated by angle <span class="texhtml mvar" style="font-style:italic;">θ</span> and are numbered as order <span class="texhtml mvar" style="font-style:italic;">n</span>.</figcaption></figure> <p>Diffraction is the process by which light interference is most commonly observed. The effect was first described in 1665 by <a href="/wiki/Francesco_Maria_Grimaldi" title="Francesco Maria Grimaldi">Francesco Maria Grimaldi</a>, who also coined the term from the Latin <span title="Latin-language text"><i lang="la">diffringere</i></span> <span class="gloss-quot">'</span><span class="gloss-text">to break into pieces</span><span class="gloss-quot">'</span>.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> Later that century, Robert Hooke and Isaac Newton also described phenomena now known to be diffraction in <a href="/wiki/Newton%27s_rings" title="Newton's rings">Newton's rings</a><sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> while <a href="/wiki/James_Gregory_(astronomer_and_mathematician)" class="mw-redirect" title="James Gregory (astronomer and mathematician)">James Gregory</a> recorded his observations of diffraction patterns from bird feathers.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </p><p>The first physical optics model of diffraction that relied on the Huygens–Fresnel principle was developed in 1803 by Thomas Young in his interference experiments with the interference patterns of two closely spaced slits. Young showed that his results could only be explained if the two slits acted as two unique sources of waves rather than corpuscles.<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> In 1815 and 1818, Augustin-Jean Fresnel firmly established the mathematics of how wave interference can account for diffraction.<sup id="cite_ref-FOOTNOTEHecht20175_64-0" class="reference"><a href="#cite_note-FOOTNOTEHecht20175-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p><p>The simplest physical models of diffraction use equations that describe the angular separation of light and dark fringes due to light of a particular wavelength (<span class="texhtml mvar" style="font-style:italic;">λ</span>). In general, the equation takes the form <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m\lambda =d\sin \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mi>λ</mi> <mo>=</mo> <mi>d</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m\lambda =d\sin \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0273bbb5ae5e6e780964ec6623918713914d7dcb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.43ex; height:2.176ex;" alt="{\displaystyle m\lambda =d\sin \theta }" /></span> where <span class="texhtml mvar" style="font-style:italic;">d</span> is the separation between two wavefront sources (in the case of Young's experiments, it was <a href="/wiki/Double-slit_experiment" title="Double-slit experiment">two slits</a>), <span class="texhtml mvar" style="font-style:italic;">θ</span> is the angular separation between the central fringe and the <span class="nowrap"><span class="texhtml mvar" style="font-style:italic;">m</span>-th</span> order fringe, where the central maximum is <span class="texhtml"><i>m</i> = 0</span>.<sup id="cite_ref-FOOTNOTEHecht2017398–399YoungFreedman20201192_65-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017398–399YoungFreedman20201192-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p><p>This equation is modified slightly to take into account a variety of situations such as diffraction through a single gap, diffraction through multiple slits, or diffraction through a <a href="/wiki/Diffraction_grating" title="Diffraction grating">diffraction grating</a> that contains a large number of slits at equal spacing.<sup id="cite_ref-FOOTNOTEHecht2017488–491YoungFreedman20201224–1225_66-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017488–491YoungFreedman20201224–1225-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> More complicated models of diffraction require working with the mathematics of <a href="/wiki/Fresnel_diffraction" title="Fresnel diffraction">Fresnel</a> or <a href="/wiki/Fraunhofer_diffraction" title="Fraunhofer diffraction">Fraunhofer diffraction</a>.<sup id="cite_ref-phyoptics_67-0" class="reference"><a href="#cite_note-phyoptics-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/X-ray_diffraction" title="X-ray diffraction">X-ray diffraction</a> makes use of the fact that atoms in a crystal have regular spacing at distances that are on the order of one <a href="/wiki/Angstrom" title="Angstrom">angstrom</a>. To see diffraction patterns, x-rays with similar wavelengths to that spacing are passed through the crystal. Since crystals are three-dimensional objects rather than two-dimensional gratings, the associated diffraction pattern varies in two directions according to <a href="/wiki/Bragg_reflection" class="mw-redirect" title="Bragg reflection">Bragg reflection</a>, with the associated bright spots occurring in <a href="/wiki/Diffraction_topography" title="Diffraction topography">unique patterns</a> and <span class="texhtml mvar" style="font-style:italic;">d</span> being twice the spacing between atoms.<sup id="cite_ref-FOOTNOTEHecht2017497YoungFreedman20201228–1230_68-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017497YoungFreedman20201228–1230-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> </p><p>Diffraction effects limit the ability of an optical detector to <a href="/wiki/Optical_resolution" title="Optical resolution">optically resolve</a> separate light sources. In general, light that is passing through an <a href="/wiki/Aperture" title="Aperture">aperture</a> will experience diffraction and the best images that can be created (as described in <a href="/wiki/Diffraction-limited_system" title="Diffraction-limited system">diffraction-limited optics</a>) appear as a central spot with surrounding bright rings, separated by dark nulls; this pattern is known as an <a href="/wiki/Airy_pattern" class="mw-redirect" title="Airy pattern">Airy pattern</a>, and the central bright lobe as an <a href="/wiki/Airy_disk" title="Airy disk">Airy disk</a>.<sup id="cite_ref-FOOTNOTEHecht2017482_69-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017482-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> The size of such a disk is given by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \theta =1.22{\frac {\lambda }{D}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mo>=</mo> <mn>1.22</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mi>D</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta =1.22{\frac {\lambda }{D}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af4709f32fba83bc3a5bed37b719af6c1ce3a04d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.326ex; height:5.343ex;" alt="{\displaystyle \sin \theta =1.22{\frac {\lambda }{D}}}" /></span> where <span class="texhtml mvar" style="font-style:italic;">θ</span> is the angular resolution, <span class="texhtml mvar" style="font-style:italic;">λ</span> is the wavelength of the light, and <span class="texhtml mvar" style="font-style:italic;">D</span> is the <a href="/wiki/Diameter" title="Diameter">diameter</a> of the lens aperture. If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved. <a href="/wiki/John_Strutt,_3rd_Baron_Rayleigh" class="mw-redirect" title="John Strutt, 3rd Baron Rayleigh">Rayleigh</a> defined the somewhat arbitrary "<a href="/wiki/Angular_resolution#The_Rayleigh_criterion" title="Angular resolution">Rayleigh criterion</a>" that two points whose angular separation is equal to the Airy disk radius (measured to first null, that is, to the first place where no light is seen) can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the finer the resolution.<sup id="cite_ref-FOOTNOTEHecht2017485YoungFreedman20201232_70-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017485YoungFreedman20201232-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Astronomical_interferometer" title="Astronomical interferometer">Interferometry</a>, with its ability to mimic extremely large baseline apertures, allows for the greatest angular resolution possible.<sup id="cite_ref-interferometry_56-1" class="reference"><a href="#cite_note-interferometry-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p><p>For astronomical imaging, the atmosphere prevents optimal resolution from being achieved in the visible spectrum due to the atmospheric <a href="/wiki/Scattering" title="Scattering">scattering</a> and dispersion which cause stars to <a href="/wiki/Scintillation_(astronomy)" class="mw-redirect" title="Scintillation (astronomy)">twinkle</a>. Astronomers refer to this effect as the quality of <a href="/wiki/Astronomical_seeing" title="Astronomical seeing">astronomical seeing</a>. Techniques known as <a href="/wiki/Adaptive_optics" title="Adaptive optics">adaptive optics</a> have been used to eliminate the atmospheric disruption of images and achieve results that approach the diffraction limit.<sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Dispersion_and_scattering">Dispersion and scattering</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=12" title="Edit section: Dispersion and scattering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">Dispersion (optics)</a> and <a href="/wiki/Scattering" title="Scattering">Scattering</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Light_dispersion_conceptual_waves.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Light_dispersion_conceptual_waves.gif/220px-Light_dispersion_conceptual_waves.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Light_dispersion_conceptual_waves.gif/330px-Light_dispersion_conceptual_waves.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Light_dispersion_conceptual_waves.gif/440px-Light_dispersion_conceptual_waves.gif 2x" data-file-width="640" data-file-height="480" /></a><figcaption>Conceptual animation of light dispersion through a prism. High frequency (blue) light is deflected the most, and low frequency (red) the least.</figcaption></figure> <p>Refractive processes take place in the physical optics limit, where the wavelength of light is similar to other distances, as a kind of scattering. The simplest type of scattering is <a href="/wiki/Thomson_scattering" title="Thomson scattering">Thomson scattering</a> which occurs when electromagnetic waves are deflected by single particles. In the limit of Thomson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to <a href="/wiki/Compton_scattering" title="Compton scattering">Compton scattering</a> which is frequency-dependent and strictly a <a href="/wiki/Quantum_mechanical" class="mw-redirect" title="Quantum mechanical">quantum mechanical</a> process, involving the nature of light as particles. In a statistical sense, elastic scattering of light by numerous particles much smaller than the wavelength of the light is a process known as <a href="/wiki/Rayleigh_scattering" title="Rayleigh scattering">Rayleigh scattering</a> while the similar process for scattering by particles that are similar or larger in wavelength is known as <a href="/wiki/Mie_scattering" title="Mie scattering">Mie scattering</a> with the <a href="/wiki/Tyndall_effect" title="Tyndall effect">Tyndall effect</a> being a commonly observed result. A small proportion of light scattering from atoms or molecules may undergo <a href="/wiki/Raman_scattering" title="Raman scattering">Raman scattering</a>, wherein the frequency changes due to excitation of the atoms and molecules. <a href="/wiki/Brillouin_scattering" title="Brillouin scattering">Brillouin scattering</a> occurs when the frequency of light changes due to local changes with time and movements of a dense material.<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> </p><p>Dispersion occurs when different frequencies of light have different <a href="/wiki/Phase_velocity" title="Phase velocity">phase velocities</a>, due either to material properties (<i>material dispersion</i>) or to the geometry of an <a href="/wiki/Optical_waveguide" class="mw-redirect" title="Optical waveguide">optical waveguide</a> (<i>waveguide dispersion</i>). The most familiar form of dispersion is a decrease in index of refraction with increasing wavelength, which is seen in most transparent materials. This is called "normal dispersion". It occurs in all <a href="/wiki/Dielectric" title="Dielectric">dielectric materials</a>, in wavelength ranges where the material does not absorb light.<sup id="cite_ref-J286_73-0" class="reference"><a href="#cite_note-J286-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> In wavelength ranges where a medium has significant absorption, the index of refraction can increase with wavelength. This is called "anomalous dispersion".<sup id="cite_ref-J286_73-1" class="reference"><a href="#cite_note-J286-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> </p><p>The separation of colours by a prism is an example of normal dispersion. At the surfaces of the prism, Snell's law predicts that light incident at an angle <span class="texhtml mvar" style="font-style:italic;">θ</span> to the normal will be refracted at an angle <span class="texhtml">arcsin(sin (<i>θ</i>) / <i>n</i>)</span>. Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known <a href="/wiki/Rainbow" title="Rainbow">rainbow</a> pattern.<sup id="cite_ref-FOOTNOTEYoungFreedman20201116_41-1" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201116-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p> <figure typeof="mw:File/Frame"><a href="/wiki/File:Wave_group.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/bd/Wave_group.gif" decoding="async" width="465" height="36" class="mw-file-element" data-file-width="465" data-file-height="36" /></a><figcaption>Dispersion: two sinusoids propagating at different speeds make a moving interference pattern. The red dot moves with the <a href="/wiki/Phase_velocity" title="Phase velocity">phase velocity</a>, and the green dots propagate with the <a href="/wiki/Group_velocity" title="Group velocity">group velocity</a>. In this case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure. In effect, the individual waves (which travel with the phase velocity) escape from the wave packet (which travels with the group velocity).</figcaption></figure> <p>Material dispersion is often characterised by the <a href="/wiki/Abbe_number" title="Abbe number">Abbe number</a>, which gives a simple measure of dispersion based on the index of refraction at three specific wavelengths. Waveguide dispersion is dependent on the <a href="/wiki/Propagation_constant" title="Propagation constant">propagation constant</a>.<sup id="cite_ref-FOOTNOTEHecht2017202–204_74-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017202–204-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> Both kinds of dispersion cause changes in the group characteristics of the wave, the features of the wave packet that change with the same frequency as the amplitude of the electromagnetic wave. "Group velocity dispersion" manifests as a spreading-out of the signal "envelope" of the radiation and can be quantified with a group dispersion delay parameter: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D={\frac {1}{v_{\mathrm {g} }^{2}}}{\frac {dv_{\mathrm {g} }}{d\lambda }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D={\frac {1}{v_{\mathrm {g} }^{2}}}{\frac {dv_{\mathrm {g} }}{d\lambda }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e9c82303f84a2c5c910cb35e79045ce1c09dbdf" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:12.275ex; height:6.676ex;" alt="{\displaystyle D={\frac {1}{v_{\mathrm {g} }^{2}}}{\frac {dv_{\mathrm {g} }}{d\lambda }}}" /></span> </p><p>where <span class="texhtml"><i>v</i><sub>g</sub></span> is the group velocity.<sup id="cite_ref-optnet_75-0" class="reference"><a href="#cite_note-optnet-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> For a uniform medium, the group velocity is </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\mathrm {g} }=c\left(n-\lambda {\frac {dn}{d\lambda }}\right)^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>c</mi> <msup> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mo>−</mo> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>n</mi> </mrow> <mrow> <mi>d</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\mathrm {g} }=c\left(n-\lambda {\frac {dn}{d\lambda }}\right)^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20b1c9cc5dad2baf5587cd361f27e16eb14a293d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.078ex; height:6.509ex;" alt="{\displaystyle v_{\mathrm {g} }=c\left(n-\lambda {\frac {dn}{d\lambda }}\right)^{-1}}" /></span> </p><p>where <span class="texhtml mvar" style="font-style:italic;">n</span> is the index of refraction and <span class="texhtml mvar" style="font-style:italic;">c</span> is the speed of light in a vacuum.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> This gives a simpler form for the dispersion delay parameter: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D=-{\frac {\lambda }{c}}\,{\frac {d^{2}n}{d\lambda ^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mi>c</mi> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>n</mi> </mrow> <mrow> <mi>d</mi> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D=-{\frac {\lambda }{c}}\,{\frac {d^{2}n}{d\lambda ^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bb8f15119155571bcfbcc59ad5834e5cb517b35" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.559ex; height:6.009ex;" alt="{\displaystyle D=-{\frac {\lambda }{c}}\,{\frac {d^{2}n}{d\lambda ^{2}}}.}" /></span> </p><p>If <span class="texhtml mvar" style="font-style:italic;">D</span> is less than zero, the medium is said to have <i>positive dispersion</i> or normal dispersion. If <span class="texhtml mvar" style="font-style:italic;">D</span> is greater than zero, the medium has <i>negative dispersion</i>. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components slow down more than the lower frequency components. The pulse therefore becomes <i>positively <a href="/wiki/Chirp" title="Chirp">chirped</a></i>, or <i>up-chirped</i>, increasing in frequency with time. This causes the spectrum coming out of a prism to appear with red light the least refracted and blue/violet light the most refracted. Conversely, if a pulse travels through an anomalously (negatively) dispersive medium, high-frequency components travel faster than the lower ones, and the pulse becomes <i>negatively chirped</i>, or <i>down-chirped</i>, decreasing in frequency with time.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> </p><p>The result of group velocity dispersion, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on <a href="/wiki/Optical_fibre" class="mw-redirect" title="Optical fibre">optical fibres</a>, since if dispersion is too high, a group of pulses representing information will each spread in time and merge, making it impossible to extract the signal.<sup id="cite_ref-optnet_75-1" class="reference"><a href="#cite_note-optnet-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Polarisation">Polarisation <span class="anchor" id="Polarization"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=13" title="Edit section: Polarisation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Polarisation_(waves)" class="mw-redirect" title="Polarisation (waves)">Polarisation (waves)</a></div> <p>Polarisation is a general property of waves that describes the orientation of their oscillations. For <a href="/wiki/Transverse_wave" title="Transverse wave">transverse waves</a> such as many electromagnetic waves, it describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. The oscillations may be oriented in a single direction (<a href="/wiki/Linear_polarisation" class="mw-redirect" title="Linear polarisation">linear polarisation</a>), or the oscillation direction may rotate as the wave travels (<a href="/wiki/Circular_polarisation" class="mw-redirect" title="Circular polarisation">circular</a> or <a href="/wiki/Elliptical_polarisation" class="mw-redirect" title="Elliptical polarisation">elliptical polarisation</a>). Circularly polarised waves can rotate rightward or leftward in the direction of travel, and which of those two rotations is present in a wave is called the wave's <a href="/wiki/Polarimetry" title="Polarimetry">chirality</a>.<sup id="cite_ref-FOOTNOTEHecht2017333–334YoungFreedman20201083,_1118_78-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017333–334YoungFreedman20201083,_1118-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup> </p><p>The typical way to consider polarisation is to keep track of the orientation of the electric field <a href="/wiki/Vector_(geometry)" class="mw-redirect" title="Vector (geometry)">vector</a> as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular <a href="/wiki/Vector_components" class="mw-redirect" title="Vector components">components</a> labeled <span class="texhtml mvar" style="font-style:italic;">x</span> and <span class="texhtml mvar" style="font-style:italic;">y</span> (with <span class="texhtml"><b>z</b></span> indicating the direction of travel). The shape traced out in the x-y plane by the electric field vector is a <a href="/wiki/Lissajous_curve" title="Lissajous curve">Lissajous figure</a> that describes the <i>polarisation state</i>.<sup id="cite_ref-FOOTNOTEHecht2017336_79-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017336-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> The following figures show some examples of the evolution of the electric field vector (blue), with time (the vertical axes), at a particular point in space, along with its <span class="texhtml mvar" style="font-style:italic;">x</span> and <span class="texhtml mvar" style="font-style:italic;">y</span> components (red/left and green/right), and the path traced by the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation. </p> <div style="float:left;width:170px"> <figure class="mw-default-size mw-halign-center skin-invert-image" typeof="mw:File"><a href="/wiki/File:Polarisation_(Linear).svg" class="mw-file-description" title="Linear polarisation diagram"><img alt="Linear polarisation diagram" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Polarisation_%28Linear%29.svg/250px-Polarisation_%28Linear%29.svg.png" decoding="async" width="250" height="625" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Polarisation_%28Linear%29.svg/375px-Polarisation_%28Linear%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Polarisation_%28Linear%29.svg/500px-Polarisation_%28Linear%29.svg.png 2x" data-file-width="250" data-file-height="625" /></a><figcaption>Linear polarisation diagram</figcaption></figure> <div class="center"><i>Linear</i></div> </div> <div style="float:left;width:170px"> <figure class="mw-default-size mw-halign-center skin-invert-image" typeof="mw:File"><a href="/wiki/File:Polarisation_(Circular).svg" class="mw-file-description" title="Circular polarisation diagram"><img alt="Circular polarisation diagram" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Polarisation_%28Circular%29.svg/250px-Polarisation_%28Circular%29.svg.png" decoding="async" width="250" height="625" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Polarisation_%28Circular%29.svg/375px-Polarisation_%28Circular%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Polarisation_%28Circular%29.svg/500px-Polarisation_%28Circular%29.svg.png 2x" data-file-width="250" data-file-height="625" /></a><figcaption>Circular polarisation diagram</figcaption></figure> <div class="center"><i>Circular</i></div> </div> <div style="float:left;width:170px"> <figure class="mw-default-size mw-halign-center skin-invert-image" typeof="mw:File"><a href="/wiki/File:Polarisation_(Elliptical).svg" class="mw-file-description" title="Elliptical polarisation diagram"><img alt="Elliptical polarisation diagram" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Polarisation_%28Elliptical%29.svg/250px-Polarisation_%28Elliptical%29.svg.png" decoding="async" width="250" height="625" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Polarisation_%28Elliptical%29.svg/375px-Polarisation_%28Elliptical%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Polarisation_%28Elliptical%29.svg/500px-Polarisation_%28Elliptical%29.svg.png 2x" data-file-width="250" data-file-height="625" /></a><figcaption>Elliptical polarisation diagram</figcaption></figure> <div class="center"><i>Elliptical polarisation</i></div> </div> <div style="clear:both;" class=""></div> <p>In the leftmost figure above, the <span class="texhtml mvar" style="font-style:italic;">x</span> and <span class="texhtml mvar" style="font-style:italic;">y</span> components of the light wave are in phase. In this case, the ratio of their strengths is constant, so the direction of the electric vector (the vector sum of these two components) is constant. Since the tip of the vector traces out a single line in the plane, this special case is called linear polarisation. The direction of this line depends on the relative amplitudes of the two components.<sup id="cite_ref-FOOTNOTEHecht2017330–332YoungFreedman20201123_80-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017330–332YoungFreedman20201123-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> </p><p>In the middle figure, the two orthogonal components have the same amplitudes and are 90° out of phase. In this case, one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: the <span class="texhtml mvar" style="font-style:italic;">x</span> component can be 90° ahead of the <span class="texhtml mvar" style="font-style:italic;">y</span> component or it can be 90° behind the <span class="texhtml mvar" style="font-style:italic;">y</span> component. In this special case, the electric vector traces out a circle in the plane, so this polarisation is called circular polarisation. The rotation direction in the circle depends on which of the two-phase relationships exists and corresponds to <i>right-hand circular polarisation</i> and <i>left-hand circular polarisation</i>.<sup id="cite_ref-FOOTNOTEHecht2017333–334YoungFreedman20201123_81-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017333–334YoungFreedman20201123-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> </p><p>In all other cases, where the two components either do not have the same amplitudes and/or their phase difference is neither zero nor a multiple of 90°, the polarisation is called elliptical polarisation because the electric vector traces out an <a href="/wiki/Ellipse" title="Ellipse">ellipse</a> in the plane (the <i>polarisation ellipse</i>).<sup id="cite_ref-FOOTNOTEHecht2017334–335YoungFreedman20201124_82-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017334–335YoungFreedman20201124-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> This is shown in the above figure on the right. Detailed mathematics of polarisation is done using <a href="/wiki/Jones_calculus" title="Jones calculus">Jones calculus</a> and is characterised by the <a href="/wiki/Stokes_parameters" title="Stokes parameters">Stokes parameters</a>.<sup id="cite_ref-FOOTNOTEHecht2017379–383_83-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017379–383-83"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Changing_polarisation">Changing polarisation</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=14" title="Edit section: Changing polarisation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Media that have different indexes of refraction for different polarisation modes are called <i><a href="/wiki/Birefringence" title="Birefringence">birefringent</a></i>.<sup id="cite_ref-FOOTNOTEYoungFreedman20201124_84-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201124-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup> Well known manifestations of this effect appear in optical <a href="/wiki/Wave_plate" class="mw-redirect" title="Wave plate">wave plates</a>/retarders (linear modes) and in <a href="/wiki/Faraday_rotation" class="mw-redirect" title="Faraday rotation">Faraday rotation</a>/<a href="/wiki/Optical_rotation" title="Optical rotation">optical rotation</a> (circular modes).<sup id="cite_ref-FOOTNOTEHecht2017367,_373_85-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017367,_373-85"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup> If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to refraction. For example, this is the case with macroscopic crystals of <a href="/wiki/Calcite" title="Calcite">calcite</a>, which present the viewer with two offset, orthogonally polarised images of whatever is viewed through them. It was this effect that provided the first discovery of polarisation, by <a href="/wiki/Erasmus_Bartholinus" class="mw-redirect" title="Erasmus Bartholinus">Erasmus Bartholinus</a> in 1669. In addition, the phase shift, and thus the change in polarisation state, is usually frequency dependent, which, in combination with <a href="/wiki/Dichroism" title="Dichroism">dichroism</a>, often gives rise to bright colours and rainbow-like effects. In <a href="/wiki/Mineralogy" title="Mineralogy">mineralogy</a>, such properties, known as <a href="/wiki/Pleochroism" title="Pleochroism">pleochroism</a>, are frequently exploited for the purpose of identifying minerals using polarisation microscopes. Additionally, many plastics that are not normally birefringent will become so when subject to <a href="/wiki/Mechanical_stress" class="mw-redirect" title="Mechanical stress">mechanical stress</a>, a phenomenon which is the basis of <a href="/wiki/Photoelasticity" title="Photoelasticity">photoelasticity</a>.<sup id="cite_ref-FOOTNOTEHecht2017372YoungFreedman20201124–1125_86-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017372YoungFreedman20201124–1125-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> Non-birefringent methods, to rotate the linear polarisation of light beams, include the use of prismatic <a href="/wiki/Polarisation_rotator" class="mw-redirect" title="Polarisation rotator">polarisation rotators</a> which use total internal reflection in a prism set designed for efficient collinear transmission.<sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-right skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Malus_law.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Malus_law.svg/350px-Malus_law.svg.png" decoding="async" width="350" height="242" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Malus_law.svg/525px-Malus_law.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Malus_law.svg/700px-Malus_law.svg.png 2x" data-file-width="230" data-file-height="159" /></a><figcaption>A polariser changing the orientation of linearly polarised light. In this picture, <span class="texhtml"><i>θ</i><sub>1</sub> – <i>θ</i><sub>0</sub> = <i>θ</i><sub>i</sub></span>.</figcaption></figure> <p>Media that reduce the amplitude of certain polarisation modes are called <i>dichroic</i>, with devices that block nearly all of the radiation in one mode known as <i>polarising filters</i> or simply "<a href="/wiki/Polariser" class="mw-redirect" title="Polariser">polarisers</a>". Malus' law, which is named after <a href="/wiki/%C3%89tienne-Louis_Malus" title="Étienne-Louis Malus">Étienne-Louis Malus</a>, says that when a perfect polariser is placed in a linear polarised beam of light, the intensity, <span class="texhtml mvar" style="font-style:italic;">I</span>, of the light that passes through is given by </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=I_{0}\cos ^{2}\theta _{\mathrm {i} },}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=I_{0}\cos ^{2}\theta _{\mathrm {i} },}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c6d4ccb642b616b4b9527cc1fae0715149eda86" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.714ex; height:3.009ex;" alt="{\displaystyle I=I_{0}\cos ^{2}\theta _{\mathrm {i} },}" /></span> where <span class="texhtml"><i>I</i><sub>0</sub></span> is the initial intensity, and <span class="texhtml"><i>θ</i><sub>i</sub></span> is the angle between the light's initial polarisation direction and the axis of the polariser.<sup id="cite_ref-FOOTNOTEHecht2017338YoungFreedman20201119–1121_88-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017338YoungFreedman20201119–1121-88"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup> </p><p>A beam of unpolarised light can be thought of as containing a uniform mixture of linear polarisations at all possible angles. Since the average value of <span class="texhtml">cos<sup>2</sup> <i>θ</i></span> is 1/2, the transmission coefficient becomes </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {I}{I_{0}}}={\frac {1}{2}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>I</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {I}{I_{0}}}={\frac {1}{2}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57bbd674b72341aadd785637d0a10e6a3fbdcb5a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.044ex; height:5.676ex;" alt="{\displaystyle {\frac {I}{I_{0}}}={\frac {1}{2}}\,.}" /></span> </p><p>In practice, some light is lost in the polariser and the actual transmission of unpolarised light will be somewhat lower than this, around 38% for Polaroid-type polarisers but considerably higher (>49.9%) for some birefringent prism types.<sup id="cite_ref-FOOTNOTEHecht2017339–342_89-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017339–342-89"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup> </p><p>In addition to birefringence and dichroism in extended media, polarisation effects can also occur at the (reflective) interface between two materials of different refractive index. These effects are treated by the <a href="/wiki/Fresnel_equations" title="Fresnel equations">Fresnel equations</a>. Part of the wave is transmitted and part is reflected, with the ratio depending on the angle of incidence and the angle of refraction. In this way, physical optics recovers <a href="/wiki/Brewster%27s_angle" title="Brewster's angle">Brewster's angle</a>.<sup id="cite_ref-FOOTNOTEHecht2017355–358_90-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017355–358-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup> When light reflects from a <a href="/wiki/Thin-film_optics" title="Thin-film optics">thin film</a> on a surface, interference between the reflections from the film's surfaces can produce polarisation in the reflected and transmitted light. </p> <div class="mw-heading mw-heading5"><h5 id="Natural_light">Natural light</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=15" title="Edit section: Natural light"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CircularPolarizer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/CircularPolarizer.jpg/500px-CircularPolarizer.jpg" decoding="async" width="400" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/CircularPolarizer.jpg/960px-CircularPolarizer.jpg 1.5x" data-file-width="2484" data-file-height="946" /></a><figcaption>The effects of a <a href="/wiki/Photographic_filter#Polarizer" title="Photographic filter">polarising filter</a> on the sky in a photograph. Left picture is taken without polariser. For the right picture, filter was adjusted to eliminate certain polarisations of the scattered blue light from the sky.</figcaption></figure> <p>Most sources of electromagnetic radiation contain a large number of atoms or molecules that emit light. The orientation of the electric fields produced by these emitters may not be <a href="/wiki/Statistical_correlation" class="mw-redirect" title="Statistical correlation">correlated</a>, in which case the light is said to be <i>unpolarised</i>. If there is partial correlation between the emitters, the light is <i>partially polarised</i>. If the polarisation is consistent across the spectrum of the source, partially polarised light can be described as a superposition of a completely unpolarised component, and a completely polarised one. One may then describe the light in terms of the <a href="/w/index.php?title=Degree_of_polarisation&action=edit&redlink=1" class="new" title="Degree of polarisation (page does not exist)">degree of polarisation</a>, and the parameters of the polarisation ellipse.<sup id="cite_ref-FOOTNOTEHecht2017336_79-1" class="reference"><a href="#cite_note-FOOTNOTEHecht2017336-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> </p><p>Light reflected by shiny transparent materials is partly or fully polarised, except when the light is normal (perpendicular) to the surface. It was this effect that allowed the mathematician Étienne-Louis Malus to make the measurements that allowed for his development of the first mathematical models for polarised light. Polarisation occurs when light is scattered in the <a href="/wiki/Earth%27s_atmosphere" class="mw-redirect" title="Earth's atmosphere">atmosphere</a>. The scattered light produces the brightness and colour in clear <a href="/wiki/Sky" title="Sky">skies</a>. This partial polarisation of scattered light can be taken advantage of using polarising filters to darken the sky in <a href="/wiki/Science_of_photography" title="Science of photography">photographs</a>. Optical polarisation is principally of importance in <a href="/wiki/Chemistry" title="Chemistry">chemistry</a> due to <a href="/wiki/Circular_dichroism" title="Circular dichroism">circular dichroism</a> and optical rotation (<i>circular birefringence</i>) exhibited by <a href="/wiki/Optical_activity" class="mw-redirect" title="Optical activity">optically active</a> (<a href="/wiki/Chirality_(chemistry)" title="Chirality (chemistry)">chiral</a>) <a href="/wiki/Molecules" class="mw-redirect" title="Molecules">molecules</a>.<sup id="cite_ref-FOOTNOTEHecht2017353–356_91-0" class="reference"><a href="#cite_note-FOOTNOTEHecht2017353–356-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Modern_optics">Modern optics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=16" title="Edit section: Modern optics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Optical_physics" class="mw-redirect" title="Optical physics">Optical physics</a> and <a href="/wiki/Optical_engineering" title="Optical engineering">Optical engineering</a></div> <p><i>Modern optics</i> encompasses the areas of optical science and engineering that became popular in the 20th century. These areas of optical science typically relate to the electromagnetic or quantum properties of light but do include other topics. A major subfield of modern optics, <a href="/wiki/Quantum_optics" title="Quantum optics">quantum optics</a>, deals with specifically quantum mechanical properties of light. Quantum optics is not just theoretical; some modern devices, such as lasers, have principles of operation that depend on quantum mechanics. Light detectors, such as <a href="/wiki/Photomultiplier" title="Photomultiplier">photomultipliers</a> and <a href="/wiki/Channeltron" class="mw-redirect" title="Channeltron">channeltrons</a>, respond to individual photons. Electronic <a href="/wiki/Image_sensor" title="Image sensor">image sensors</a>, such as <a href="/wiki/Charge-coupled_device" title="Charge-coupled device">CCDs</a>, exhibit <a href="/wiki/Shot_noise" title="Shot noise">shot noise</a> corresponding to the statistics of individual photon events. <a href="/wiki/Light-emitting_diode" title="Light-emitting diode">Light-emitting diodes</a> and <a href="/wiki/Photovoltaic_cell" class="mw-redirect" title="Photovoltaic cell">photovoltaic cells</a>, too, cannot be understood without quantum mechanics. In the study of these devices, quantum optics often overlaps with <a href="/wiki/Quantum_electronics" class="mw-redirect" title="Quantum electronics">quantum electronics</a>.<sup id="cite_ref-92" class="reference"><a href="#cite_note-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup> </p><p>Specialty areas of optics research include the study of how light interacts with specific materials as in <a href="/wiki/Crystal_optics" title="Crystal optics">crystal optics</a> and <a href="/wiki/Metamaterial" title="Metamaterial">metamaterials</a>. Other research focuses on the phenomenology of electromagnetic waves as in <a href="/wiki/Optical_vortex" title="Optical vortex">singular optics</a>, <a href="/wiki/Non-imaging_optics" class="mw-redirect" title="Non-imaging optics">non-imaging optics</a>, <a href="/wiki/Non-linear_optics" class="mw-redirect" title="Non-linear optics">non-linear optics</a>, statistical optics, and <a href="/wiki/Radiometry" title="Radiometry">radiometry</a>. Additionally, <a href="/wiki/Computer_engineer" class="mw-redirect" title="Computer engineer">computer engineers</a> have taken an interest in <a href="/wiki/Integrated_optics" class="mw-redirect" title="Integrated optics">integrated optics</a>, <a href="/wiki/Machine_vision" title="Machine vision">machine vision</a>, and <a href="/wiki/Photonic_computing" class="mw-redirect" title="Photonic computing">photonic computing</a> as possible components of the "next generation" of computers.<sup id="cite_ref-93" class="reference"><a href="#cite_note-93"><span class="cite-bracket">[</span>93<span class="cite-bracket">]</span></a></sup> </p><p>Today, the pure science of optics is called optical science or <a href="/wiki/Optical_physics" class="mw-redirect" title="Optical physics">optical physics</a> to distinguish it from applied optical sciences, which are referred to as <a href="/wiki/Optical_engineering" title="Optical engineering">optical engineering</a>. Prominent subfields of optical engineering include <a href="/wiki/Lighting" title="Lighting">illumination engineering</a>, <a href="/wiki/Photonics" title="Photonics">photonics</a>, and <a href="/wiki/Optoelectronics" title="Optoelectronics">optoelectronics</a> with practical applications like <a href="/wiki/Optical_lens_design" title="Optical lens design">lens design</a>, <a href="/wiki/Fabrication_and_testing_(optical_components)" class="mw-redirect" title="Fabrication and testing (optical components)">fabrication and testing of optical components</a>, and <a href="/wiki/Image_processing" class="mw-redirect" title="Image processing">image processing</a>. Some of these fields overlap, with nebulous boundaries between the subjects' terms that mean slightly different things in different parts of the world and in different areas of industry. A professional community of researchers in nonlinear optics has developed in the last several decades due to advances in laser technology.<sup id="cite_ref-94" class="reference"><a href="#cite_note-94"><span class="cite-bracket">[</span>94<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Lasers">Lasers</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=17" title="Edit section: Lasers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Laser" title="Laser">Laser</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Military_laser_experiment.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Military_laser_experiment.jpg/250px-Military_laser_experiment.jpg" decoding="async" width="220" height="143" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Military_laser_experiment.jpg/330px-Military_laser_experiment.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Military_laser_experiment.jpg/500px-Military_laser_experiment.jpg 2x" data-file-width="3008" data-file-height="1960" /></a><figcaption>Experiments such as this one with high-power <a href="/wiki/Laser" title="Laser">lasers</a> are part of the modern optics research.</figcaption></figure> <p>A laser is a device that emits light, a kind of electromagnetic radiation, through a process called <i><a href="/wiki/Stimulated_emission" title="Stimulated emission">stimulated emission</a></i>. The term <i>laser</i> is an <a href="/wiki/Acronym" title="Acronym">acronym</a> for <span class="gloss-quot">'</span><span class="gloss-text">Light Amplification by Stimulated Emission of Radiation</span><span class="gloss-quot">'</span>.<sup id="cite_ref-95" class="reference"><a href="#cite_note-95"><span class="cite-bracket">[</span>95<span class="cite-bracket">]</span></a></sup> Laser light is usually spatially <a href="/wiki/Coherence_(physics)" title="Coherence (physics)">coherent</a>, which means that the light either is emitted in a narrow, <a href="/wiki/Beam_divergence" title="Beam divergence">low-divergence beam</a>, or can be converted into one with the help of optical components such as lenses. Because the microwave equivalent of the laser, the <i>maser</i>, was developed first, devices that emit microwave and <a href="/wiki/Radio_frequency" title="Radio frequency">radio</a> frequencies are usually called <i>masers</i>.<sup id="cite_ref-96" class="reference"><a href="#cite_note-96"><span class="cite-bracket">[</span>96<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:The_VLT%E2%80%99s_Artificial_Star.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/The_VLT%E2%80%99s_Artificial_Star.jpg/220px-The_VLT%E2%80%99s_Artificial_Star.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/The_VLT%E2%80%99s_Artificial_Star.jpg/330px-The_VLT%E2%80%99s_Artificial_Star.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/The_VLT%E2%80%99s_Artificial_Star.jpg/440px-The_VLT%E2%80%99s_Artificial_Star.jpg 2x" data-file-width="5760" data-file-height="3840" /></a><figcaption><a href="/wiki/Very_Large_Telescope" title="Very Large Telescope">VLT</a>'s laser guide star<sup id="cite_ref-97" class="reference"><a href="#cite_note-97"><span class="cite-bracket">[</span>97<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The first working laser was demonstrated on 16 May 1960 by <a href="/wiki/Theodore_Maiman" title="Theodore Maiman">Theodore Maiman</a> at <a href="/wiki/Hughes_Research_Laboratories" class="mw-redirect" title="Hughes Research Laboratories">Hughes Research Laboratories</a>.<sup id="cite_ref-98" class="reference"><a href="#cite_note-98"><span class="cite-bracket">[</span>98<span class="cite-bracket">]</span></a></sup> When first invented, they were called "a solution looking for a problem".<sup id="cite_ref-99" class="reference"><a href="#cite_note-99"><span class="cite-bracket">[</span>99<span class="cite-bracket">]</span></a></sup> Since then, lasers have become a multibillion-dollar industry, finding utility in thousands of highly varied applications. The first application of lasers visible in the daily lives of the general population was the supermarket <a href="/wiki/Barcode" title="Barcode">barcode</a> scanner, introduced in 1974.<sup id="cite_ref-100" class="reference"><a href="#cite_note-100"><span class="cite-bracket">[</span>100<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Laserdisc" class="mw-redirect" title="Laserdisc">laserdisc</a> player, introduced in 1978, was the first successful consumer product to include a laser, but the <a href="/wiki/Compact_disc" title="Compact disc">compact disc</a> player was the first laser-equipped device to become truly common in consumers' homes, beginning in 1982.<sup id="cite_ref-BBC6950933_101-0" class="reference"><a href="#cite_note-BBC6950933-101"><span class="cite-bracket">[</span>101<span class="cite-bracket">]</span></a></sup> These <a href="/wiki/Optical_storage" title="Optical storage">optical storage</a> devices use a <a href="/wiki/Semiconductor_laser" class="mw-redirect" title="Semiconductor laser">semiconductor laser</a> less than a millimetre wide to scan the surface of the disc for data retrieval. <a href="/wiki/Fibre-optic_communication" class="mw-redirect" title="Fibre-optic communication">Fibre-optic communication</a> relies on lasers to transmit large amounts of information at the speed of light. Other common applications of lasers include <a href="/wiki/Laser_printers" class="mw-redirect" title="Laser printers">laser printers</a> and <a href="/wiki/Laser_pointer" title="Laser pointer">laser pointers</a>. Lasers are used in medicine in areas such as <a href="/wiki/Bloodless_surgery" title="Bloodless surgery">bloodless surgery</a>, <a href="/wiki/Laser_eye_surgery" class="mw-redirect" title="Laser eye surgery">laser eye surgery</a>, and <a href="/wiki/Laser_capture_microdissection" title="Laser capture microdissection">laser capture microdissection</a> and in military applications such as <a href="/wiki/Airborne_Laser" title="Airborne Laser">missile defence systems</a>, <a href="/wiki/DIRCM" class="mw-redirect" title="DIRCM">electro-optical countermeasures (EOCM)</a>, and <a href="/wiki/Lidar" title="Lidar">lidar</a>. Lasers are also used in <a href="/wiki/Holograms" class="mw-redirect" title="Holograms">holograms</a>, <a href="/wiki/Bubblegram" title="Bubblegram">bubblegrams</a>, <a href="/wiki/Laser_lighting_display" title="Laser lighting display">laser light shows</a>, and <a href="/wiki/Laser_hair_removal" title="Laser hair removal">laser hair removal</a>.<sup id="cite_ref-102" class="reference"><a href="#cite_note-102"><span class="cite-bracket">[</span>102<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Kapitsa–Dirac_effect"><span id="Kapitsa.E2.80.93Dirac_effect"></span>Kapitsa–Dirac effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=18" title="Edit section: Kapitsa–Dirac effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Kapitsa%E2%80%93Dirac_effect" title="Kapitsa–Dirac effect">Kapitsa–Dirac effect</a> causes beams of particles to diffract as the result of meeting a standing wave of light. Light can be used to position matter using various phenomena (see <a href="/wiki/Optical_tweezers" title="Optical tweezers">optical tweezers</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=19" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Optics is part of everyday life. The ubiquity of <a href="/wiki/Visual_system" title="Visual system">visual systems</a> in biology indicates the central role optics plays as the science of one of the <a href="/wiki/Sense" title="Sense">five senses</a>. Many people benefit from <a href="/wiki/Eyeglasses" class="mw-redirect" title="Eyeglasses">eyeglasses</a> or <a href="/wiki/Contact_lenses" class="mw-redirect" title="Contact lenses">contact lenses</a>, and optics are integral to the functioning of many consumer goods including <a href="/wiki/Cameras" class="mw-redirect" title="Cameras">cameras</a>. Rainbows and mirages are examples of optical phenomena. <a href="/wiki/Optical_communication" title="Optical communication">Optical communication</a> provides the backbone for both the <a href="/wiki/Internet" title="Internet">Internet</a> and modern <a href="/wiki/Telephony" title="Telephony">telephony</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Human_eye">Human eye</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=20" title="Edit section: Human eye"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Eye-diagram_no_circles_border.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Eye-diagram_no_circles_border.svg/300px-Eye-diagram_no_circles_border.svg.png" decoding="async" width="300" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Eye-diagram_no_circles_border.svg/450px-Eye-diagram_no_circles_border.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Eye-diagram_no_circles_border.svg/600px-Eye-diagram_no_circles_border.svg.png 2x" data-file-width="1237" data-file-height="1208" /></a><figcaption>Model of a human eye. Features mentioned in this article are 1. <a href="/wiki/Vitreous_humour" class="mw-redirect" title="Vitreous humour">vitreous humour</a> 3. <a href="/wiki/Ciliary_muscle" title="Ciliary muscle">ciliary muscle</a>, 6. <a href="/wiki/Pupil" title="Pupil">pupil</a>, 7. <a href="/wiki/Anterior_chamber" class="mw-redirect" title="Anterior chamber">anterior chamber</a>, 8. <a href="/wiki/Cornea" title="Cornea">cornea</a>, 10. <a href="/wiki/Lens_cortex" class="mw-redirect" title="Lens cortex">lens cortex</a>, 22. <a href="/wiki/Optic_nerve" title="Optic nerve">optic nerve</a>, 26. <a href="/wiki/Fovea_centralis" title="Fovea centralis">fovea</a>, 30. <a href="/wiki/Retina" title="Retina">retina</a>.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Human_eye" title="Human eye">Human eye</a> and <a href="/wiki/Photometry_(optics)" title="Photometry (optics)">Photometry (optics)</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Human_eye_with_limbal_ring,_anterior_view.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Human_eye_with_limbal_ring%2C_anterior_view.jpg/250px-Human_eye_with_limbal_ring%2C_anterior_view.jpg" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Human_eye_with_limbal_ring%2C_anterior_view.jpg/330px-Human_eye_with_limbal_ring%2C_anterior_view.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Human_eye_with_limbal_ring%2C_anterior_view.jpg/500px-Human_eye_with_limbal_ring%2C_anterior_view.jpg 2x" data-file-width="1200" data-file-height="675" /></a><figcaption>The <a href="/wiki/Human_eye" title="Human eye">human eye</a> is a living optical device. The <a href="/wiki/Iris_(anatomy)" title="Iris (anatomy)">iris</a> (light brown region), <a href="/wiki/Pupil" title="Pupil">pupil</a> (black circle in the centre), and <a href="/wiki/Sclera" title="Sclera">sclera</a> (white surrounding area) are visible in this image, along with the <a href="/wiki/Eyelid" title="Eyelid">eyelids</a> and <a href="/wiki/Eyelash" title="Eyelash">eyelashes</a> which protect the eye</figcaption></figure> <p>The human eye functions by focusing light onto a layer of <a href="/wiki/Photoreceptor_cell" title="Photoreceptor cell">photoreceptor cells</a> called the retina, which forms the inner lining of the back of the eye. The focusing is accomplished by a series of transparent media. Light entering the eye passes first through the cornea, which provides much of the eye's optical power. The light then continues through the fluid just behind the cornea—the <a href="/wiki/Anterior_chamber" class="mw-redirect" title="Anterior chamber">anterior chamber</a>, then passes through the <a href="/wiki/Pupil" title="Pupil">pupil</a>. The light then passes through the <a href="/wiki/Lens_(anatomy)" class="mw-redirect" title="Lens (anatomy)">lens</a>, which focuses the light further and allows adjustment of focus. The light then passes through the main body of fluid in the eye—the <a href="/wiki/Vitreous_humour" class="mw-redirect" title="Vitreous humour">vitreous humour</a>, and reaches the retina. The cells in the retina line the back of the eye, except for where the optic nerve exits; this results in a <a href="/wiki/Blind_spot_(vision)" title="Blind spot (vision)">blind spot</a>. </p><p>There are two types of photoreceptor cells, rods and cones, which are sensitive to different aspects of light.<sup id="cite_ref-eyeoptics_103-0" class="reference"><a href="#cite_note-eyeoptics-103"><span class="cite-bracket">[</span>103<span class="cite-bracket">]</span></a></sup> Rod cells are sensitive to the intensity of light over a wide frequency range, thus are responsible for <a href="/wiki/Scotopic_vision" title="Scotopic vision">black-and-white vision</a>. Rod cells are not present on the fovea, the area of the retina responsible for central vision, and are not as responsive as cone cells to spatial and temporal changes in light. There are, however, twenty times more rod cells than cone cells in the retina because the rod cells are present across a wider area. Because of their wider distribution, rods are responsible for <a href="/wiki/Peripheral_vision" title="Peripheral vision">peripheral vision</a>.<sup id="cite_ref-Kandel_104-0" class="reference"><a href="#cite_note-Kandel-104"><span class="cite-bracket">[</span>104<span class="cite-bracket">]</span></a></sup> </p><p>In contrast, cone cells are less sensitive to the overall intensity of light, but come in three varieties that are sensitive to different frequency-ranges and thus are used in the perception of <a href="/wiki/Colour" class="mw-redirect" title="Colour">colour</a> and <a href="/wiki/Photopic_vision" title="Photopic vision">photopic vision</a>. Cone cells are highly concentrated in the fovea and have a high visual acuity meaning that they are better at spatial resolution than rod cells. Since cone cells are not as sensitive to dim light as rod cells, most <a href="/wiki/Night_vision" title="Night vision">night vision</a> is limited to rod cells. Likewise, since cone cells are in the fovea, central vision (including the vision needed to do most reading, fine detail work such as sewing, or careful examination of objects) is done by cone cells.<sup id="cite_ref-Kandel_104-1" class="reference"><a href="#cite_note-Kandel-104"><span class="cite-bracket">[</span>104<span class="cite-bracket">]</span></a></sup> </p><p>Ciliary muscles around the lens allow the eye's focus to be adjusted. This process is known as <a href="/wiki/Accommodation_(eye)" class="mw-redirect" title="Accommodation (eye)">accommodation</a>. The <a href="/wiki/Near_point" title="Near point">near point</a> and <a href="/wiki/Far_point" title="Far point">far point</a> define the nearest and farthest distances from the eye at which an object can be brought into sharp focus. For a person with normal vision, the far point is located at infinity. The near point's location depends on how much the muscles can increase the curvature of the lens, and how inflexible the lens has become with age. <a href="/wiki/Optometrist" class="mw-redirect" title="Optometrist">Optometrists</a>, <a href="/wiki/Ophthalmologist" class="mw-redirect" title="Ophthalmologist">ophthalmologists</a>, and <a href="/wiki/Optician" title="Optician">opticians</a> usually consider an appropriate near point to be closer than normal reading distance—approximately 25 cm.<sup id="cite_ref-eyeoptics_103-1" class="reference"><a href="#cite_note-eyeoptics-103"><span class="cite-bracket">[</span>103<span class="cite-bracket">]</span></a></sup> </p><p>Defects in vision can be explained using optical principles. As people age, the lens becomes less flexible and the near point recedes from the eye, a condition known as <a href="/wiki/Presbyopia" title="Presbyopia">presbyopia</a>. Similarly, people suffering from <a href="/wiki/Hyperopia" class="mw-redirect" title="Hyperopia">hyperopia</a> cannot decrease the focal length of their lens enough to allow for nearby objects to be imaged on their retina. Conversely, people who cannot increase the focal length of their lens enough to allow for distant objects to be imaged on the retina suffer from <a href="/wiki/Myopia" title="Myopia">myopia</a> and have a far point that is considerably closer than infinity. A condition known as <a href="/wiki/Astigmatism_(eye)" class="mw-redirect" title="Astigmatism (eye)">astigmatism</a> results when the cornea is not spherical but instead is more curved in one direction. This causes horizontally extended objects to be focused on different parts of the retina than vertically extended objects, and results in distorted images.<sup id="cite_ref-eyeoptics_103-2" class="reference"><a href="#cite_note-eyeoptics-103"><span class="cite-bracket">[</span>103<span class="cite-bracket">]</span></a></sup> </p><p>All of these conditions can be corrected using <a href="/wiki/Corrective_lens" title="Corrective lens">corrective lenses</a>. For presbyopia and hyperopia, a <a href="/wiki/Converging_lens" class="mw-redirect" title="Converging lens">converging lens</a> provides the extra curvature necessary to bring the near point closer to the eye while for myopia a <a href="/wiki/Diverging_lens" class="mw-redirect" title="Diverging lens">diverging lens</a> provides the curvature necessary to send the far point to infinity. Astigmatism is corrected with a <a href="/wiki/Cylinder_(geometry)" class="mw-redirect" title="Cylinder (geometry)">cylindrical surface</a> lens that curves more strongly in one direction than in another, compensating for the non-uniformity of the cornea.<sup id="cite_ref-lensdesign_105-0" class="reference"><a href="#cite_note-lensdesign-105"><span class="cite-bracket">[</span>105<span class="cite-bracket">]</span></a></sup> </p><p>The optical power of corrective lenses is measured in <a href="/wiki/Diopter" class="mw-redirect" title="Diopter">diopters</a>, a value equal to the <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">reciprocal</a> of the focal length measured in metres; with a positive focal length corresponding to a converging lens and a negative focal length corresponding to a diverging lens. For lenses that correct for astigmatism as well, three numbers are given: one for the spherical power, one for the cylindrical power, and one for the angle of orientation of the astigmatism.<sup id="cite_ref-lensdesign_105-1" class="reference"><a href="#cite_note-lensdesign-105"><span class="cite-bracket">[</span>105<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Visual_effects">Visual effects</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=21" title="Edit section: Visual effects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Optical_illusion" title="Optical illusion">Optical illusion</a> and <a href="/wiki/Perspective_(graphical)" title="Perspective (graphical)">Perspective (graphical)</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">For the visual effects used in film, video, and computer graphics, see <a href="/wiki/Visual_effects" title="Visual effects">visual effects</a>.</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ponzo_illusion.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Ponzo_illusion.gif/220px-Ponzo_illusion.gif" decoding="async" width="220" height="162" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/02/Ponzo_illusion.gif 1.5x" data-file-width="225" data-file-height="166" /></a><figcaption>The Ponzo Illusion relies on the fact that parallel lines appear to converge as they approach infinity.</figcaption></figure> <p>Optical illusions (also called visual illusions) are characterized by visually perceived images that differ from objective reality. The information gathered by the eye is processed in the brain to give a <a href="/wiki/Percept" class="mw-redirect" title="Percept">percept</a> that differs from the object being imaged. Optical illusions can be the result of a variety of phenomena including physical effects that create images that are different from the objects that make them, the physiological effects on the eyes and brain of excessive stimulation (e.g. brightness, tilt, colour, movement), and cognitive illusions where the eye and brain make <a href="/wiki/Unconscious_inference" title="Unconscious inference">unconscious inferences</a>.<sup id="cite_ref-106" class="reference"><a href="#cite_note-106"><span class="cite-bracket">[</span>106<span class="cite-bracket">]</span></a></sup> </p><p>Cognitive illusions include some which result from the unconscious misapplication of certain optical principles. For example, the <a href="/wiki/Ames_room" title="Ames room">Ames room</a>, <a href="/wiki/Hering_illusion" title="Hering illusion">Hering</a>, <a href="/wiki/M%C3%BCller-Lyer_illusion" title="Müller-Lyer illusion">Müller-Lyer</a>, <a href="/wiki/Orbison%27s_illusion" class="mw-redirect" title="Orbison's illusion">Orbison</a>, <a href="/wiki/Ponzo_illusion" title="Ponzo illusion">Ponzo</a>, <a href="/wiki/Sander_illusion" title="Sander illusion">Sander</a>, and <a href="/wiki/Wundt_illusion" title="Wundt illusion">Wundt illusions</a> all rely on the suggestion of the appearance of distance by using converging and diverging lines, in the same way that parallel light rays (or indeed any set of parallel lines) appear to converge at a <a href="/wiki/Vanishing_point" title="Vanishing point">vanishing point</a> at infinity in two-dimensionally rendered images with artistic perspective.<sup id="cite_ref-107" class="reference"><a href="#cite_note-107"><span class="cite-bracket">[</span>107<span class="cite-bracket">]</span></a></sup> This suggestion is also responsible for the famous <a href="/wiki/Moon_illusion" title="Moon illusion">moon illusion</a> where the moon, despite having essentially the same angular size, appears much larger near the <a href="/wiki/Horizon" title="Horizon">horizon</a> than it does at <a href="/wiki/Zenith" title="Zenith">zenith</a>.<sup id="cite_ref-108" class="reference"><a href="#cite_note-108"><span class="cite-bracket">[</span>108<span class="cite-bracket">]</span></a></sup> This illusion so confounded <a href="/wiki/Ptolemy_of_Alexandria" class="mw-redirect" title="Ptolemy of Alexandria">Ptolemy</a> that he incorrectly attributed it to atmospheric refraction when he described it in his treatise, <i><a href="/wiki/Optics_(Ptolemy)" title="Optics (Ptolemy)">Optics</a></i>.<sup id="cite_ref-Ptolemy_8-1" class="reference"><a href="#cite_note-Ptolemy-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Another type of optical illusion exploits broken patterns to trick the mind into perceiving symmetries or asymmetries that are not present. Examples include the <a href="/wiki/Caf%C3%A9_wall_illusion" title="Café wall illusion">café wall</a>, <a href="/wiki/Ehrenstein_illusion" title="Ehrenstein illusion">Ehrenstein</a>, <a href="/wiki/Fraser_spiral_illusion" title="Fraser spiral illusion">Fraser spiral</a>, <a href="/wiki/Poggendorff_illusion" title="Poggendorff illusion">Poggendorff</a>, and <a href="/wiki/Z%C3%B6llner_illusion" title="Zöllner illusion">Zöllner illusions</a>. Related, but not strictly illusions, are patterns that occur due to the superimposition of periodic structures. For example, <a href="/wiki/Transparency_(optics)" class="mw-redirect" title="Transparency (optics)">transparent</a> tissues with a grid structure produce shapes known as <a href="/wiki/Moir%C3%A9_pattern" title="Moiré pattern">moiré patterns</a>, while the superimposition of periodic transparent patterns comprising parallel opaque lines or curves produces <a href="/wiki/Line_moir%C3%A9" title="Line moiré">line moiré</a> patterns.<sup id="cite_ref-109" class="reference"><a href="#cite_note-109"><span class="cite-bracket">[</span>109<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Optical_instruments">Optical instruments</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=22" title="Edit section: Optical instruments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Table_of_Opticks,_Cyclopaedia,_Volume_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg/330px-Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg" decoding="async" width="300" height="486" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg/500px-Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg/960px-Table_of_Opticks%2C_Cyclopaedia%2C_Volume_2.jpg 2x" data-file-width="1789" data-file-height="2899" /></a><figcaption>Illustrations of various optical instruments from the 1728 <i><a href="/wiki/Cyclopaedia,_or_an_Universal_Dictionary_of_Arts_and_Sciences" class="mw-redirect" title="Cyclopaedia, or an Universal Dictionary of Arts and Sciences">Cyclopaedia</a></i></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Optical_instruments" class="mw-redirect" title="Optical instruments">Optical instruments</a></div> <p>Single lenses have a variety of applications including <a href="/wiki/Photographic_lens" class="mw-redirect" title="Photographic lens">photographic lenses</a>, corrective lenses, and magnifying glasses while single mirrors are used in parabolic reflectors and <a href="/wiki/Rear-view_mirror" title="Rear-view mirror">rear-view mirrors</a>. Combining a number of mirrors, prisms, and lenses produces compound optical instruments which have practical uses. For example, a <a href="/wiki/Periscope" title="Periscope">periscope</a> is simply two plane mirrors aligned to allow for viewing around obstructions. The most famous compound optical instruments in science are the microscope and the telescope which were both invented by the Dutch in the late 16th century.<sup id="cite_ref-FOOTNOTEYoungFreedman20201171–1175_110-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201171–1175-110"><span class="cite-bracket">[</span>110<span class="cite-bracket">]</span></a></sup> </p><p>Microscopes were first developed with just two lenses: an <a href="/wiki/Objective_lens" class="mw-redirect" title="Objective lens">objective lens</a> and an <a href="/wiki/Eyepiece" title="Eyepiece">eyepiece</a>. The objective lens is essentially a magnifying glass and was designed with a very small focal length while the eyepiece generally has a longer focal length. This has the effect of producing magnified images of close objects. Generally, an additional source of illumination is used since magnified images are dimmer due to the <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a> and the spreading of light rays over a larger surface area. Modern microscopes, known as <i>compound microscopes</i> have many lenses in them (typically four) to optimize the functionality and enhance image stability.<sup id="cite_ref-FOOTNOTEYoungFreedman20201171–1173_111-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201171–1173-111"><span class="cite-bracket">[</span>111<span class="cite-bracket">]</span></a></sup> A slightly different variety of microscope, the <a href="/wiki/Comparison_microscope" title="Comparison microscope">comparison microscope</a>, looks at side-by-side images to produce a <a href="/wiki/Stereoscopy" title="Stereoscopy">stereoscopic</a> <a href="/wiki/Binocular_vision" title="Binocular vision">binocular</a> view that appears three dimensional when used by humans.<sup id="cite_ref-112" class="reference"><a href="#cite_note-112"><span class="cite-bracket">[</span>112<span class="cite-bracket">]</span></a></sup> </p><p>The first telescopes, called refracting telescopes, were also developed with a single objective and eyepiece lens. In contrast to the microscope, the objective lens of the telescope was designed with a large focal length to avoid optical aberrations. The objective focuses an image of a distant object at its focal point which is adjusted to be at the focal point of an eyepiece of a much smaller focal length. The main goal of a telescope is not necessarily magnification, but rather the collection of light which is determined by the physical size of the objective lens. Thus, telescopes are normally indicated by the diameters of their objectives rather than by the magnification which can be changed by switching eyepieces. Because the magnification of a telescope is equal to the focal length of the objective divided by the focal length of the eyepiece, smaller focal-length eyepieces cause greater magnification.<sup id="cite_ref-FOOTNOTEYoungFreedman20201174_113-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201174-113"><span class="cite-bracket">[</span>113<span class="cite-bracket">]</span></a></sup> </p><p>Since crafting large lenses is much more difficult than crafting large mirrors, most modern telescopes are <i><a href="/wiki/Reflecting_telescope" title="Reflecting telescope">reflecting telescopes</a></i>, that is, telescopes that use a primary mirror rather than an objective lens. The same general optical considerations apply to reflecting telescopes that applied to refracting telescopes, namely, the larger the primary mirror, the more light collected, and the magnification is still equal to the focal length of the primary mirror divided by the focal length of the eyepiece. Professional telescopes generally do not have eyepieces and instead place an instrument (often a charge-coupled device) at the focal point instead.<sup id="cite_ref-FOOTNOTEYoungFreedman20201175_114-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201175-114"><span class="cite-bracket">[</span>114<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Photography">Photography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=23" title="Edit section: Photography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Science_of_photography" title="Science of photography">Science of photography</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Jonquil_flowers_at_f32.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Jonquil_flowers_at_f32.jpg/330px-Jonquil_flowers_at_f32.jpg" decoding="async" width="300" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Jonquil_flowers_at_f32.jpg/500px-Jonquil_flowers_at_f32.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Jonquil_flowers_at_f32.jpg/960px-Jonquil_flowers_at_f32.jpg 2x" data-file-width="1600" data-file-height="1054" /></a><figcaption>Photograph taken with aperture <style data-mw-deduplicate="TemplateStyles:r1263863036">.mw-parser-output span.fnumber,.mw-parser-output .fnumber-fallback{display:inline-block;white-space:nowrap;width:max-content}.mw-parser-output span.fnumber::first-letter,.mw-parser-output .fnumber-fallback .first-letter{font-style:italic;font-family:Trebuchet MS,Candara,Georgia,Calibri,Corbel,serif}</style><span class="fnumber-fallback"><span class="first-letter">f</span>/</span>32</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Jonquil_flowers_at_f5.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Jonquil_flowers_at_f5.jpg/330px-Jonquil_flowers_at_f5.jpg" decoding="async" width="300" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Jonquil_flowers_at_f5.jpg/500px-Jonquil_flowers_at_f5.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Jonquil_flowers_at_f5.jpg/960px-Jonquil_flowers_at_f5.jpg 2x" data-file-width="1600" data-file-height="1054" /></a><figcaption>Photograph taken with aperture <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1263863036" /><span class="fnumber-fallback"><span class="first-letter">f</span>/</span>5</figcaption></figure> <p>The optics of photography involves both lenses and the medium in which the electromagnetic radiation is recorded, whether it be a <a href="/wiki/Photographic_plates" class="mw-redirect" title="Photographic plates">plate</a>, <a href="/wiki/Photographic_film" title="Photographic film">film</a>, or charge-coupled device. Photographers must consider the <a href="/wiki/Reciprocity_(photography)" title="Reciprocity (photography)">reciprocity</a> of the camera and the shot which is summarized by the relation </p> <dl><dd>Exposure ∝ ApertureArea × ExposureTime × SceneLuminance<sup id="cite_ref-115" class="reference"><a href="#cite_note-115"><span class="cite-bracket">[</span>115<span class="cite-bracket">]</span></a></sup></dd></dl> <p>In other words, the smaller the aperture (giving greater depth of focus), the less light coming in, so the length of time has to be increased (leading to possible blurriness if motion occurs). An example of the use of the law of reciprocity is the <a href="/wiki/Sunny_16_rule" title="Sunny 16 rule">Sunny 16 rule</a> which gives a rough estimate for the settings needed to estimate the proper <a href="/wiki/Exposure_(photography)" title="Exposure (photography)">exposure</a> in daylight.<sup id="cite_ref-116" class="reference"><a href="#cite_note-116"><span class="cite-bracket">[</span>116<span class="cite-bracket">]</span></a></sup> </p><p>A camera's aperture is measured by a unitless number called the <a href="/wiki/F-number" title="F-number">f-number</a> or f-stop, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1263863036" /><span class="fnumber-fallback"><span class="first-letter">f</span>/</span>#, often notated as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" /></span>, and given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f/\#=N={\frac {f}{D}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">#</mi> <mo>=</mo> <mi>N</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <mi>D</mi> </mfrac> </mrow> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f/\#=N={\frac {f}{D}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c57b73a41758446ebf19496902fad6c375a597b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.979ex; height:5.343ex;" alt="{\displaystyle f/\#=N={\frac {f}{D}}\ }" /></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" /></span> is the focal length, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" /></span> is the diameter of the entrance pupil. By convention, "<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1263863036" /><span class="fnumber-fallback"><span class="first-letter">f</span>/</span>#" is treated as a single symbol, and specific values of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1263863036" /><span class="fnumber-fallback"><span class="first-letter">f</span>/</span># are written by replacing the <a href="/wiki/Number_sign" title="Number sign">number sign</a> with the value. The two ways to increase the f-stop are to either decrease the diameter of the entrance pupil or change to a longer focal length (in the case of a <a href="/wiki/Zoom_lens" title="Zoom lens">zoom lens</a>, this can be done by simply adjusting the lens). Higher f-numbers also have a larger <a href="/wiki/Depth_of_field" title="Depth of field">depth of field</a> due to the lens approaching the limit of a pinhole camera which is able to focus all images perfectly, regardless of distance, but requires very long exposure times.<sup id="cite_ref-117" class="reference"><a href="#cite_note-117"><span class="cite-bracket">[</span>117<span class="cite-bracket">]</span></a></sup> </p><p>The field of view that the lens will provide changes with the focal length of the lens. There are three basic classifications based on the relationship to the diagonal size of the film or sensor size of the camera to the focal length of the lens:<sup id="cite_ref-Bruce_Warren,_Photography,_page_71_118-0" class="reference"><a href="#cite_note-Bruce_Warren,_Photography,_page_71-118"><span class="cite-bracket">[</span>118<span class="cite-bracket">]</span></a></sup> </p> <ul><li><a href="/wiki/Normal_lens" title="Normal lens">Normal lens</a>: angle of view of about 50° (called <i>normal</i> because this angle considered roughly equivalent to human vision<sup id="cite_ref-Bruce_Warren,_Photography,_page_71_118-1" class="reference"><a href="#cite_note-Bruce_Warren,_Photography,_page_71-118"><span class="cite-bracket">[</span>118<span class="cite-bracket">]</span></a></sup>) and a focal length approximately equal to the diagonal of the film or sensor.<sup id="cite_ref-119" class="reference"><a href="#cite_note-119"><span class="cite-bracket">[</span>119<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Wide-angle_lens" title="Wide-angle lens">Wide-angle lens</a>: angle of view wider than 60° and focal length shorter than a normal lens.<sup id="cite_ref-120" class="reference"><a href="#cite_note-120"><span class="cite-bracket">[</span>120<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Long_focus_lens" class="mw-redirect" title="Long focus lens">Long focus lens</a>: angle of view narrower than a normal lens. This is any lens with a focal length longer than the diagonal measure of the film or sensor.<sup id="cite_ref-121" class="reference"><a href="#cite_note-121"><span class="cite-bracket">[</span>121<span class="cite-bracket">]</span></a></sup> The most common type of long focus lens is the <a href="/wiki/Telephoto_lens" title="Telephoto lens">telephoto lens</a>, a design that uses a special <i>telephoto group</i> to be physically shorter than its focal length.<sup id="cite_ref-122" class="reference"><a href="#cite_note-122"><span class="cite-bracket">[</span>122<span class="cite-bracket">]</span></a></sup></li></ul> <p>Modern zoom lenses may have some or all of these attributes. </p><p>The absolute value for the exposure time required depends on how <a href="/wiki/Sensitometry" title="Sensitometry">sensitive</a> to light the medium being used is (measured by the <a href="/wiki/Film_speed" title="Film speed">film speed</a>, or, for digital media, by the <a href="/wiki/Quantum_efficiency" title="Quantum efficiency">quantum efficiency</a>).<sup id="cite_ref-123" class="reference"><a href="#cite_note-123"><span class="cite-bracket">[</span>123<span class="cite-bracket">]</span></a></sup> Early photography used media that had very low light sensitivity, and so exposure times had to be long even for very bright shots. As technology has improved, so has the sensitivity through film cameras and digital cameras.<sup id="cite_ref-124" class="reference"><a href="#cite_note-124"><span class="cite-bracket">[</span>124<span class="cite-bracket">]</span></a></sup> </p><p>Other results from physical and geometrical optics apply to camera optics. For example, the maximum resolution capability of a particular camera set-up is determined by the <a href="/wiki/Diffraction_limit" class="mw-redirect" title="Diffraction limit">diffraction limit</a> associated with the pupil size and given, roughly, by the Rayleigh criterion.<sup id="cite_ref-125" class="reference"><a href="#cite_note-125"><span class="cite-bracket">[</span>125<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Atmospheric_optics">Atmospheric optics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=24" title="Edit section: Atmospheric optics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Atmospheric_optics" title="Atmospheric optics">Atmospheric optics</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Firesunset2edit.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Firesunset2edit.jpg/330px-Firesunset2edit.jpg" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Firesunset2edit.jpg/500px-Firesunset2edit.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Firesunset2edit.jpg/960px-Firesunset2edit.jpg 2x" data-file-width="2816" data-file-height="2112" /></a><figcaption>A colourful sky is often due to scattering of light off particulates and pollution, as in this photograph of a sunset during the <a href="/wiki/October_2007_California_wildfires" title="October 2007 California wildfires">October 2007 California wildfires</a>.</figcaption></figure> <p>The unique optical properties of the atmosphere cause a wide range of spectacular optical phenomena. The blue colour of the sky is a direct result of Rayleigh scattering which redirects higher frequency (blue) sunlight back into the field of view of the observer. Because blue light is scattered more easily than red light, the sun takes on a reddish hue when it is observed through a thick atmosphere, as during a <a href="/wiki/Sunrise" title="Sunrise">sunrise</a> or <a href="/wiki/Sunset" title="Sunset">sunset</a>. Additional particulate matter in the sky can scatter different colours at different angles creating colourful glowing skies at dusk and dawn. Scattering off of ice crystals and other particles in the atmosphere are responsible for <a href="/wiki/Halo_(optical_phenomenon)" title="Halo (optical phenomenon)">halos</a>, <a href="/wiki/Afterglow" title="Afterglow">afterglows</a>, <a href="/wiki/Corona_(meteorology)" class="mw-redirect" title="Corona (meteorology)">coronas</a>, <a href="/wiki/Crepuscular_rays" title="Crepuscular rays">rays of sunlight</a>, and <a href="/wiki/Sun_dog" title="Sun dog">sun dogs</a>. The variation in these kinds of phenomena is due to different particle sizes and geometries.<sup id="cite_ref-autogenerated1_126-0" class="reference"><a href="#cite_note-autogenerated1-126"><span class="cite-bracket">[</span>126<span class="cite-bracket">]</span></a></sup> </p><p>Mirages are optical phenomena in which light rays are bent due to thermal variations in the refraction index of air, producing displaced or heavily distorted images of distant objects. Other dramatic optical phenomena associated with this include the <a href="/wiki/Novaya_Zemlya_effect" title="Novaya Zemlya effect">Novaya Zemlya effect</a> where the sun appears to rise earlier than predicted with a distorted shape. A spectacular form of refraction occurs with a <a href="/wiki/Inversion_(meteorology)" title="Inversion (meteorology)">temperature inversion</a> called the <a href="/wiki/Fata_Morgana_(mirage)" title="Fata Morgana (mirage)">Fata Morgana</a> where objects on the horizon or even beyond the horizon, such as islands, cliffs, ships or icebergs, appear elongated and elevated, like "fairy tale castles".<sup id="cite_ref-127" class="reference"><a href="#cite_note-127"><span class="cite-bracket">[</span>127<span class="cite-bracket">]</span></a></sup> </p><p>Rainbows are the result of a combination of internal reflection and dispersive refraction of light in raindrops. A single reflection off the backs of an array of raindrops produces a rainbow with an angular size on the sky that ranges from 40° to 42° with red on the outside. Double rainbows are produced by two internal reflections with angular size of 50.5° to 54° with violet on the outside. Because rainbows are seen with the sun 180° away from the centre of the rainbow, rainbows are more prominent the closer the sun is to the horizon.<sup id="cite_ref-FOOTNOTEYoungFreedman20201117–1118_128-0" class="reference"><a href="#cite_note-FOOTNOTEYoungFreedman20201117–1118-128"><span class="cite-bracket">[</span>128<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=25" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/40px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="25" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/60px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li></ul> <ul><li><a href="/wiki/Ion_optics" class="mw-redirect" title="Ion optics">Ion optics</a></li> <li><a href="/wiki/List_of_publications_in_physics#Optics" title="List of publications in physics">Important publications in optics</a></li> <li><a href="/wiki/List_of_optical_topics" class="mw-redirect" title="List of optical topics">List of optical topics</a></li> <li><a href="/wiki/List_of_textbooks_in_electromagnetism" title="List of textbooks in electromagnetism">List of textbooks in electromagnetism</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=26" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-McGrawHill-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-McGrawHill_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-McGrawHill_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1"><i>McGraw-Hill Encyclopedia of Science and Technology</i> (5th ed.). McGraw-Hill. 1993.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=McGraw-Hill+Encyclopedia+of+Science+and+Technology&rft.edition=5th&rft.pub=McGraw-Hill&rft.date=1993&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://news.bbc.co.uk/1/hi/sci/tech/380186.stm">"World's oldest telescope?"</a>. <i>BBC News</i>. July 1, 1999. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090201185740/http://news.bbc.co.uk/1/hi/sci/tech/380186.stm">Archived</a> from the original on February 1, 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">Jan 3,</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=BBC+News&rft.atitle=World%27s+oldest+telescope%3F&rft.date=1999-07-01&rft_id=http%3A%2F%2Fnews.bbc.co.uk%2F1%2Fhi%2Fsci%2Ftech%2F380186.stm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFT.F._Hoad1996" class="citation book cs1">T.F. Hoad (1996). <a rel="nofollow" class="external text" href="https://archive.org/details/conciseoxforddic00tfho"><i>The Concise Oxford Dictionary of English Etymology</i></a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-283098-2" title="Special:BookSources/978-0-19-283098-2"><bdi>978-0-19-283098-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Concise+Oxford+Dictionary+of+English+Etymology&rft.date=1996&rft.isbn=978-0-19-283098-2&rft.au=T.F.+Hoad&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fconciseoxforddic00tfho&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.stanford.edu/class/history13/earlysciencelab/body/eyespages/eye.html">A History Of The Eye</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120120085632/http://www.stanford.edu/class/history13/earlysciencelab/body/eyespages/eye.html">Archived</a> 2012-01-20 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. stanford.edu. Retrieved 2012-06-10.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFT.L._Heath2003" class="citation book cs1">T.L. Heath (2003). <i>A manual of greek mathematics</i>. Courier Dover Publications. pp. <span class="nowrap">181–</span>182. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-43231-1" title="Special:BookSources/978-0-486-43231-1"><bdi>978-0-486-43231-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+manual+of+greek+mathematics&rft.pages=%3Cspan+class%3D%22nowrap%22%3E181-%3C%2Fspan%3E182&rft.pub=Courier+Dover+Publications&rft.date=2003&rft.isbn=978-0-486-43231-1&rft.au=T.L.+Heath&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWilliam_R._Uttal1983" class="citation book cs1">William R. Uttal (1983). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rhVOVKp0-5wC&pg=PA25"><i>Visual Form Detection in 3-Dimensional Space</i></a>. Psychology Press. pp. 25–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-89859-289-4" title="Special:BookSources/978-0-89859-289-4"><bdi>978-0-89859-289-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160503123615/https://books.google.com/books?id=rhVOVKp0-5wC&pg=PA25">Archived</a> from the original on 2016-05-03.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Visual+Form+Detection+in+3-Dimensional+Space&rft.pages=25-&rft.pub=Psychology+Press&rft.date=1983&rft.isbn=978-0-89859-289-4&rft.au=William+R.+Uttal&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DrhVOVKp0-5wC%26pg%3DPA25&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFEuclid1999" class="citation book cs1">Euclid (1999). Elaheh Kheirandish (ed.). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/arabicversionofe0000eucl"><i>The Arabic version of Euclid's optics = Kitāb Uqlīdis fī ikhtilāf al-manāẓir</i></a></span>. New York: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-98523-7" title="Special:BookSources/978-0-387-98523-7"><bdi>978-0-387-98523-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Arabic+version+of+Euclid%27s+optics+%3D+Kit%C4%81b+Uql%C4%ABdis+f%C4%AB+ikhtil%C4%81f+al-man%C4%81%E1%BA%93ir&rft.pub=New+York%3A+Springer&rft.date=1999&rft.isbn=978-0-387-98523-7&rft.au=Euclid&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Farabicversionofe0000eucl&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-Ptolemy-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Ptolemy_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Ptolemy_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPtolemy1996" class="citation book cs1">Ptolemy (1996). A. Mark Smith (ed.). <i>Ptolemy's theory of visual perception: an English translation of the Optics with introduction and commentary</i>. DIANE Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-87169-862-9" title="Special:BookSources/978-0-87169-862-9"><bdi>978-0-87169-862-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ptolemy%27s+theory+of+visual+perception%3A+an+English+translation+of+the+Optics+with+introduction+and+commentary&rft.pub=DIANE+Publishing&rft.date=1996&rft.isbn=978-0-87169-862-9&rft.au=Ptolemy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Adamson, Peter (2006). "Al-Kindi¯ and the reception of Greek philosophy". In Adamson, Peter; Taylor, R.. The Cambridge companion to Arabic philosophy. Cambridge University Press. p. 45. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-52069-0" title="Special:BookSources/978-0-521-52069-0">978-0-521-52069-0</a>.</span> </li> <li id="cite_note-j1-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-j1_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-j1_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRashed1990" class="citation journal cs1">Rashed, Roshdi (1990). "A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses". <i>Isis</i>. <b>81</b> (3): <span class="nowrap">464–</span>491. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F355456">10.1086/355456</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/233423">233423</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:144361526">144361526</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=A+pioneer+in+anaclastics%3A+Ibn+Sahl+on+burning+mirrors+and+lenses&rft.volume=81&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E464-%3C%2Fspan%3E491&rft.date=1990&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144361526%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F233423%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1086%2F355456&rft.aulast=Rashed&rft.aufirst=Roshdi&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist" style="display:inline;"><ul style="display:inline;"><li style="margin-bottom:.5em; display:block;;display:inline; margin:0;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHogendijkSabra2003" class="citation book cs1">Hogendijk, Jan P.; Sabra, Abdelhamid I., eds. (2003). <i>The Enterprise of Science in Islam: New Perspectives</i>. MIT Press. pp. <span class="nowrap">85–</span>118. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-19482-2" title="Special:BookSources/978-0-262-19482-2"><bdi>978-0-262-19482-2</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/50252039">50252039</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Enterprise+of+Science+in+Islam%3A+New+Perspectives&rft.pages=%3Cspan+class%3D%22nowrap%22%3E85-%3C%2Fspan%3E118&rft.pub=MIT+Press&rft.date=2003&rft_id=info%3Aoclcnum%2F50252039&rft.isbn=978-0-262-19482-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li><li style="margin-bottom:.5em; display:block;;margin-top:.5em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFG._Hatfield1996" class="citation book cs1">G. Hatfield (1996). "Was the Scientific Revolution Really a Revolution in Science?". In F.J. Ragep; P. Sally; S.J. Livesey (eds.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Kl1COWj9ubAC&pg=PA489"><i>Tradition, Transmission, Transformation: Proceedings of Two Conferences on Pre-modern Science held at the University of Oklahoma</i></a>. Brill Publishers. p. 500. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-04-10119-7" title="Special:BookSources/978-90-04-10119-7"><bdi>978-90-04-10119-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160427045853/https://books.google.com/books?id=Kl1COWj9ubAC&pg=PA489">Archived</a> from the original on 2016-04-27.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Was+the+Scientific+Revolution+Really+a+Revolution+in+Science%3F&rft.btitle=Tradition%2C+Transmission%2C+Transformation%3A+Proceedings+of+Two+Conferences+on+Pre-modern+Science+held+at+the+University+of+Oklahoma&rft.pages=500&rft.pub=Brill+Publishers&rft.date=1996&rft.isbn=978-90-04-10119-7&rft.au=G.+Hatfield&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DKl1COWj9ubAC%26pg%3DPA489&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li><li style="margin-bottom:.5em; display:block;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNader_El-Bizri2005" class="citation journal cs1">Nader El-Bizri (2005). "A Philosophical Perspective on Alhazen's Optics". <i>Arabic Sciences and Philosophy</i>. <b>15</b> (2): <span class="nowrap">189–</span>218. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0957423905000172">10.1017/S0957423905000172</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:123057532">123057532</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Arabic+Sciences+and+Philosophy&rft.atitle=A+Philosophical+Perspective+on+Alhazen%27s+Optics&rft.volume=15&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E189-%3C%2Fspan%3E218&rft.date=2005&rft_id=info%3Adoi%2F10.1017%2FS0957423905000172&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A123057532%23id-name%3DS2CID&rft.au=Nader+El-Bizri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li><li style="margin-bottom:.5em; display:block;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNader_El-Bizri2007" class="citation journal cs1">Nader El-Bizri (2007). "In Defence of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place". <i>Arabic Sciences and Philosophy</i>. <b>17</b>: <span class="nowrap">57–</span>80. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0957423907000367">10.1017/S0957423907000367</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:170960993">170960993</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Arabic+Sciences+and+Philosophy&rft.atitle=In+Defence+of+the+Sovereignty+of+Philosophy%3A+al-Baghdadi%27s+Critique+of+Ibn+al-Haytham%27s+Geometrisation+of+Place&rft.volume=17&rft.pages=%3Cspan+class%3D%22nowrap%22%3E57-%3C%2Fspan%3E80&rft.date=2007&rft_id=info%3Adoi%2F10.1017%2FS0957423907000367&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A170960993%23id-name%3DS2CID&rft.au=Nader+El-Bizri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li><li style="margin-bottom:.5em; display:block;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFG._Simon2006" class="citation journal cs1">G. Simon (2006). "The Gaze in Ibn al-Haytham". <i>The Medieval History Journal</i>. <b>9</b>: <span class="nowrap">89–</span>98. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F097194580500900105">10.1177/097194580500900105</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:170628785">170628785</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Medieval+History+Journal&rft.atitle=The+Gaze+in+Ibn+al-Haytham&rft.volume=9&rft.pages=%3Cspan+class%3D%22nowrap%22%3E89-%3C%2Fspan%3E98&rft.date=2006&rft_id=info%3Adoi%2F10.1177%2F097194580500900105&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A170628785%23id-name%3DS2CID&rft.au=G.+Simon&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li></ul></div></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFIan_P._HowardBrian_J._Rogers1995" class="citation book cs1">Ian P. Howard; Brian J. Rogers (1995). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=I8vqITdETe0C&pg=PA7"><i>Binocular Vision and Stereopsis</i></a>. Oxford University Press. p. 7. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-508476-4" title="Special:BookSources/978-0-19-508476-4"><bdi>978-0-19-508476-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160506053650/https://books.google.com/books?id=I8vqITdETe0C&pg=PA7">Archived</a> from the original on 2016-05-06.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Binocular+Vision+and+Stereopsis&rft.pages=7&rft.pub=Oxford+University+Press&rft.date=1995&rft.isbn=978-0-19-508476-4&rft.au=Ian+P.+Howard&rft.au=Brian+J.+Rogers&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DI8vqITdETe0C%26pg%3DPA7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFElena_AgazziEnrico_GiannettoFranco_Giudice2010" class="citation book cs1">Elena Agazzi; Enrico Giannetto; Franco Giudice (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ipyT7askd8EC&pg=PA42"><i>Representing Light Across Arts and Sciences: Theories and Practices</i></a>. V&R unipress GmbH. p. 42. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-89971-735-8" title="Special:BookSources/978-3-89971-735-8"><bdi>978-3-89971-735-8</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160510030553/https://books.google.com/books?id=ipyT7askd8EC&pg=PA42">Archived</a> from the original on 2016-05-10.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Representing+Light+Across+Arts+and+Sciences%3A+Theories+and+Practices&rft.pages=42&rft.pub=V%26R+unipress+GmbH&rft.date=2010&rft.isbn=978-3-89971-735-8&rft.au=Elena+Agazzi&rft.au=Enrico+Giannetto&rft.au=Franco+Giudice&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DipyT7askd8EC%26pg%3DPA42&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFEl-Bizri2010" class="citation book cs1"><a href="/wiki/Nader_El-Bizri" title="Nader El-Bizri">El-Bizri, Nader</a> (2010). "Classical Optics and the Perspectiva Traditions Leading to the Renaissance". In <a href="/wiki/John_Shannon_Hendrix" title="John Shannon Hendrix">Hendrix, John Shannon</a>; Carman, Charles H. (eds.). <i>Renaissance Theories of Vision (Visual Culture in Early Modernity)</i>. Farnham, Surrey: <a href="/wiki/Ashgate_Publishing" title="Ashgate Publishing">Ashgate Publishing</a>. pp. <span class="nowrap">11–</span>30. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4094-0024-0" title="Special:BookSources/978-1-4094-0024-0"><bdi>978-1-4094-0024-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Classical+Optics+and+the+Perspectiva+Traditions+Leading+to+the+Renaissance&rft.btitle=Renaissance+Theories+of+Vision+%28Visual+Culture+in+Early+Modernity%29&rft.place=Farnham%2C+Surrey&rft.pages=%3Cspan+class%3D%22nowrap%22%3E11-%3C%2Fspan%3E30&rft.pub=Ashgate+Publishing&rft.date=2010&rft.isbn=978-1-4094-0024-0&rft.aulast=El-Bizri&rft.aufirst=Nader&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span>; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFEl-Bizri2014" class="citation book cs1"><a href="/wiki/Nader_El-Bizri" title="Nader El-Bizri">El-Bizri, Nader</a> (2014). "Seeing Reality in Perspective: 'The Art of Optics' and the 'Science of Painting'<span class="cs1-kern-right"></span>". In Lupacchini, Rossella; Angelini, Annarita (eds.). <i>The Art of Science: From Perspective Drawing to Quantum Randomness</i>. Doredrecht: Springer. pp. <span class="nowrap">25–</span>47.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Seeing+Reality+in+Perspective%3A+%27The+Art+of+Optics%27+and+the+%27Science+of+Painting%27&rft.btitle=The+Art+of+Science%3A+From+Perspective+Drawing+to+Quantum+Randomness&rft.place=Doredrecht&rft.pages=%3Cspan+class%3D%22nowrap%22%3E25-%3C%2Fspan%3E47&rft.pub=Springer&rft.date=2014&rft.aulast=El-Bizri&rft.aufirst=Nader&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">D.C. Lindberg, <i>Theories of Vision from al-Kindi to Kepler</i>, (Chicago: Univ. of Chicago Pr., 1976), pp. 94–99.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFIlardi2007" class="citation book cs1">Ilardi, Vincent (2007). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_peIL7hVQUmwC"><i>Renaissance Vision from Spectacles to Telescopes</i></a>. Philadelphia: American Philosophical Society. pp. <span class="nowrap">4–</span>5. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-87169-259-7" title="Special:BookSources/978-0-87169-259-7"><bdi>978-0-87169-259-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Renaissance+Vision+from+Spectacles+to+Telescopes&rft.place=Philadelphia&rft.pages=%3Cspan+class%3D%22nowrap%22%3E4-%3C%2Fspan%3E5&rft.pub=American+Philosophical+Society&rft.date=2007&rft.isbn=978-0-87169-259-7&rft.aulast=Ilardi&rft.aufirst=Vincent&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_peIL7hVQUmwC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://galileo.rice.edu/sci/instruments/telescope.html">"The Galileo Project > Science > The Telescope" by Al Van Helden</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120320091537/http://galileo.rice.edu/sci/instruments/telescope.html">Archived</a> 2012-03-20 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Galileo.rice.edu. Retrieved 2012-06-10.</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHenry_C._King2003" class="citation book cs1">Henry C. King (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KAWwzHlDVksC&pg=PR1"><i>The History of the Telescope</i></a>. Courier Dover Publications. p. 27. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-43265-6" title="Special:BookSources/978-0-486-43265-6"><bdi>978-0-486-43265-6</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160617095507/https://books.google.com/books?id=KAWwzHlDVksC&pg=PR1">Archived</a> from the original on 2016-06-17.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+History+of+the+Telescope&rft.pages=27&rft.pub=Courier+Dover+Publications&rft.date=2003&rft.isbn=978-0-486-43265-6&rft.au=Henry+C.+King&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DKAWwzHlDVksC%26pg%3DPR1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPaul_S._AgutterDenys_N._Wheatley2008" class="citation book cs1">Paul S. Agutter; Denys N. Wheatley (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Gm4bqeBMR8cC&pg=PA17"><i>Thinking about Life: The History and Philosophy of Biology and Other Sciences</i></a>. Springer. p. 17. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-8865-0" title="Special:BookSources/978-1-4020-8865-0"><bdi>978-1-4020-8865-0</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160516134901/https://books.google.com/books?id=Gm4bqeBMR8cC&pg=PA17">Archived</a> from the original on 2016-05-16.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thinking+about+Life%3A+The+History+and+Philosophy+of+Biology+and+Other+Sciences&rft.pages=17&rft.pub=Springer&rft.date=2008&rft.isbn=978-1-4020-8865-0&rft.au=Paul+S.+Agutter&rft.au=Denys+N.+Wheatley&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DGm4bqeBMR8cC%26pg%3DPA17&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEIlardi2007[httpsarchiveorgdetailsbub_gb_peIL7hVQUmwCpagen221_210]-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEIlardi2007[httpsarchiveorgdetailsbub_gb_peIL7hVQUmwCpagen221_210]_20-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFIlardi2007">Ilardi (2007)</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_peIL7hVQUmwC/page/n221">210</a>.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://nobelprize.org/educational_games/physics/microscopes/timeline/index.html">Microscopes: Time Line</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100109122901/http://nobelprize.org/educational_games/physics/microscopes/timeline/index.html">Archived</a> 2010-01-09 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Nobel Foundation. Retrieved April 3, 2009</span> </li> <li id="cite_note-LZZginzib4C_page_55-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-LZZginzib4C_page_55_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWatson2007" class="citation book cs1">Watson, Fred (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=2LZZginzib4C&pg=PA55"><i>Stargazer: The Life and Times of the Telescope</i></a>. Allen & Unwin. p. 55. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-74175-383-7" title="Special:BookSources/978-1-74175-383-7"><bdi>978-1-74175-383-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160508185423/https://books.google.com/books?id=2LZZginzib4C&pg=PA55">Archived</a> from the original on 2016-05-08.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Stargazer%3A+The+Life+and+Times+of+the+Telescope&rft.pages=55&rft.pub=Allen+%26+Unwin&rft.date=2007&rft.isbn=978-1-74175-383-7&rft.aulast=Watson&rft.aufirst=Fred&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D2LZZginzib4C%26pg%3DPA55&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCaspar1993" class="citation book cs1">Caspar, Max (1993) [First published 1959]. <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/kepler00casp/"><i>Kepler</i></a></span>. Dover Publications. pp. <span class="nowrap">142–</span>146. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-67605-6" title="Special:BookSources/0-486-67605-6"><bdi>0-486-67605-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Kepler&rft.pages=%3Cspan+class%3D%22nowrap%22%3E142-%3C%2Fspan%3E146&rft.pub=Dover+Publications&rft.date=1993&rft.isbn=0-486-67605-6&rft.aulast=Caspar&rft.aufirst=Max&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fkepler00casp%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEIlardi2007[httpsarchiveorgdetailsbub_gb_peIL7hVQUmwCpagen255_244]-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEIlardi2007[httpsarchiveorgdetailsbub_gb_peIL7hVQUmwCpagen255_244]_24-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFIlardi2007">Ilardi (2007)</a>, p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_peIL7hVQUmwC/page/n255">244</a>.</span> </li> <li id="cite_note-FOOTNOTECaspar1993[httpsarchiveorgdetailskepler00casppage192mode2up_192–202]-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECaspar1993[httpsarchiveorgdetailskepler00casppage192mode2up_192–202]_25-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCaspar1993">Caspar (1993)</a>, pp. <a rel="nofollow" class="external text" href="https://archive.org/details/kepler00casp/page/192/mode/2up">192–202</a>.</span> </li> <li id="cite_note-Sabra-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-Sabra_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Sabra_26-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFA.I._Sabra1981" class="citation book cs1">A.I. Sabra (1981). <i>Theories of light, from Descartes to Newton</i>. CUP Archive. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-28436-3" title="Special:BookSources/978-0-521-28436-3"><bdi>978-0-521-28436-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theories+of+light%2C+from+Descartes+to+Newton&rft.pub=CUP+Archive&rft.date=1981&rft.isbn=978-0-521-28436-3&rft.au=A.I.+Sabra&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFW.F._Magie1935" class="citation book cs1">W.F. Magie (1935). <a rel="nofollow" class="external text" href="https://archive.org/details/in.ernet.dli.2015.449479"><i>A Source Book in Physics</i></a>. Harvard University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/in.ernet.dli.2015.449479/page/n323">309</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Source+Book+in+Physics&rft.pages=309&rft.pub=Harvard+University+Press&rft.date=1935&rft.au=W.F.+Magie&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fin.ernet.dli.2015.449479&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJ.C._Maxwell1865" class="citation journal cs1">J.C. Maxwell (1865). <a href="/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field" title="A Dynamical Theory of the Electromagnetic Field">"A Dynamical Theory of the Electromagnetic Field"</a>. <i>Philosophical Transactions of the Royal Society of London</i>. <b>155</b>: <span class="nowrap">459–</span>512. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1865RSPT..155..459M">1865RSPT..155..459M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1865.0008">10.1098/rstl.1865.0008</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:186207827">186207827</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London&rft.atitle=A+Dynamical+Theory+of+the+Electromagnetic+Field&rft.volume=155&rft.pages=%3Cspan+class%3D%22nowrap%22%3E459-%3C%2Fspan%3E512&rft.date=1865&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A186207827%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1098%2Frstl.1865.0008&rft_id=info%3Abibcode%2F1865RSPT..155..459M&rft.au=J.C.+Maxwell&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">For a solid approach to the complexity of Planck's intellectual motivations for the quantum, for his reluctant acceptance of its implications, see H. Kragh, <a rel="nofollow" class="external text" href="http://physicsworld.com/cws/article/print/373">Max Planck: the reluctant revolutionary</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120401221617/http://physicsworld.com/cws/article/print/373">Archived</a> 2012-04-01 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <i>Physics World</i>. December 2000.</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFEinstein1967" class="citation book cs1"><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein, A.</a> (1967). "On a heuristic viewpoint concerning the production and transformation of light". In Ter Haar, D. (ed.). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/oldquantumtheory0000haar"><i>The Old Quantum Theory</i></a></span>. Pergamon. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/oldquantumtheory0000haar/page/91">91–107</a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/534625">534625</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=On+a+heuristic+viewpoint+concerning+the+production+and+transformation+of+light&rft.btitle=The+Old+Quantum+Theory&rft.pages=91-107&rft.pub=Pergamon&rft.date=1967&rft_id=info%3Aoclcnum%2F534625&rft.aulast=Einstein&rft.aufirst=A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foldquantumtheory0000haar&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span> The chapter is an English translation of Einstein's 1905 paper on the photoelectric effect.</span> </li> <li id="cite_note-AnnPhysik322132-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-AnnPhysik322132_31-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFEinstein1905" class="citation journal cs1 cs1-prop-foreign-lang-source">Einstein, A. (1905). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19053220607">"Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt"</a> [On a heuristic viewpoint concerning the production and transformation of light]. <i>Annalen der Physik</i> (in German). <b>322</b> (6): <span class="nowrap">132–</span>148. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1905AnP...322..132E">1905AnP...322..132E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19053220607">10.1002/andp.19053220607</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=%C3%9Cber+einen+die+Erzeugung+und+Verwandlung+des+Lichtes+betreffenden+heuristischen+Gesichtspunkt&rft.volume=322&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E132-%3C%2Fspan%3E148&rft.date=1905&rft_id=info%3Adoi%2F10.1002%2Fandp.19053220607&rft_id=info%3Abibcode%2F1905AnP...322..132E&rft.aulast=Einstein&rft.aufirst=A.&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252Fandp.19053220607&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation journal cs1 cs1-prop-long-vol"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070704225134/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Bohr/Bohr-1913a.html">"On the Constitution of Atoms and Molecules"</a>. <i>Philosophical Magazine</i>. 26, Series 6: <span class="nowrap">1–</span>25. 1913. Archived from <a rel="nofollow" class="external text" href="http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Bohr/Bohr-1913a.html">the original</a> on July 4, 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=On+the+Constitution+of+Atoms+and+Molecules&rft.volume=26%2C+Series+6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E25&rft.date=1913&rft_id=http%3A%2F%2Fdbhs.wvusd.k12.ca.us%2Fwebdocs%2FChem-History%2FBohr%2FBohr-1913a.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span>. The landmark paper laying the <a href="/wiki/Bohr_model_of_the_atom" class="mw-redirect" title="Bohr model of the atom">Bohr model of the atom</a> and <a href="/wiki/Molecular_bond" class="mw-redirect" title="Molecular bond">molecular bonding</a>.</span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFR._Feynman1985" class="citation book cs1"><a href="/wiki/Richard_Feynman" title="Richard Feynman">R. Feynman</a> (1985). "Chapter 1". <i>QED: The Strange Theory of Light and Matter</i>. Princeton University Press. p. 6. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-08388-9" title="Special:BookSources/978-0-691-08388-9"><bdi>978-0-691-08388-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+1&rft.btitle=QED%3A+The+Strange+Theory+of+Light+and+Matter&rft.pages=6&rft.pub=Princeton+University+Press&rft.date=1985&rft.isbn=978-0-691-08388-9&rft.au=R.+Feynman&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFN._Taylor2000" class="citation book cs1">N. Taylor (2000). <i>LASER: The inventor, the Nobel laureate, and the thirty-year patent war</i>. New York: Simon & Schuster. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-684-83515-0" title="Special:BookSources/978-0-684-83515-0"><bdi>978-0-684-83515-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=LASER%3A+The+inventor%2C+the+Nobel+laureate%2C+and+the+thirty-year+patent+war&rft.place=New+York&rft.pub=Simon+%26+Schuster&rft.date=2000&rft.isbn=978-0-684-83515-0&rft.au=N.+Taylor&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAriel_LipsonStephen_G._LipsonHenry_Lipson2010" class="citation book cs1">Ariel Lipson; Stephen G. Lipson; Henry Lipson (28 October 2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=aow3o0dhyjYC&pg=PA48"><i>Optical Physics</i></a>. Cambridge University Press. p. 48. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-49345-1" title="Special:BookSources/978-0-521-49345-1"><bdi>978-0-521-49345-1</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130528233136/http://books.google.com/books?id=aow3o0dhyjYC&pg=PA48">Archived</a> from the original on 28 May 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">12 July</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optical+Physics&rft.pages=48&rft.pub=Cambridge+University+Press&rft.date=2010-10-28&rft.isbn=978-0-521-49345-1&rft.au=Ariel+Lipson&rft.au=Stephen+G.+Lipson&rft.au=Henry+Lipson&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Daow3o0dhyjYC%26pg%3DPA48&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFArthur_Schuster1904" class="citation book cs1">Arthur Schuster (1904). <a rel="nofollow" class="external text" href="https://archive.org/details/anintroductiont02schugoog"><i>An Introduction to the Theory of Optics</i></a>. E. Arnold. p. <a rel="nofollow" class="external text" href="https://archive.org/details/anintroductiont02schugoog/page/n62">41</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+the+Theory+of+Optics&rft.pages=41&rft.pub=E.+Arnold&rft.date=1904&rft.au=Arthur+Schuster&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fanintroductiont02schugoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJ.E._Greivenkamp2004" class="citation book cs1">J.E. Greivenkamp (2004). <i>Field Guide to Geometrical Optics. SPIE Field Guides vol. <b>FG01</b><span></span></i>. SPIE. pp. <span class="nowrap">19–</span>20. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8194-5294-8" title="Special:BookSources/978-0-8194-5294-8"><bdi>978-0-8194-5294-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Field+Guide+to+Geometrical+Optics.+SPIE+Field+Guides+vol.+FG01&rft.pages=%3Cspan+class%3D%22nowrap%22%3E19-%3C%2Fspan%3E20&rft.pub=SPIE&rft.date=2004&rft.isbn=978-0-8194-5294-8&rft.au=J.E.+Greivenkamp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201109-38"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEYoungFreedman20201109_38-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEYoungFreedman20201109_38-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1109.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201112–1113-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201112–1113_39-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1112–1113.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201142–1143,_1145-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201142–1143,_1145_40-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1142–1143, 1145.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201116-41"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEYoungFreedman20201116_41-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEYoungFreedman20201116_41-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1116.</span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMarchand1978" class="citation book cs1">Marchand, E.W. (1978). <i>Gradient Index Optics</i>. New York: Academic Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gradient+Index+Optics&rft.place=New+York&rft.pub=Academic+Press&rft.date=1978&rft.aulast=Marchand&rft.aufirst=E.W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201113–1115-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201113–1115_43-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1113–1115.</span> </li> <li id="cite_note-FOOTNOTEHecht2017159-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017159_44-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 159.</span> </li> <li id="cite_note-FOOTNOTEHecht2017165-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017165_45-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 165.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201157-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201157_46-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1157.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201143,1163,1175-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201143,1163,1175_47-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1143,1163,1175.</span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text">MV Klein & TE Furtak, 1986, Optics, John Wiley & Sons, New York <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-87297-0" title="Special:BookSources/0-471-87297-0">0-471-87297-0</a>.</span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMaxwell1865" class="citation journal cs1"><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell, James Clerk</a> (1865). <a class="external text" href="https://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf">"A dynamical theory of the electromagnetic field"</a> <span class="cs1-format">(PDF)</span>. <i>Philosophical Transactions of the Royal Society of London</i>. <b>155</b>: 499. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1865RSPT..155..459M">1865RSPT..155..459M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1865.0008">10.1098/rstl.1865.0008</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:186207827">186207827</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110728140123/http://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2011-07-28.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London&rft.atitle=A+dynamical+theory+of+the+electromagnetic+field&rft.volume=155&rft.pages=499&rft.date=1865&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A186207827%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1098%2Frstl.1865.0008&rft_id=info%3Abibcode%2F1865RSPT..155..459M&rft.aulast=Maxwell&rft.aufirst=James+Clerk&rft_id=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2F1%2F19%2FA_Dynamical_Theory_of_the_Electromagnetic_Field.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span> This article accompanied a December 8, 1864, presentation by Maxwell to the Royal Society. See also <a href="/wiki/A_dynamical_theory_of_the_electromagnetic_field" class="mw-redirect" title="A dynamical theory of the electromagnetic field">A dynamical theory of the electromagnetic field</a>.</span> </li> <li id="cite_note-Born_and_Wolf-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-Born_and_Wolf_50-0">^</a></b></span> <span class="reference-text">M. Born and E. Wolf (1999). <i>Principle of Optics</i>. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-64222-1" title="Special:BookSources/0-521-64222-1">0-521-64222-1</a>.</span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJ._Goodman2005" class="citation book cs1">J. Goodman (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ow5xs_Rtt9AC"><i>Introduction to Fourier Optics</i></a> (3rd ed.). Roberts & Co Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-9747077-2-3" title="Special:BookSources/978-0-9747077-2-3"><bdi>978-0-9747077-2-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Fourier+Optics&rft.edition=3rd&rft.pub=Roberts+%26+Co+Publishers&rft.date=2005&rft.isbn=978-0-9747077-2-3&rft.au=J.+Goodman&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dow5xs_Rtt9AC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFA.E._Siegman1986" class="citation book cs1">A.E. Siegman (1986). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/lasers0000sieg"><i>Lasers</i></a></span>. University Science Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-935702-11-8" title="Special:BookSources/978-0-935702-11-8"><bdi>978-0-935702-11-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lasers&rft.pub=University+Science+Books&rft.date=1986&rft.isbn=978-0-935702-11-8&rft.au=A.E.+Siegman&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Flasers0000sieg&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span> Chapter 16.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201187–1188-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201187–1188_53-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1187–1188.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman2020512,_1189-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman2020512,_1189_54-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 512, 1189.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201191–1192-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201191–1192_55-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1191–1192.</span> </li> <li id="cite_note-interferometry-56"><span class="mw-cite-backlink">^ <a href="#cite_ref-interferometry_56-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-interferometry_56-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFP._Hariharan2003" class="citation book cs1">P. Hariharan (2003). <a rel="nofollow" class="external text" href="http://www.astro.lsa.umich.edu/~monnier/Publications/ROP2003_final.pdf"><i>Optical Interferometry</i></a> <span class="cs1-format">(PDF)</span> (2nd ed.). San Diego, US: Academic Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-325220-3" title="Special:BookSources/978-0-12-325220-3"><bdi>978-0-12-325220-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080406215913/http://www.astro.lsa.umich.edu/~monnier/Publications/ROP2003_final.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2008-04-06.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optical+Interferometry&rft.place=San+Diego%2C+US&rft.edition=2nd&rft.pub=Academic+Press&rft.date=2003&rft.isbn=978-0-12-325220-3&rft.au=P.+Hariharan&rft_id=http%3A%2F%2Fwww.astro.lsa.umich.edu%2F~monnier%2FPublications%2FROP2003_final.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFE.R._Hoover1977" class="citation book cs1">E.R. Hoover (1977). <i>Cradle of Greatness: National and World Achievements of Ohio's Western Reserve</i>. Cleveland: Shaker Savings Association.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cradle+of+Greatness%3A+National+and+World+Achievements+of+Ohio%27s+Western+Reserve&rft.place=Cleveland&rft.pub=Shaker+Savings+Association&rft.date=1977&rft.au=E.R.+Hoover&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201198–1200-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201198–1200_58-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1198–1200.</span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAubert1760" class="citation book cs1 cs1-prop-foreign-lang-source">Aubert, J. L. (1760). <a rel="nofollow" class="external text" href="https://archive.org/details/memoirespourlhi146aubegoog"><i>Memoires pour l'histoire des sciences et des beaux arts</i></a> [<i>Memoirs for the history of science and fine arts</i>] (in French). Paris: Impr. de S.A.S.; Chez E. Ganeau. p. <a rel="nofollow" class="external text" href="https://archive.org/details/memoirespourlhi146aubegoog/page/n151">149</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Memoires+pour+l%27histoire+des+sciences+et+des+beaux+arts&rft.place=Paris&rft.pages=149&rft.pub=Impr.+de+S.A.S.%3B+Chez+E.+Ganeau&rft.date=1760&rft.aulast=Aubert&rft.aufirst=J.+L.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmemoirespourlhi146aubegoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBrewster1831" class="citation book cs1">Brewster, D. (1831). <a rel="nofollow" class="external text" href="https://archive.org/details/atreatiseonopti00brewgoog"><i>A Treatise on Optics</i></a>. London: Longman, Rees, Orme, Brown & Green and John Taylor. p. <a rel="nofollow" class="external text" href="https://archive.org/details/atreatiseonopti00brewgoog/page/n113">95</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Treatise+on+Optics&rft.place=London&rft.pages=95&rft.pub=Longman%2C+Rees%2C+Orme%2C+Brown+%26+Green+and+John+Taylor&rft.date=1831&rft.aulast=Brewster&rft.aufirst=D.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fatreatiseonopti00brewgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHooke1665" class="citation book cs1">Hooke, R. (1665). <a rel="nofollow" class="external text" href="https://archive.org/details/micrographiaorso00hook"><i>Micrographia: or, Some physiological descriptions of minute bodies made by magnifying glasses</i></a>. London: J. Martyn and J. Allestry. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-49564-4" title="Special:BookSources/978-0-486-49564-4"><bdi>978-0-486-49564-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Micrographia%3A+or%2C+Some+physiological+descriptions+of+minute+bodies+made+by+magnifying+glasses&rft.place=London&rft.pub=J.+Martyn+and+J.+Allestry&rft.date=1665&rft.isbn=978-0-486-49564-4&rft.aulast=Hooke&rft.aufirst=R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmicrographiaorso00hook&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFTurnbull1940–1941" class="citation journal cs1">Turnbull, H. W. (1940–1941). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsnr.1940.0003">"Early Scottish Relations with the Royal Society: I. James Gregory, F.R.S. (1638–1675)"</a>. <i>Notes and Records of the Royal Society of London</i>. <b>3</b>: <span class="nowrap">22–</span>38. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsnr.1940.0003">10.1098/rsnr.1940.0003</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notes+and+Records+of+the+Royal+Society+of+London&rft.atitle=Early+Scottish+Relations+with+the+Royal+Society%3A+I.+James+Gregory%2C+F.R.S.+%281638%E2%80%931675%29&rft.volume=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E22-%3C%2Fspan%3E38&rft.date=1940%2F1941&rft_id=info%3Adoi%2F10.1098%2Frsnr.1940.0003&rft.aulast=Turnbull&rft.aufirst=H.+W.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frsnr.1940.0003&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-63">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRothman2003" class="citation book cs1"><a href="/wiki/Tony_Rothman" title="Tony Rothman">Rothman, T.</a> (2003). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/everythingsrelat0000roth"><i>Everything's Relative and Other Fables in Science and Technology</i></a></span>. New Jersey: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-20257-8" title="Special:BookSources/978-0-471-20257-8"><bdi>978-0-471-20257-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Everything%27s+Relative+and+Other+Fables+in+Science+and+Technology&rft.place=New+Jersey&rft.pub=Wiley&rft.date=2003&rft.isbn=978-0-471-20257-8&rft.aulast=Rothman&rft.aufirst=T.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Feverythingsrelat0000roth&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEHecht20175-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht20175_64-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 5.</span> </li> <li id="cite_note-FOOTNOTEHecht2017398–399YoungFreedman20201192-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017398–399YoungFreedman20201192_65-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 398–399; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1192.</span> </li> <li id="cite_note-FOOTNOTEHecht2017488–491YoungFreedman20201224–1225-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017488–491YoungFreedman20201224–1225_66-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 488–491; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1224–1225.</span> </li> <li id="cite_note-phyoptics-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-phyoptics_67-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFLonghurst1968" class="citation book cs1">Longhurst, R. S. (1968). <i>Geometrical and Physical Optics</i> (2nd ed.). London: Longmans. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1967gpo..book.....L">1967gpo..book.....L</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometrical+and+Physical+Optics&rft.place=London&rft.edition=2nd&rft.pub=Longmans&rft.date=1968&rft_id=info%3Abibcode%2F1967gpo..book.....L&rft.aulast=Longhurst&rft.aufirst=R.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEHecht2017497YoungFreedman20201228–1230-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017497YoungFreedman20201228–1230_68-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 497; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1228–1230.</span> </li> <li id="cite_note-FOOTNOTEHecht2017482-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017482_69-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 482.</span> </li> <li id="cite_note-FOOTNOTEHecht2017485YoungFreedman20201232-70"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017485YoungFreedman20201232_70-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 485; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1232.</span> </li> <li id="cite_note-71"><span class="mw-cite-backlink"><b><a href="#cite_ref-71">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFTubbs2003" class="citation thesis cs1">Tubbs, Robert Nigel (September 2003). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081005013157/http://www.mrao.cam.ac.uk/telescopes/coast/theses/rnt/"><i>Lucky Exposures: Diffraction limited astronomical imaging through the atmosphere</i></a> (PhD thesis). Cambridge University. Archived from <a rel="nofollow" class="external text" href="http://www.mrao.cam.ac.uk/telescopes/coast/theses/rnt/">the original</a> on 2008-10-05.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Lucky+Exposures%3A+Diffraction+limited+astronomical+imaging+through+the+atmosphere&rft.inst=Cambridge+University&rft.date=2003-09&rft.aulast=Tubbs&rft.aufirst=Robert+Nigel&rft_id=http%3A%2F%2Fwww.mrao.cam.ac.uk%2Ftelescopes%2Fcoast%2Ftheses%2Frnt%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-72"><span class="mw-cite-backlink"><b><a href="#cite_ref-72">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFC.F._BohrenD.R._Huffman1983" class="citation book cs1">C.F. Bohren & D.R. Huffman (1983). <i>Absorption and Scattering of Light by Small Particles</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-29340-8" title="Special:BookSources/978-0-471-29340-8"><bdi>978-0-471-29340-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Absorption+and+Scattering+of+Light+by+Small+Particles&rft.pub=Wiley&rft.date=1983&rft.isbn=978-0-471-29340-8&rft.au=C.F.+Bohren&rft.au=D.R.+Huffman&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-J286-73"><span class="mw-cite-backlink">^ <a href="#cite_ref-J286_73-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-J286_73-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJ.D._Jackson1975" class="citation book cs1">J.D. Jackson (1975). <a rel="nofollow" class="external text" href="https://archive.org/details/classicalelectro00jack_0/page/286"><i>Classical Electrodynamics</i></a> (2nd ed.). Wiley. p. <a rel="nofollow" class="external text" href="https://archive.org/details/classicalelectro00jack_0/page/286">286</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-43132-9" title="Special:BookSources/978-0-471-43132-9"><bdi>978-0-471-43132-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+Electrodynamics&rft.pages=286&rft.edition=2nd&rft.pub=Wiley&rft.date=1975&rft.isbn=978-0-471-43132-9&rft.au=J.D.+Jackson&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fclassicalelectro00jack_0%2Fpage%2F286&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEHecht2017202–204-74"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017202–204_74-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 202–204.</span> </li> <li id="cite_note-optnet-75"><span class="mw-cite-backlink">^ <a href="#cite_ref-optnet_75-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-optnet_75-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFR._RamaswamiK.N._Sivarajan1998" class="citation book cs1">R. Ramaswami; K.N. Sivarajan (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=WpByp4Ip0z8C"><i>Optical Networks: A Practical Perspective</i></a>. London: Academic Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-374092-2" title="Special:BookSources/978-0-12-374092-2"><bdi>978-0-12-374092-2</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151027164628/https://books.google.com/books?id=WpByp4Ip0z8C&printsec=frontcover">Archived</a> from the original on 2015-10-27.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optical+Networks%3A+A+Practical+Perspective&rft.place=London&rft.pub=Academic+Press&rft.date=1998&rft.isbn=978-0-12-374092-2&rft.au=R.+Ramaswami&rft.au=K.N.+Sivarajan&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DWpByp4Ip0z8C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-76"><span class="mw-cite-backlink"><b><a href="#cite_ref-76">^</a></b></span> <span class="reference-text">Brillouin, Léon. <i>Wave Propagation and Group Velocity</i>. Academic Press Inc., New York (1960)</span> </li> <li id="cite_note-77"><span class="mw-cite-backlink"><b><a href="#cite_ref-77">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFM._BornE._Wolf1999" class="citation book cs1"><a href="/wiki/Max_Born" title="Max Born">M. Born</a> & E. Wolf (1999). <i>Principle of Optics</i>. Cambridge: Cambridge University Press. pp. <span class="nowrap">14–</span>24. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-64222-4" title="Special:BookSources/978-0-521-64222-4"><bdi>978-0-521-64222-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principle+of+Optics&rft.place=Cambridge&rft.pages=%3Cspan+class%3D%22nowrap%22%3E14-%3C%2Fspan%3E24&rft.pub=Cambridge+University+Press&rft.date=1999&rft.isbn=978-0-521-64222-4&rft.au=M.+Born&rft.au=E.+Wolf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEHecht2017333–334YoungFreedman20201083,_1118-78"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017333–334YoungFreedman20201083,_1118_78-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 333–334; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1083, 1118.</span> </li> <li id="cite_note-FOOTNOTEHecht2017336-79"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEHecht2017336_79-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHecht2017336_79-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 336.</span> </li> <li id="cite_note-FOOTNOTEHecht2017330–332YoungFreedman20201123-80"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017330–332YoungFreedman20201123_80-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 330–332; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1123.</span> </li> <li id="cite_note-FOOTNOTEHecht2017333–334YoungFreedman20201123-81"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017333–334YoungFreedman20201123_81-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 333–334; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1123.</span> </li> <li id="cite_note-FOOTNOTEHecht2017334–335YoungFreedman20201124-82"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017334–335YoungFreedman20201124_82-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 334–335; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1124.</span> </li> <li id="cite_note-FOOTNOTEHecht2017379–383-83"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017379–383_83-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 379–383.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201124-84"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201124_84-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1124.</span> </li> <li id="cite_note-FOOTNOTEHecht2017367,_373-85"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017367,_373_85-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 367, 373.</span> </li> <li id="cite_note-FOOTNOTEHecht2017372YoungFreedman20201124–1125-86"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017372YoungFreedman20201124–1125_86-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 372; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1124–1125.</span> </li> <li id="cite_note-87"><span class="mw-cite-backlink"><b><a href="#cite_ref-87">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFF.J._Duarte2015" class="citation book cs1"><a href="/wiki/F._J._Duarte" title="F. J. Duarte">F.J. Duarte</a> (2015). <a rel="nofollow" class="external text" href="http://www.tunablelaseroptics.com"><i>Tunable Laser Optics</i></a> (2nd ed.). New York: CRC. pp. <span class="nowrap">117–</span>120. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4822-4529-5" title="Special:BookSources/978-1-4822-4529-5"><bdi>978-1-4822-4529-5</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150402145942/https://www.tunablelaseroptics.com/">Archived</a> from the original on 2015-04-02.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Tunable+Laser+Optics&rft.place=New+York&rft.pages=%3Cspan+class%3D%22nowrap%22%3E117-%3C%2Fspan%3E120&rft.edition=2nd&rft.pub=CRC&rft.date=2015&rft.isbn=978-1-4822-4529-5&rft.au=F.J.+Duarte&rft_id=http%3A%2F%2Fwww.tunablelaseroptics.com&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEHecht2017338YoungFreedman20201119–1121-88"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017338YoungFreedman20201119–1121_88-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, p. 338; <a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1119–1121.</span> </li> <li id="cite_note-FOOTNOTEHecht2017339–342-89"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017339–342_89-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 339–342.</span> </li> <li id="cite_note-FOOTNOTEHecht2017355–358-90"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017355–358_90-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 355–358.</span> </li> <li id="cite_note-FOOTNOTEHecht2017353–356-91"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHecht2017353–356_91-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHecht2017">Hecht (2017)</a>, pp. 353–356.</span> </li> <li id="cite_note-92"><span class="mw-cite-backlink"><b><a href="#cite_ref-92">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWallsMilburn1994" class="citation book cs1"><a href="/wiki/Daniel_Frank_Walls" class="mw-redirect" title="Daniel Frank Walls">Walls, Daniel Frank</a>; Milburn, G. J. (1994). <i>Quantum Optics</i>. Springer.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Optics&rft.pub=Springer&rft.date=1994&rft.aulast=Walls&rft.aufirst=Daniel+Frank&rft.au=Milburn%2C+G.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-93"><span class="mw-cite-backlink"><b><a href="#cite_ref-93">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMcAulay1991" class="citation book cs1">McAulay, Alastair D. (16 January 1991). <i>Optical Computer Architectures: The Application of Optical Concepts to Next Generation Computers</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-63242-9" title="Special:BookSources/978-0-471-63242-9"><bdi>978-0-471-63242-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optical+Computer+Architectures%3A+The+Application+of+Optical+Concepts+to+Next+Generation+Computers&rft.pub=Wiley&rft.date=1991-01-16&rft.isbn=978-0-471-63242-9&rft.aulast=McAulay&rft.aufirst=Alastair+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-94"><span class="mw-cite-backlink"><b><a href="#cite_ref-94">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFShen1984" class="citation book cs1">Shen, Y. R. (1984). <i>The Principles of Nonlinear Optics</i>. New York: Wiley-Interscience. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-88998-4" title="Special:BookSources/978-0-471-88998-4"><bdi>978-0-471-88998-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Principles+of+Nonlinear+Optics&rft.place=New+York&rft.pub=Wiley-Interscience&rft.date=1984&rft.isbn=978-0-471-88998-4&rft.aulast=Shen&rft.aufirst=Y.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-95"><span class="mw-cite-backlink"><b><a href="#cite_ref-95">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://dictionary.reference.com/browse/laser">"laser"</a>. Reference.com. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080331135923/http://dictionary.reference.com/browse/laser">Archived</a> from the original on 2008-03-31<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-05-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=laser&rft.pub=Reference.com&rft_id=http%3A%2F%2Fdictionary.reference.com%2Fbrowse%2Flaser&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-96"><span class="mw-cite-backlink"><b><a href="#cite_ref-96">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://nobelprize.org/physics/laureates/1964/townes-lecture.pdf">Charles H. Townes – Nobel Lecture</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081011162942/http://nobelprize.org/physics/laureates/1964/townes-lecture.pdf">Archived</a> 2008-10-11 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. nobelprize.org</span> </li> <li id="cite_note-97"><span class="mw-cite-backlink"><b><a href="#cite_ref-97">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://www.eso.org/public/images/potw1425a/">"The VLT's Artificial Star"</a>. <i>ESO Picture of the Week</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140703151816/http://www.eso.org/public/images/potw1425a/">Archived</a> from the original on 3 July 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">25 June</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ESO+Picture+of+the+Week&rft.atitle=The+VLT%27s+Artificial+Star&rft_id=http%3A%2F%2Fwww.eso.org%2Fpublic%2Fimages%2Fpotw1425a%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-98"><span class="mw-cite-backlink"><b><a href="#cite_ref-98">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFC.H._Townes" class="citation web cs1">C.H. Townes. <a rel="nofollow" class="external text" href="http://www.press.uchicago.edu/Misc/Chicago/284158_townes.html">"The first laser"</a>. University of Chicago. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080517082709/http://www.press.uchicago.edu/Misc/Chicago/284158_townes.html">Archived</a> from the original on 2008-05-17<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-05-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+first+laser&rft.pub=University+of+Chicago&rft.au=C.H.+Townes&rft_id=http%3A%2F%2Fwww.press.uchicago.edu%2FMisc%2FChicago%2F284158_townes.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-99"><span class="mw-cite-backlink"><b><a href="#cite_ref-99">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFC.H._Townes2003" class="citation book cs1"><a href="/wiki/Charles_Hard_Townes" class="mw-redirect" title="Charles Hard Townes">C.H. Townes</a> (2003). <a rel="nofollow" class="external text" href="http://www.press.uchicago.edu/Misc/Chicago/284158_townes.html">"The first laser"</a>. In <a href="/wiki/Laura_Garwin" title="Laura Garwin">Laura Garwin</a>; Tim Lincoln (eds.). <a rel="nofollow" class="external text" href="https://archive.org/details/centuryofnaturet00garw/page/107"><i>A Century of Nature: Twenty-One Discoveries that Changed Science and the World</i></a>. University of Chicago Press. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/centuryofnaturet00garw/page/107">107–112</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-28413-2" title="Special:BookSources/978-0-226-28413-2"><bdi>978-0-226-28413-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+first+laser&rft.btitle=A+Century+of+Nature%3A+Twenty-One+Discoveries+that+Changed+Science+and+the+World&rft.pages=107-112&rft.pub=University+of+Chicago+Press&rft.date=2003&rft.isbn=978-0-226-28413-2&rft.au=C.H.+Townes&rft_id=http%3A%2F%2Fwww.press.uchicago.edu%2FMisc%2FChicago%2F284158_townes.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-100"><span class="mw-cite-backlink"><b><a href="#cite_ref-100">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.denso-wave.com/en/adcd/fundamental/barcode/index.html">What is a bar code?</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120423030551/http://www.denso-wave.com/en/adcd/fundamental/barcode/index.html">Archived</a> 2012-04-23 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> denso-wave.com</span> </li> <li id="cite_note-BBC6950933-101"><span class="mw-cite-backlink"><b><a href="#cite_ref-BBC6950933_101-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://news.bbc.co.uk/2/hi/technology/6950933.stm">"How the CD was developed"</a>. <i>BBC News</i>. 2007-08-17. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120107064451/http://news.bbc.co.uk/2/hi/technology/6950933.stm">Archived</a> from the original on 2012-01-07<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-08-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=BBC+News&rft.atitle=How+the+CD+was+developed&rft.date=2007-08-17&rft_id=http%3A%2F%2Fnews.bbc.co.uk%2F2%2Fhi%2Ftechnology%2F6950933.stm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-102"><span class="mw-cite-backlink"><b><a href="#cite_ref-102">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJ._WilsonJ.F.B._Hawkes1987" class="citation book cs1">J. Wilson & J.F.B. Hawkes (1987). <i>Lasers: Principles and Applications, Prentice Hall International Series in Optoelectronics</i>. Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-523697-0" title="Special:BookSources/978-0-13-523697-0"><bdi>978-0-13-523697-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lasers%3A+Principles+and+Applications%2C+Prentice+Hall+International+Series+in+Optoelectronics&rft.pub=Prentice+Hall&rft.date=1987&rft.isbn=978-0-13-523697-0&rft.au=J.+Wilson&rft.au=J.F.B.+Hawkes&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-eyeoptics-103"><span class="mw-cite-backlink">^ <a href="#cite_ref-eyeoptics_103-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-eyeoptics_103-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-eyeoptics_103-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFD._AtchisonG._Smith2000" class="citation book cs1">D. Atchison & G. Smith (2000). <i>Optics of the Human Eye</i>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-3775-6" title="Special:BookSources/978-0-7506-3775-6"><bdi>978-0-7506-3775-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optics+of+the+Human+Eye&rft.pub=Elsevier&rft.date=2000&rft.isbn=978-0-7506-3775-6&rft.au=D.+Atchison&rft.au=G.+Smith&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-Kandel-104"><span class="mw-cite-backlink">^ <a href="#cite_ref-Kandel_104-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Kandel_104-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFE.R._KandelJ.H._SchwartzT.M._Jessell2000" class="citation book cs1">E.R. Kandel; J.H. Schwartz; T.M. Jessell (2000). <a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780838577011/page/507"><i>Principles of Neural Science</i></a> (4th ed.). New York: McGraw-Hill. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780838577011/page/507">507–513</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8385-7701-1" title="Special:BookSources/978-0-8385-7701-1"><bdi>978-0-8385-7701-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Neural+Science&rft.place=New+York&rft.pages=507-513&rft.edition=4th&rft.pub=McGraw-Hill&rft.date=2000&rft.isbn=978-0-8385-7701-1&rft.au=E.R.+Kandel&rft.au=J.H.+Schwartz&rft.au=T.M.+Jessell&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_9780838577011%2Fpage%2F507&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-lensdesign-105"><span class="mw-cite-backlink">^ <a href="#cite_ref-lensdesign_105-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-lensdesign_105-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFD._Meister" class="citation web cs1">D. Meister. <a rel="nofollow" class="external text" href="http://www.opticampus.com/cecourse.php?url=lens_design/&OPTICAMP=f1e4252df70c63961503c46d0c8d8b60">"Ophthalmic Lens Design"</a>. OptiCampus.com. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081227021113/http://www.opticampus.com/cecourse.php?url=lens_design%2F&OPTICAMP=f1e4252df70c63961503c46d0c8d8b60">Archived</a> from the original on December 27, 2008<span class="reference-accessdate">. Retrieved <span class="nowrap">November 12,</span> 2008</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Ophthalmic+Lens+Design&rft.pub=OptiCampus.com&rft.au=D.+Meister&rft_id=http%3A%2F%2Fwww.opticampus.com%2Fcecourse.php%3Furl%3Dlens_design%2F%26OPTICAMP%3Df1e4252df70c63961503c46d0c8d8b60&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-106"><span class="mw-cite-backlink"><b><a href="#cite_ref-106">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJ._Bryner2008" class="citation web cs1">J. Bryner (2008-06-02). <a rel="nofollow" class="external text" href="http://www.livescience.com/strangenews/080602-foresee-future.html">"Key to All Optical Illusions Discovered"</a>. LiveScience. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080905122802/http://www.livescience.com/strangenews/080602-foresee-future.html">Archived</a> from the original on 2008-09-05.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Key+to+All+Optical+Illusions+Discovered&rft.pub=LiveScience&rft.date=2008-06-02&rft.au=J.+Bryner&rft_id=http%3A%2F%2Fwww.livescience.com%2Fstrangenews%2F080602-foresee-future.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-107"><span class="mw-cite-backlink"><b><a href="#cite_ref-107">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=477&bodyId=598">Geometry of the Vanishing Point</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080622055904/http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=477&bodyId=598">Archived</a> 2008-06-22 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> at <a rel="nofollow" class="external text" href="http://mathdl.maa.org/convergence/1/">Convergence</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070713083148/http://mathdl.maa.org/convergence/1/">Archived</a> 2007-07-13 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-108"><span class="mw-cite-backlink"><b><a href="#cite_ref-108">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://facstaff.uww.edu/mccreadd/">"The Moon Illusion Explained"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151204212728/http://facstaff.uww.edu/mccreadd/">Archived</a> 2015-12-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Don McCready, University of Wisconsin-Whitewater</span> </li> <li id="cite_note-109"><span class="mw-cite-backlink"><b><a href="#cite_ref-109">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFA.K._JainM._FigueiredoJ._Zerubia2001" class="citation book cs1">A.K. Jain; M. Figueiredo; J. Zerubia (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=yb8otde21fcC&pg=RA1-PA198"><i>Energy Minimization Methods in Computer Vision and Pattern Recognition</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-42523-6" title="Special:BookSources/978-3-540-42523-6"><bdi>978-3-540-42523-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Energy+Minimization+Methods+in+Computer+Vision+and+Pattern+Recognition&rft.pub=Springer&rft.date=2001&rft.isbn=978-3-540-42523-6&rft.au=A.K.+Jain&rft.au=M.+Figueiredo&rft.au=J.+Zerubia&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dyb8otde21fcC%26pg%3DRA1-PA198&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201171–1175-110"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201171–1175_110-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1171–1175.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201171–1173-111"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201171–1173_111-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1171–1173.</span> </li> <li id="cite_note-112"><span class="mw-cite-backlink"><b><a href="#cite_ref-112">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFP.E._NothnagleW._ChambersM.W._Davidson" class="citation web cs1">P.E. Nothnagle; W. Chambers; M.W. Davidson. <a rel="nofollow" class="external text" href="http://www.microscopyu.com/articles/stereomicroscopy/stereointro.html">"Introduction to Stereomicroscopy"</a>. Nikon MicroscopyU. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110916115256/http://www.microscopyu.com/articles/stereomicroscopy/stereointro.html">Archived</a> from the original on 2011-09-16.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Introduction+to+Stereomicroscopy&rft.pub=Nikon+MicroscopyU&rft.au=P.E.+Nothnagle&rft.au=W.+Chambers&rft.au=M.W.+Davidson&rft_id=http%3A%2F%2Fwww.microscopyu.com%2Farticles%2Fstereomicroscopy%2Fstereointro.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201174-113"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201174_113-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, p. 1174.</span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201175-114"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201175_114-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1175.</span> </li> <li id="cite_note-115"><span class="mw-cite-backlink"><b><a href="#cite_ref-115">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSamuel_Edward_SheppardCharles_Edward_Kenneth_Mees1907" class="citation book cs1">Samuel Edward Sheppard & Charles Edward Kenneth Mees (1907). <a rel="nofollow" class="external text" href="https://archive.org/details/investigationso01meesgoog"><i>Investigations on the Theory of the Photographic Process</i></a>. Longmans, Green and Co. p. <a rel="nofollow" class="external text" href="https://archive.org/details/investigationso01meesgoog/page/n232">214</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Investigations+on+the+Theory+of+the+Photographic+Process&rft.pages=214&rft.pub=Longmans%2C+Green+and+Co&rft.date=1907&rft.au=Samuel+Edward+Sheppard&rft.au=Charles+Edward+Kenneth+Mees&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Finvestigationso01meesgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-116"><span class="mw-cite-backlink"><b><a href="#cite_ref-116">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFB.J._Suess2003" class="citation book cs1">B.J. Suess (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7LaRPNINH_YC&pg=PT112"><i>Mastering Black-and-White Photography</i></a>. Allworth Communications. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-58115-306-4" title="Special:BookSources/978-1-58115-306-4"><bdi>978-1-58115-306-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mastering+Black-and-White+Photography&rft.pub=Allworth+Communications&rft.date=2003&rft.isbn=978-1-58115-306-4&rft.au=B.J.+Suess&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7LaRPNINH_YC%26pg%3DPT112&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-117"><span class="mw-cite-backlink"><b><a href="#cite_ref-117">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFM.J._Langford2000" class="citation book cs1">M.J. Langford (2000). <a rel="nofollow" class="external text" href="https://archive.org/details/basicphotography00lang"><i>Basic Photography</i></a>. Focal Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-240-51592-2" title="Special:BookSources/978-0-240-51592-2"><bdi>978-0-240-51592-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Basic+Photography&rft.pub=Focal+Press&rft.date=2000&rft.isbn=978-0-240-51592-2&rft.au=M.J.+Langford&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbasicphotography00lang&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-Bruce_Warren,_Photography,_page_71-118"><span class="mw-cite-backlink">^ <a href="#cite_ref-Bruce_Warren,_Photography,_page_71_118-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Bruce_Warren,_Photography,_page_71_118-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWarren2001" class="citation book cs1">Warren, Bruce (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=sbdGeFem1zwC&pg=PA71"><i>Photography</i></a>. Cengage Learning. p. 71. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7668-1777-7" title="Special:BookSources/978-0-7668-1777-7"><bdi>978-0-7668-1777-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160819020407/https://books.google.com/books?id=sbdGeFem1zwC&pg=PA71">Archived</a> from the original on 2016-08-19.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Photography&rft.pages=71&rft.pub=Cengage+Learning&rft.date=2001&rft.isbn=978-0-7668-1777-7&rft.aulast=Warren&rft.aufirst=Bruce&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DsbdGeFem1zwC%26pg%3DPA71&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-119"><span class="mw-cite-backlink"><b><a href="#cite_ref-119">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFLeslie_D._Stroebel1999" class="citation book cs1">Leslie D. Stroebel (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=71zxDuunAvMC&pg=PA136"><i>View Camera Technique</i></a>. Focal Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-240-80345-6" title="Special:BookSources/978-0-240-80345-6"><bdi>978-0-240-80345-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=View+Camera+Technique&rft.pub=Focal+Press&rft.date=1999&rft.isbn=978-0-240-80345-6&rft.au=Leslie+D.+Stroebel&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D71zxDuunAvMC%26pg%3DPA136&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-120"><span class="mw-cite-backlink"><b><a href="#cite_ref-120">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFS._Simmons1992" class="citation book cs1">S. Simmons (1992). <i>Using the View Camera</i>. Amphoto Books. p. 35. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8174-6353-3" title="Special:BookSources/978-0-8174-6353-3"><bdi>978-0-8174-6353-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Using+the+View+Camera&rft.pages=35&rft.pub=Amphoto+Books&rft.date=1992&rft.isbn=978-0-8174-6353-3&rft.au=S.+Simmons&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-121"><span class="mw-cite-backlink"><b><a href="#cite_ref-121">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSidney_F._Ray2002" class="citation book cs1">Sidney F. Ray (2002). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cuzYl4hx-B8C&pg=PA294"><i>Applied Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging</i></a>. Focal Press. p. 294. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-240-51540-3" title="Special:BookSources/978-0-240-51540-3"><bdi>978-0-240-51540-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160819003154/https://books.google.com/books?id=cuzYl4hx-B8C&pg=PA294">Archived</a> from the original on 2016-08-19.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Applied+Photographic+Optics%3A+Lenses+and+Optical+Systems+for+Photography%2C+Film%2C+Video%2C+Electronic+and+Digital+Imaging&rft.pages=294&rft.pub=Focal+Press&rft.date=2002&rft.isbn=978-0-240-51540-3&rft.au=Sidney+F.+Ray&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DcuzYl4hx-B8C%26pg%3DPA294&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-122"><span class="mw-cite-backlink"><b><a href="#cite_ref-122">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNew_York_Times_Staff2004" class="citation book cs1">New York Times Staff (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=zqkdNwRxSooC&pg=PA109"><i>The New York Times Guide to Essential Knowledge</i></a>. Macmillan. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-312-31367-8" title="Special:BookSources/978-0-312-31367-8"><bdi>978-0-312-31367-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+New+York+Times+Guide+to+Essential+Knowledge&rft.pub=Macmillan&rft.date=2004&rft.isbn=978-0-312-31367-8&rft.au=New+York+Times+Staff&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DzqkdNwRxSooC%26pg%3DPA109&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-123"><span class="mw-cite-backlink"><b><a href="#cite_ref-123">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFR.R._CarltonA._McKenna_Adler2000" class="citation book cs1">R.R. Carlton; A. McKenna Adler (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=oA-eBHsapX8C&pg=PA318"><i>Principles of Radiographic Imaging: An Art and a Science</i></a>. Thomson Delmar Learning. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7668-1300-7" title="Special:BookSources/978-0-7668-1300-7"><bdi>978-0-7668-1300-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Radiographic+Imaging%3A+An+Art+and+a+Science&rft.pub=Thomson+Delmar+Learning&rft.date=2000&rft.isbn=978-0-7668-1300-7&rft.au=R.R.+Carlton&rft.au=A.+McKenna+Adler&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DoA-eBHsapX8C%26pg%3DPA318&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-124"><span class="mw-cite-backlink"><b><a href="#cite_ref-124">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFW._Crawford1979" class="citation book cs1">W. Crawford (1979). <i>The Keepers of Light: A History and Working Guide to Early Photographic Processes</i>. Dobbs Ferry, NY: Morgan & Morgan. p. 20. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-87100-158-0" title="Special:BookSources/978-0-87100-158-0"><bdi>978-0-87100-158-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Keepers+of+Light%3A+A+History+and+Working+Guide+to+Early+Photographic+Processes&rft.place=Dobbs+Ferry%2C+NY&rft.pages=20&rft.pub=Morgan+%26+Morgan&rft.date=1979&rft.isbn=978-0-87100-158-0&rft.au=W.+Crawford&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-125"><span class="mw-cite-backlink"><b><a href="#cite_ref-125">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJ.M._Cowley1975" class="citation book cs1">J.M. Cowley (1975). <i>Diffraction physics</i>. Amsterdam: North-Holland. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-10791-6" title="Special:BookSources/978-0-444-10791-6"><bdi>978-0-444-10791-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Diffraction+physics&rft.place=Amsterdam&rft.pub=North-Holland&rft.date=1975&rft.isbn=978-0-444-10791-6&rft.au=J.M.+Cowley&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-autogenerated1-126"><span class="mw-cite-backlink"><b><a href="#cite_ref-autogenerated1_126-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFC.D._Ahrens1994" class="citation book cs1">C.D. Ahrens (1994). <a rel="nofollow" class="external text" href="https://archive.org/details/meteorologytoday00ahre/page/88"><i>Meteorology Today: an introduction to weather, climate, and the environment</i></a> (5th ed.). West Publishing Company. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/meteorologytoday00ahre/page/88">88–89</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-314-02779-5" title="Special:BookSources/978-0-314-02779-5"><bdi>978-0-314-02779-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Meteorology+Today%3A+an+introduction+to+weather%2C+climate%2C+and+the+environment&rft.pages=88-89&rft.edition=5th&rft.pub=West+Publishing+Company&rft.date=1994&rft.isbn=978-0-314-02779-5&rft.au=C.D.+Ahrens&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmeteorologytoday00ahre%2Fpage%2F88&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-127"><span class="mw-cite-backlink"><b><a href="#cite_ref-127">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFA._Young" class="citation web cs1">A. Young. <a rel="nofollow" class="external text" href="http://mintaka.sdsu.edu/GF/mirages/mirintro.html">"An Introduction to Mirages"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100110045709/http://mintaka.sdsu.edu/GF/mirages/mirintro.html">Archived</a> from the original on 2010-01-10.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=An+Introduction+to+Mirages&rft.au=A.+Young&rft_id=http%3A%2F%2Fmintaka.sdsu.edu%2FGF%2Fmirages%2Fmirintro.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEYoungFreedman20201117–1118-128"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEYoungFreedman20201117–1118_128-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFYoungFreedman2020">Young & Freedman (2020)</a>, pp. 1117–1118.</span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Works_cited">Works cited</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=27" title="Edit section: Works cited"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-hanging-indents refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHecht2017" class="citation book cs1">Hecht, Eugene (2017). <i>Optics</i> (5th ed.). Pearson Education. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-133-97722-6" title="Special:BookSources/978-0-133-97722-6"><bdi>978-0-133-97722-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optics&rft.edition=5th&rft.pub=Pearson+Education&rft.date=2017&rft.isbn=978-0-133-97722-6&rft.aulast=Hecht&rft.aufirst=Eugene&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFYoungFreedman2020" class="citation book cs1">Young, Hugh D.; Freedman, Roger A. (2020). <i>University Physics: Extended Version With Modern Physics</i> (15th ed.). Pearson Education. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-292-31473-0" title="Special:BookSources/978-1-292-31473-0"><bdi>978-1-292-31473-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=University+Physics%3A+Extended+Version+With+Modern+Physics&rft.edition=15th&rft.pub=Pearson+Education&rft.date=2020&rft.isbn=978-1-292-31473-0&rft.aulast=Young&rft.aufirst=Hugh+D.&rft.au=Freedman%2C+Roger+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Further_reading">Further reading</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=28" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBornWolf2002" class="citation book cs1">Born, Max; Wolf, Emil (2002). <i><a href="/wiki/Principles_of_Optics" title="Principles of Optics">Principles of Optics</a></i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-139-64340-5" title="Special:BookSources/978-1-139-64340-5"><bdi>978-1-139-64340-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Optics&rft.pub=Cambridge+University+Press&rft.date=2002&rft.isbn=978-1-139-64340-5&rft.aulast=Born&rft.aufirst=Max&rft.au=Wolf%2C+Emil&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFowles1975" class="citation book cs1">Fowles, Grant R. (1975). <i>Introduction to Modern Optics</i> (4th ed.). Addison-Wesley Longman.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Modern+Optics&rft.edition=4th&rft.pub=Addison-Wesley+Longman&rft.date=1975&rft.aulast=Fowles&rft.aufirst=Grant+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFLipsonLipsonTannhauser1995" class="citation book cs1">Lipson, Stephen G.; Lipson, Henry; Tannhauser, David Stefan (1995). <i>Optical Physics</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-43631-1" title="Special:BookSources/978-0-521-43631-1"><bdi>978-0-521-43631-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optical+Physics&rft.pub=Cambridge+University+Press&rft.date=1995&rft.isbn=978-0-521-43631-1&rft.aulast=Lipson&rft.aufirst=Stephen+G.&rft.au=Lipson%2C+Henry&rft.au=Tannhauser%2C+David+Stefan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSerwayJewett2004" class="citation book cs1">Serway, Raymond A.; Jewett, John W. (2004). <a rel="nofollow" class="external text" href="https://archive.org/details/physicssciengv2p00serw"><i>Physics for Scientists and Engineers</i></a> (6th, Illustrated ed.). Belmont, California: Thomson-Brooks/Cole. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-534-40842-8" title="Special:BookSources/978-0-534-40842-8"><bdi>978-0-534-40842-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Scientists+and+Engineers&rft.place=Belmont%2C+California&rft.edition=6th%2C+Illustrated&rft.pub=Thomson-Brooks%2FCole&rft.date=2004&rft.isbn=978-0-534-40842-8&rft.aulast=Serway&rft.aufirst=Raymond+A.&rft.au=Jewett%2C+John+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fphysicssciengv2p00serw&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFTiplerMosca2004" class="citation book cs1">Tipler, Paul A.; Mosca, Gene (2004). <i>Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics</i>. Vol. 2. W. H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-0810-0" title="Special:BookSources/978-0-7167-0810-0"><bdi>978-0-7167-0810-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Scientists+and+Engineers%3A+Electricity%2C+Magnetism%2C+Light%2C+and+Elementary+Modern+Physics&rft.pub=W.+H.+Freeman&rft.date=2004&rft.isbn=978-0-7167-0810-0&rft.aulast=Tipler&rft.aufirst=Paul+A.&rft.au=Mosca%2C+Gene&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOptics" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Optics&action=edit&section=29" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media 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plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Optics" class="extiw" title="commons:Category:Optics">Optics</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735" /><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikiversity_logo_2017.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/40px-Wikiversity_logo_2017.svg.png" decoding="async" width="40" height="33" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/60px-Wikiversity_logo_2017.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/80px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" /></a></span></div> <div class="side-box-text plainlist">Wikiversity has learning resources about <i><b><a href="https://en.wikiversity.org/wiki/Special:Search/Optics" class="extiw" title="v:Special:Search/Optics">Optics</a></b></i></div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735" /><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikibooks-logo-en-noslogan.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/120px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></a></span></div> <div class="side-box-text plainlist">Wikibooks has a book on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/Optics" class="extiw" title="wikibooks:Optics">Optics</a></b></i></div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735" /><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikibooks-logo-en-noslogan.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/120px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></a></span></div> <div class="side-box-text plainlist">Wikibooks has a book on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/Physics_Study_Guide/Optics" class="extiw" title="wikibooks:Physics Study Guide/Optics">Physics Study Guide/Optics</a></b></i></div></div> </div> <dl><dt>Relevant discussions</dt></dl> <ul><li><a rel="nofollow" class="external text" href="https://www.bbc.co.uk/programmes/b00774t5">Optics</a> on <a href="/wiki/In_Our_Time_(radio_series)" title="In Our Time (radio series)"><i>In Our Time</i></a> at the <a href="/wiki/BBC" title="BBC">BBC</a></li></ul> <dl><dt>Textbooks and tutorials</dt></dl> <ul><li><a rel="nofollow" class="external text" href="http://lightandmatter.com/lm/">Light and Matter</a> – an open-source textbook, containing a treatment of optics in ch. 28–32</li> <li><a rel="nofollow" class="external text" href="http://www.optics2001.com">Optics2001</a> – Optics library and community</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20141110224226/http://marketplace.idexop.com/store/SupportDocuments/Fundamental_Optics_OverviewWEB.pdf">Fundamental Optics</a> – Melles Griot Technical Guide</li> <li><a rel="nofollow" class="external text" href="http://optics.byu.edu/textbook.aspx">Physics of Light and Optics</a> – <a href="/wiki/Brigham_Young_University" title="Brigham Young University">Brigham Young University</a> Undergraduate Book</li> <li><a rel="nofollow" class="external text" href="https://www.pvlighthouse.com.au/cms/lectures/altermatt/optics">Optics for PV</a> – a step-by-step introduction to classical optics</li></ul> <dl><dt>Further reading</dt></dl> <ul><li><a rel="nofollow" class="external text" href="http://www.iop.org/publications/iop/2009/page_38205.html">Optics and photonics: Physics enhancing our lives</a> by <a rel="nofollow" class="external text" href="http://www.iop.org/publications/iop/index.html">Institute of Physics publications</a></li></ul> <dl><dt>Societies</dt></dl> <style data-mw-deduplicate="TemplateStyles:r1216972533">.mw-parser-output .col-begin{border-collapse:collapse;padding:0;color:inherit;width:100%;border:0;margin:0}.mw-parser-output .col-begin-small{font-size:90%}.mw-parser-output .col-break{vertical-align:top;text-align:left}.mw-parser-output .col-break-2{width:50%}.mw-parser-output .col-break-3{width:33.3%}.mw-parser-output .col-break-4{width:25%}.mw-parser-output .col-break-5{width:20%}@media(max-width:720px){.mw-parser-output .col-begin,.mw-parser-output .col-begin>tbody,.mw-parser-output .col-begin>tbody>tr,.mw-parser-output .col-begin>tbody>tr>td{display:block!important;width:100%!important}.mw-parser-output .col-break{padding-left:0!important}}</style><div> <table class="col-begin" role="presentation"> <tbody><tr> <td class="col-break" style="width: 50%;"> <ul><li><a href="/wiki/European_Optical_Society" title="European Optical Society">European Optical Society</a> – <a rel="nofollow" class="external text" href="http://www.myeos.org">link</a></li> <li><a href="/wiki/The_Optical_Society" class="mw-redirect" title="The Optical Society">The Optical Society</a> (OSA) – <a rel="nofollow" class="external text" href="http://www.osa.org">link</a></li> <li><a href="/wiki/SPIE" title="SPIE">SPIE</a> – <a rel="nofollow" class="external text" href="http://www.spie.org">link</a></li></ul> </td> <td class="col-break" style="width: 50%;"> <ul><li><a href="/wiki/European_Photonics_Industry_Consortium" title="European Photonics Industry Consortium">European Photonics Industry Consortium</a> – <a rel="nofollow" class="external text" href="http://www.epic-assoc.com">link</a></li></ul> <p>  </p> </td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid 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.navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Major_branches_of_physics48" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Branches_of_physics" title="Template:Branches of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Branches_of_physics" title="Template talk:Branches of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Branches_of_physics" title="Special:EditPage/Template:Branches of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_branches_of_physics48" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Branches_of_physics" title="Branches of physics">branches of physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Basic_research" title="Basic research">Pure</a></li> <li><a href="/wiki/Applied_physics" title="Applied physics">Applied</a> <ul><li><a href="/wiki/Engineering_physics" title="Engineering physics">Engineering</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Experimental_physics" title="Experimental physics">Experimental</a></li> <li><a href="/wiki/Theoretical_physics" title="Theoretical physics">Theoretical</a> <ul><li><a href="/wiki/Computational_physics" title="Computational physics">Computational</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a> <ul><li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newtonian</a></li> <li><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li></ul></li> <li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></li> <li><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Classical electromagnetism</a></li> <li><a href="/wiki/Classical_optics" class="mw-redirect" title="Classical optics">Classical optics</a> <ul><li><a href="/wiki/Geometrical_optics" title="Geometrical optics">Ray</a></li> <li><a href="/wiki/Physical_optics" title="Physical optics">Wave</a></li></ul></li> <li><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Relativistic_mechanics" title="Relativistic mechanics">Relativistic mechanics</a> <ul><li><a href="/wiki/Special_relativity" title="Special relativity">Special</a></li> <li><a href="/wiki/General_relativity" title="General relativity">General</a></li></ul></li> <li><a href="/wiki/Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li> <li><a href="/wiki/Particle_physics" title="Particle physics">Particle physics</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li> <li><a href="/wiki/Atomic,_molecular,_and_optical_physics" title="Atomic, molecular, and optical physics">Atomic, molecular, and optical physics</a> <ul><li><a href="/wiki/Atomic_physics" title="Atomic physics">Atomic</a></li> <li><a href="/wiki/Molecular_physics" title="Molecular physics">Molecular</a></li> <li><a class="mw-selflink-fragment" href="#Modern_optics">Modern optics</a></li></ul></li> <li><a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">Condensed matter physics</a> <ul><li><a href="/wiki/Solid-state_physics" title="Solid-state physics">Solid-state physics</a></li> <li><a href="/wiki/Crystallography" title="Crystallography">Crystallography</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Applied_and_interdisciplinary_physics" title="Category:Applied and interdisciplinary physics">Interdisciplinary</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astrophysics" title="Astrophysics">Astrophysics</a></li> <li><a href="/wiki/Atmospheric_physics" title="Atmospheric physics">Atmospheric physics</a></li> <li><a href="/wiki/Biophysics" title="Biophysics">Biophysics</a></li> <li><a href="/wiki/Chemical_physics" title="Chemical physics">Chemical physics</a></li> <li><a href="/wiki/Geophysics" title="Geophysics">Geophysics</a></li> <li><a href="/wiki/Materials_science" title="Materials science">Materials science</a></li> <li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical physics</a></li> <li><a href="/wiki/Medical_physics" title="Medical physics">Medical physics</a></li> <li><a href="/wiki/Physical_oceanography" title="Physical oceanography">Ocean physics</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_physics" title="History of physics">History of physics</a></li> <li><a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a></li> <li><a href="/wiki/Philosophy_of_physics" title="Philosophy of physics">Philosophy of physics</a></li> <li><a href="/wiki/Physics_education" title="Physics education">Physics education</a> <ul><li><a href="/wiki/Physics_education_research" title="Physics education research">research</a></li></ul></li> <li><a href="/wiki/Timeline_of_fundamental_physics_discoveries" title="Timeline of fundamental physics discoveries">Timeline of physics discoveries</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Glass_science_topics124" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Glass_science" title="Template:Glass science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Glass_science" title="Template talk:Glass science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Glass_science" title="Special:EditPage/Template:Glass science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Glass_science_topics124" style="font-size:114%;margin:0 4em"><a href="/wiki/Glass" title="Glass">Glass</a> science topics</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glass" title="Glass">Glass</a></li> <li><a href="/wiki/Glass_transition" title="Glass transition">Glass transition</a></li> <li><a href="/wiki/Supercooling" title="Supercooling">Supercooling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formulation</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AgInSbTe" title="AgInSbTe">AgInSbTe</a></li> <li><a href="/wiki/Bioglass" class="mw-redirect" title="Bioglass">Bioglass</a></li> <li><a href="/wiki/Borophosphosilicate_glass" title="Borophosphosilicate glass">Borophosphosilicate glass</a></li> <li><a href="/wiki/Borosilicate_glass" title="Borosilicate glass">Borosilicate glass</a></li> <li><a href="/wiki/Ceramic_glaze" title="Ceramic glaze">Ceramic glaze</a></li> <li><a href="/wiki/Chalcogenide_glass" title="Chalcogenide glass">Chalcogenide glass</a></li> <li><a href="/wiki/Cobalt_glass" title="Cobalt glass">Cobalt glass</a></li> <li><a href="/wiki/Cranberry_glass" title="Cranberry glass">Cranberry glass</a></li> <li><a href="/wiki/Crown_glass_(optics)" title="Crown glass (optics)">Crown glass</a></li> <li><a href="/wiki/Flint_glass" title="Flint glass">Flint glass</a></li> <li><a href="/wiki/Fluorosilicate_glass" title="Fluorosilicate glass">Fluorosilicate glass</a></li> <li><a href="/wiki/Fused_quartz" title="Fused quartz">Fused quartz</a></li> <li><a href="/wiki/GeSbTe" title="GeSbTe">GeSbTe</a></li> <li><a href="/wiki/Cranberry_glass" title="Cranberry glass">Gold ruby glass</a></li> <li><a href="/wiki/Lead_glass" title="Lead glass">Lead glass</a></li> <li><a href="/wiki/Milk_glass" title="Milk glass">Milk glass</a></li> <li><a href="/wiki/Phosphosilicate_glass" title="Phosphosilicate glass">Phosphosilicate glass</a></li> <li><a href="/wiki/Photochromic_lens" title="Photochromic lens">Photochromic lens glass</a></li> <li><a href="/wiki/Glass#Silicate_glass" title="Glass">Silicate glass</a></li> <li><a href="/wiki/Soda%E2%80%93lime_glass" title="Soda–lime glass">Soda–lime glass</a></li> <li><a href="/wiki/Sodium_hexametaphosphate" title="Sodium hexametaphosphate">Sodium hexametaphosphate</a></li> <li><a href="/wiki/Sodium_silicate" title="Sodium silicate">Soluble glass</a></li> <li><a href="/wiki/Tellurite_glass" title="Tellurite glass">Tellurite glass</a></li> <li><a href="/wiki/Thoriated_glass" title="Thoriated glass">Thoriated glass</a></li> <li><a href="/wiki/Ultra_low_expansion_glass" title="Ultra low expansion glass">Ultra low expansion glass</a></li> <li><a href="/wiki/Uranium_glass" title="Uranium glass">Uranium glass</a></li> <li><a href="/wiki/Vitreous_enamel" title="Vitreous enamel">Vitreous enamel</a></li> <li><a href="/wiki/Wood%27s_glass" title="Wood's glass">Wood's glass</a></li> <li><a href="/wiki/ZBLAN" title="ZBLAN">ZBLAN</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Glass-ceramic" title="Glass-ceramic">Glass-ceramics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bioactive_glass" title="Bioactive glass">Bioactive glass</a></li> <li><a href="/wiki/CorningWare" title="CorningWare">CorningWare</a></li> <li><a href="/wiki/Glass-ceramic-to-metal_seals" title="Glass-ceramic-to-metal seals">Glass-ceramic-to-metal seals</a></li> <li><a href="/wiki/Macor" title="Macor">Macor</a></li> <li><a href="/wiki/Zerodur" title="Zerodur">Zerodur</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Preparation</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Annealing_(glass)" title="Annealing (glass)">Annealing</a></li> <li><a href="/wiki/Chemical_vapor_deposition" title="Chemical vapor deposition">Chemical vapor deposition</a></li> <li><a href="/wiki/Glass_batch_calculation" title="Glass batch calculation">Glass batch calculation</a></li> <li><a href="/wiki/Glass_production" title="Glass production">Glass forming</a></li> <li><a href="/wiki/Glass_production#Hot_end" title="Glass production">Glass melting</a></li> <li><a href="/wiki/Calculation_of_glass_properties" title="Calculation of glass properties">Glass modeling</a></li> <li><a href="/wiki/Ion_implantation" title="Ion implantation">Ion implantation</a></li> <li><a href="/wiki/Liquidus" class="mw-redirect" title="Liquidus">Liquidus temperature</a></li> <li><a href="/wiki/Sol%E2%80%93gel_process" title="Sol–gel process">sol–gel technique</a></li> <li><a href="/wiki/Viscosity#Viscosity_of_amorphous_materials" title="Viscosity">Viscosity</a></li> <li><a href="/wiki/Vitrification" title="Vitrification">Vitrification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Optics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Achromatic_lens" title="Achromatic lens">Achromat</a></li> <li><a href="/wiki/Dispersion_(optics)" title="Dispersion (optics)">Dispersion</a></li> <li><a href="/wiki/Gradient-index_optics" title="Gradient-index optics">Gradient-index optics</a></li> <li><a href="/wiki/Hydrogen_darkening" title="Hydrogen darkening">Hydrogen darkening</a></li> <li><a href="/wiki/Optical_amplifier" title="Optical amplifier">Optical amplifier</a></li> <li><a href="/wiki/Optical_fiber" title="Optical fiber">Optical fiber</a></li> <li><a href="/wiki/Optical_lens_design" title="Optical lens design">Optical lens design</a></li> <li><a href="/wiki/Photochromic_lens" title="Photochromic lens">Photochromic lens</a></li> <li><a href="/wiki/Photosensitive_glass" title="Photosensitive glass">Photosensitive glass</a></li> <li><a href="/wiki/Refraction" title="Refraction">Refraction</a></li> <li><a href="/wiki/Transparency_and_translucency" title="Transparency and translucency">Transparent materials</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Surface<br />modification</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anti-reflective_coating" title="Anti-reflective coating">Anti-reflective coating</a></li> <li><a href="/wiki/Chemically_strengthened_glass" title="Chemically strengthened glass">Chemically strengthened glass</a></li> <li><a href="/wiki/Corrosion#Corrosion_of_glasses" title="Corrosion">Corrosion</a></li> <li><a href="/wiki/Dealkalization" title="Dealkalization">Dealkalization</a></li> <li><a href="/wiki/DNA_microarray" title="DNA microarray">DNA microarray</a></li> <li><a href="/wiki/Hydrogen_darkening" title="Hydrogen darkening">Hydrogen darkening</a></li> <li><a href="/wiki/Insulated_glazing" title="Insulated glazing">Insulated glazing</a></li> <li><a href="/wiki/Porous_glass" title="Porous glass">Porous glass</a></li> <li><a href="/wiki/Self-cleaning_glass" title="Self-cleaning glass">Self-cleaning glass</a></li> <li><a href="/wiki/Sol%E2%80%93gel_process" title="Sol–gel process">sol–gel technique</a></li> <li><a href="/wiki/Tempered_glass" title="Tempered glass">Tempered glass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Diverse<br />topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Conservation_and_restoration_of_glass_objects" title="Conservation and restoration of glass objects">Conservation and restoration of glass objects</a></li> <li><a href="/wiki/Glass-coated_wire" title="Glass-coated wire">Glass-coated wire</a></li> <li><a href="/wiki/Safety_glass" title="Safety glass">Safety glass</a></li> <li><a href="/wiki/Glass_databases" title="Glass databases">Glass databases</a></li> <li><a href="/wiki/Glass_electrode" title="Glass electrode">Glass electrode</a></li> <li><a href="/wiki/Glass_fiber_reinforced_concrete" title="Glass fiber reinforced concrete">Glass fiber reinforced concrete</a></li> <li><a href="/wiki/Glass_ionomer_cement" title="Glass ionomer cement">Glass ionomer cement</a></li> <li><a href="/wiki/Glass_microsphere" title="Glass microsphere">Glass microspheres</a></li> <li><a href="/wiki/Fiberglass" title="Fiberglass">Glass-reinforced plastic</a></li> <li><a href="/wiki/Glass_cloth" title="Glass cloth">Glass cloth</a></li> <li><a href="/wiki/Glass-to-metal_seal" title="Glass-to-metal seal">Glass-to-metal seal</a></li> <li><a href="/wiki/Porous_glass" title="Porous glass">Porous glass</a></li> <li><a href="/wiki/Pre-preg" title="Pre-preg">Pre-preg</a></li> <li><a href="/wiki/Prince_Rupert%27s_drop" title="Prince Rupert's drop">Prince Rupert's drops</a></li> <li><a href="/wiki/Radioactive_waste#Vitrification" title="Radioactive waste">Radioactive waste vitrification</a></li> <li><a href="/wiki/Windshield" title="Windshield">Windshield</a></li> <li><a href="/wiki/Glass_fiber" title="Glass fiber">Glass fiber</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-label="Navbox1122" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q14620#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 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text" href="https://www.nli.org.il/en/authorities/987007548411505171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://auth.wikimedia.org/loginwiki/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Optics&oldid=1278959999">https://en.wikipedia.org/w/index.php?title=Optics&oldid=1278959999</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Optics" title="Category:Optics">Optics</a></li><li><a href="/wiki/Category:Light" title="Category:Light">Light</a></li><li><a href="/wiki/Category:Electromagnetic_radiation" 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<script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-7dbbdd594f-vdrcw","wgBackendResponseTime":248,"wgPageParseReport":{"limitreport":{"cputime":"1.437","walltime":"1.797","ppvisitednodes":{"value":11247,"limit":1000000},"postexpandincludesize":{"value":250007,"limit":2097152},"templateargumentsize":{"value":8879,"limit":2097152},"expansiondepth":{"value":16,"limit":100},"expensivefunctioncount":{"value":30,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":388758,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1420.092 1 -total"," 37.22% 528.538 1 Template:Reflist"," 25.63% 363.899 67 Template:Cite_book"," 9.27% 131.681 34 Template:Sfnp"," 7.88% 111.889 3 Template:Lang"," 7.62% 108.229 1 Template:TopicTOC-Physics"," 7.34% 104.288 1 Template:Sidebar_with_collapsible_lists"," 6.67% 94.727 1 Template:Short_description"," 3.98% 56.566 4 Template:Sister_project"," 3.80% 53.985 4 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[\"CITEREFEinstein1967\"] = 1,\n [\"CITEREFEl-Bizri2010\"] = 1,\n [\"CITEREFEl-Bizri2014\"] = 1,\n [\"CITEREFElena_AgazziEnrico_GiannettoFranco_Giudice2010\"] = 1,\n [\"CITEREFEuclid1999\"] = 1,\n [\"CITEREFF.J._Duarte2015\"] = 1,\n [\"CITEREFFowles1975\"] = 1,\n [\"CITEREFG._Hatfield1996\"] = 1,\n [\"CITEREFG._Simon2006\"] = 1,\n [\"CITEREFHecht2017\"] = 1,\n [\"CITEREFHenry_C._King2003\"] = 1,\n [\"CITEREFHogendijkSabra2003\"] = 1,\n [\"CITEREFHooke1665\"] = 1,\n [\"CITEREFIan_P._HowardBrian_J._Rogers1995\"] = 1,\n [\"CITEREFIlardi2007\"] = 1,\n [\"CITEREFJ.C._Maxwell1865\"] = 1,\n [\"CITEREFJ.D._Jackson1975\"] = 1,\n [\"CITEREFJ.E._Greivenkamp2004\"] = 1,\n [\"CITEREFJ.M._Cowley1975\"] = 1,\n [\"CITEREFJ._Bryner2008\"] = 1,\n [\"CITEREFJ._Goodman2005\"] = 1,\n [\"CITEREFJ._WilsonJ.F.B._Hawkes1987\"] = 1,\n [\"CITEREFLeslie_D._Stroebel1999\"] = 1,\n [\"CITEREFLipsonLipsonTannhauser1995\"] = 1,\n [\"CITEREFLonghurst1968\"] = 1,\n [\"CITEREFM.J._Langford2000\"] = 1,\n [\"CITEREFM._BornE._Wolf1999\"] = 1,\n [\"CITEREFMarchand1978\"] = 1,\n [\"CITEREFMaxwell1865\"] = 1,\n [\"CITEREFMcAulay1991\"] = 1,\n [\"CITEREFN._Taylor2000\"] = 1,\n [\"CITEREFNader_El-Bizri2005\"] = 1,\n [\"CITEREFNader_El-Bizri2007\"] = 1,\n [\"CITEREFNew_York_Times_Staff2004\"] = 1,\n [\"CITEREFP.E._NothnagleW._ChambersM.W._Davidson\"] = 1,\n [\"CITEREFP._Hariharan2003\"] = 1,\n [\"CITEREFPaul_S._AgutterDenys_N._Wheatley2008\"] = 1,\n [\"CITEREFPtolemy1996\"] = 1,\n [\"CITEREFR.R._CarltonA._McKenna_Adler2000\"] = 1,\n [\"CITEREFR._Feynman1985\"] = 1,\n [\"CITEREFR._RamaswamiK.N._Sivarajan1998\"] = 1,\n [\"CITEREFRashed1990\"] = 1,\n [\"CITEREFRothman2003\"] = 1,\n [\"CITEREFS._Simmons1992\"] = 1,\n [\"CITEREFSamuel_Edward_SheppardCharles_Edward_Kenneth_Mees1907\"] = 1,\n [\"CITEREFSerwayJewett2004\"] = 1,\n [\"CITEREFShen1984\"] = 1,\n [\"CITEREFSidney_F._Ray2002\"] = 1,\n [\"CITEREFT.F._Hoad1996\"] = 1,\n [\"CITEREFT.L._Heath2003\"] = 1,\n [\"CITEREFTiplerMosca2004\"] = 1,\n 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