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class="vector-toc-link" href="#Deviation_angle_and_dispersion"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Deviation angle and dispersion</span> </div> </a> <ul id="toc-Deviation_angle_and_dispersion-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</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" > <input type="checkbox" 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Available in 73 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-73" 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">73 leids</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/Prisma" title="Prisma – Afrikaans" lang="af" hreflang="af" data-title="Prisma" 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/%D9%85%D9%88%D8%B4%D9%88%D8%B1_(%D8%A8%D8%B5%D8%B1%D9%8A%D8%A7%D8%AA)" title="موشور (بصريات) – Arabic" lang="ar" hreflang="ar" data-title="موشور (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/Prisma_(%C3%B3ptica)" title="Prisma (óptica) – Asturian" lang="ast" hreflang="ast" data-title="Prisma (óptica)" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Призма (оптика) – Bashkir" lang="ba" hreflang="ba" data-title="Призма (оптика)" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Призма (оптика) – Bulgairien" lang="bg" hreflang="bg" data-title="Призма (оптика)" data-language-autonym="Български" data-language-local-name="Bulgairien" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%9C%E0%A6%AE_(%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="প্রিজম (আলোকবিজ্ঞান) – Bangla" lang="bn" hreflang="bn" data-title="প্রিজম (আলোকবিজ্ঞান)" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Kengereg" title="Kengereg – Breton" lang="br" hreflang="br" data-title="Kengereg" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Prizma_(optika)" title="Prizma (optika) – Bosnian" lang="bs" hreflang="bs" data-title="Prizma (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/Prisma_%C3%B2ptic" title="Prisma òptic – Catalan" lang="ca" hreflang="ca" data-title="Prisma òptic" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Optick%C3%BD_hranol" title="Optický hranol – Czech" lang="cs" hreflang="cs" data-title="Optický hranol" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Optisk_prisme" title="Optisk prisme – Dens" lang="da" hreflang="da" data-title="Optisk prisme" data-language-autonym="Dansk" data-language-local-name="Dens" 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/Prisma_(Optik)" title="Prisma (Optik) – German" lang="de" hreflang="de" data-title="Prisma (Optik)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%81%CE%AF%CF%83%CE%BC%CE%B1_(%CE%BF%CF%80%CF%84%CE%B9%CE%BA%CE%AE)" title="Πρίσμα (οπτική) – Greek" lang="el" hreflang="el" data-title="Πρίσμα (οπτική)" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Prism_(optics)" title="Prism (optics) – Inglis" lang="en" hreflang="en" data-title="Prism (optics)" data-language-autonym="English" data-language-local-name="Inglis" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Prismo_(optiko)" title="Prismo (optiko) – Esperanto" lang="eo" hreflang="eo" data-title="Prismo (optiko)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Prisma_(%C3%B3ptica)" title="Prisma (óptica) – Spainish" lang="es" hreflang="es" data-title="Prisma (óptica)" data-language-autonym="Español" data-language-local-name="Spainish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Optiline_prisma" title="Optiline prisma – Eastlands" lang="et" hreflang="et" data-title="Optiline prisma" data-language-autonym="Eesti" data-language-local-name="Eastlands" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Prisma_optiko" title="Prisma optiko – Basque" lang="eu" hreflang="eu" data-title="Prisma optiko" 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%85%D9%86%D8%B4%D9%88%D8%B1" title="منشور – Persian" lang="fa" hreflang="fa" data-title="منشور" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Prisma_(optiikka)" title="Prisma (optiikka) – Finnish" lang="fi" hreflang="fi" data-title="Prisma (optiikka)" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Prisme_(optique)" title="Prisme (optique) – French" lang="fr" hreflang="fr" data-title="Prisme (optique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Prisma_(optika)" title="Prisma (optika) – Western Frisian" lang="fy" hreflang="fy" data-title="Prisma (optika)" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E4%B8%89%E7%A8%9C%E9%8F%A1" title="三稜鏡 – Gan" lang="gan" hreflang="gan" data-title="三稜鏡" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A0%D7%A1%D7%A8%D7%94_(%D7%90%D7%95%D7%A4%D7%98%D7%99%D7%A7%D7%94)" title="מנסרה (אופטיקה) – Ebrew" lang="he" hreflang="he" data-title="מנסרה (אופטיקה)" data-language-autonym="עברית" data-language-local-name="Ebrew" class="interlanguage-link-target"><span>עברית</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%BF%E0%A4%9C%E0%A4%BC%E0%A5%8D%E0%A4%AE" title="प्रिज़्म – Hindi" lang="hi" hreflang="hi" data-title="प्रिज़्म" 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/Prizma_(optika)" title="Prizma (optika) – Croatian" lang="hr" hreflang="hr" data-title="Prizma (optika)" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Prizma" title="Prizma – Hungarian" lang="hu" hreflang="hu" data-title="Prizma" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D6%80%D5%AB%D5%A6%D5%B4%D5%A1_(%D6%85%D5%BA%D5%BF%D5%AB%D5%AF%D5%A1)" title="Պրիզմա (օպտիկա) – Armenian" lang="hy" hreflang="hy" data-title="Պրիզմա (օպտիկա)" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Prisma_(optik)" title="Prisma (optik) – Indonesian" lang="id" hreflang="id" data-title="Prisma (optik)" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Glerstrendingur" title="Glerstrendingur – Icelandic" lang="is" hreflang="is" data-title="Glerstrendingur" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%97%E3%83%AA%E3%82%BA%E3%83%A0" title="プリズム – Japanese" lang="ja" hreflang="ja" data-title="プリズム" 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-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Prizim" title="Prizim – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Prizim" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%B6%E0%B3%8D%E0%B2%B0%E0%B2%95" title="ಅಶ್ರಕ – Kannada" lang="kn" hreflang="kn" data-title="ಅಶ್ರಕ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%84%EB%A6%AC%EC%A6%98" title="프리즘 – Korean" lang="ko" hreflang="ko" data-title="프리즘" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Prisma" title="Prisma – Laitin" lang="la" hreflang="la" data-title="Prisma" data-language-autonym="Latina" data-language-local-name="Laitin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Prizm%C4%97" title="Prizmė – Lithuanie" lang="lt" hreflang="lt" data-title="Prizmė" data-language-autonym="Lietuvių" data-language-local-name="Lithuanie" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Prizma_(optika)" title="Prizma (optika) – Letts" lang="lv" hreflang="lv" data-title="Prizma (optika)" data-language-autonym="Latviešu" data-language-local-name="Letts" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Призма (оптика) – Macedonian" lang="mk" hreflang="mk" data-title="Призма (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%BF%E0%B4%B8%E0%B4%82" title="പ്രിസം – Malayalam" lang="ml" hreflang="ml" data-title="പ്രിസം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B2%E0%A5%8B%E0%A4%B2%E0%A4%95" title="लोलक – Marathi" lang="mr" hreflang="mr" data-title="लोलक" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Prisma" title="Prisma – Malay" lang="ms" hreflang="ms" data-title="Prisma" 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-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Pri%C5%BCma" title="Priżma – Maltese" lang="mt" hreflang="mt" data-title="Priżma" data-language-autonym="Malti" data-language-local-name="Maltese" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Prisma_(optica)" title="Prisma (optica) – Dutch" lang="nl" hreflang="nl" data-title="Prisma (optica)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Optisk_prisme" title="Optisk prisme – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Optisk prisme" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Prisme_(optikk)" title="Prisme (optikk) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Prisme (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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B0%E0%A9%B0%E0%A8%97%E0%A8%BE%E0%A8%B5%E0%A8%B2" title="ਰੰਗਾਵਲ – Punjabi" lang="pa" hreflang="pa" data-title="ਰੰਗਾਵਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pryzmat" title="Pryzmat – Polls" lang="pl" hreflang="pl" data-title="Pryzmat" data-language-autonym="Polski" data-language-local-name="Polls" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Prisma_(%C3%B2tica)" title="Prisma (òtica) – Piedmontese" lang="pms" hreflang="pms" data-title="Prisma (òtica)" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Prisma_(%C3%B3ptica)" title="Prisma (óptica) – Portuguese" lang="pt" hreflang="pt" data-title="Prisma (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/Prism%C4%83_(optic%C4%83)" title="Prismă (optică) – Roumains" lang="ro" hreflang="ro" data-title="Prismă (optică)" data-language-autonym="Română" data-language-local-name="Roumains" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Призма (оптика) – Roushien" lang="ru" hreflang="ru" data-title="Призма (оптика)" data-language-autonym="Русский" data-language-local-name="Roushien" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Prizma_(optika)" title="Prizma (optika) – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Prizma (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-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B7%83%E0%B7%8A%E0%B6%B8%E0%B6%BA" title="ප්‍රිස්මය – Sinhala" lang="si" hreflang="si" data-title="ප්‍රිස්මය" 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/Prism_(optics)" title="Prism (optics) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Prism (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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Optick%C3%BD_hranol" title="Optický hranol – Slovak" lang="sk" hreflang="sk" data-title="Optický hranol" 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/Opti%C4%8Dna_prizma" title="Optična prizma – Slovein" lang="sl" hreflang="sl" data-title="Optična prizma" data-language-autonym="Slovenščina" data-language-local-name="Slovein" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Prizmi_(optik%C3%AB)" title="Prizmi (optikë) – Albainien" lang="sq" hreflang="sq" data-title="Prizmi (optikë)" data-language-autonym="Shqip" data-language-local-name="Albainien" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Призма (оптика) – Serbian" lang="sr" hreflang="sr" data-title="Призма (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-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Prisma_(optik)" title="Prisma (optik) – Sundanese" lang="su" hreflang="su" data-title="Prisma (optik)" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Prisma_(optik)" title="Prisma (optik) – Swaidish" lang="sv" hreflang="sv" data-title="Prisma (optik)" data-language-autonym="Svenska" data-language-local-name="Swaidish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%95%E0%AE%AE%E0%AF%8D" title="பட்டகம் – Tamil" lang="ta" hreflang="ta" data-title="பட்டகம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AA%E0%B0%9F%E0%B1%8D%E0%B0%9F%E0%B0%95%E0%B0%82" title="పట్టకం – Telugu" lang="te" hreflang="te" data-title="పట్టకం" 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%9B%E0%B8%A3%E0%B8%B4%E0%B8%8B%E0%B8%B6%E0%B8%A1_(%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="ปริซึม (ทัศนศาสตร์) – Thai" lang="th" hreflang="th" data-title="ปริซึม (ทัศนศาสตร์)" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Prizma" title="Prizma – Turkish" lang="tr" hreflang="tr" data-title="Prizma" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Призма (оптика) – Tatar" lang="tt" hreflang="tt" data-title="Призма (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-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%B7%D0%BC%D0%B0_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Призма (оптика) – Ukrainian" lang="uk" hreflang="uk" data-title="Призма (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/%D9%85%D9%86%D8%B4%D9%88%D8%B1_(%D8%A8%D8%B5%D8%B1%DB%8C%D8%A7%D8%AA)" title="منشور (بصریات) – Urdu" lang="ur" hreflang="ur" data-title="منشور (بصریات)" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Dispersion_prizmalar" title="Dispersion prizmalar – Uzbek" lang="uz" hreflang="uz" data-title="Dispersion prizmalar" 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-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C4%83ng_k%C3%ADnh" title="Lăng kính – Vietnamese" lang="vi" hreflang="vi" data-title="Lăng kính" 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-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Prisma_(optika)" title="Prisma (optika) – Waray" lang="war" hreflang="war" data-title="Prisma (optika)" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%A3%B1%E9%95%9C" title="棱镜 – Wu" lang="wuu" hreflang="wuu" data-title="棱镜" 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-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%A8%9C%E9%8F%A1" title="稜鏡 – Cheenese" lang="zh" hreflang="zh" data-title="稜鏡" data-language-autonym="中文" data-language-local-name="Cheenese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%B8%89%E7%A8%9C%E9%8F%A1" title="三稜鏡 – Cantonese" lang="yue" hreflang="yue" data-title="三稜鏡" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q165896#sitelinks-wikipedia" title="Eedit interleid airtins" class="wbc-editpage">Eedit airtins</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Prism" title="Leuk at the content page [c]" accesskey="c"><span>Airticle</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Collogue:Prism&action=edit&redlink=1" rel="discussion" class="new" title="Discussion anent the content page (page disna exeest) [t]" accesskey="t"><span>Collogue</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Scots</span> </label> <div class="vector-dropdown-content"> <div 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href="/w/index.php?title=Prism&action=history" title="Auld revisions o this page [h]" accesskey="h"><span>See history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tuilkist" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tuilkist</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tuils</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">Dern</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li 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title="Ae leet o aw wiki pages that airt here [j]" accesskey="j"><span>Whit airts tae here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Prism" rel="nofollow" title="Recynt chynges in pages linkt fae this page [k]" accesskey="k"><span>Relatit chynges</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=sco" title="Uplaid files [u]" accesskey="u"><span>Uplaid file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="Ae leet o aw byordinar pages [q]" accesskey="q"><span>Byordinar pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Prism&oldid=854424" title="Permanent link til this reveesion o the page"><span>Permanent airtin</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Prism&action=info" title="Mair information anent this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Prism&id=854424&wpFormIdentifier=titleform" title="Information on hou tae cite this page"><span>Cite this airticle</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fsco.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DPrism%26section%3D4%26veaction%3Dedit"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fsco.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DPrism%26section%3D4%26veaction%3Dedit"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Prent/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Special:Book&bookcmd=book_creator&referer=Prism"><span>Create a beuk</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Prism&action=show-download-screen"><span>Doonload as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Prism&printable=yes" title="Prentable version o this page [p]" accesskey="p"><span>Prent version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In ither projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Prisms_(optics)" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q165896" title="Airt tae connected data reposeterie item [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">Dern</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Frae Wikipedia, the free beuk o knawledge</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sco" dir="ltr"><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Prism-side-fs_PNr%C2%B00117.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Prism-side-fs_PNr%C2%B00117.jpg/170px-Prism-side-fs_PNr%C2%B00117.jpg" decoding="async" width="170" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Prism-side-fs_PNr%C2%B00117.jpg/255px-Prism-side-fs_PNr%C2%B00117.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Prism-side-fs_PNr%C2%B00117.jpg/340px-Prism-side-fs_PNr%C2%B00117.jpg 2x" data-file-width="1781" data-file-height="2123" /></a><figcaption>A plastic prism</figcaption></figure> <p>A <b>prism</b> is a speicial bit <a href="/wiki/Gless" title="Gless">gless</a>, <a href="/wiki/Crystal" class="mw-redirect" title="Crystal">crystal</a>, or <a href="/wiki/Plastic" title="Plastic">plastic</a> that bends licht. The licht bends cause it muves mair slawer in the gless, crystal or plastic as it dis in <a href="/wiki/Air" class="mw-redirect" title="Air">air</a>. If different <a href="/wiki/Colour" title="Colour">colors</a> o licht muves at different speeds, ilka color bends a different amoont. This is dispersion and it splits the licht intil a baund o different colors cryed a <a href="/w/index.php?title=Spectrum&action=edit&redlink=1" class="new" title="Spectrum (page disna exeest)">spectrum</a>. This spectrum haes the same colors as a rainbowe dis, cause rainbowes is makkit the same wey, wi bendin licht. Thay happen whan licht is bent by totie draps watter floatin in the air. If the licht disna come oot whan it's sheent intil the prism, it is caaed internal reflection. </p><p>Some prisms is uised tae disperse licht. Binoculars uises prisms an aa, for tae reflect licht. This lats the tubes o the <a href="/wiki/Binoculars" title="Binoculars">binoculars</a> be cuttie. Some cameras uises a prism tae send licht til the viewfinder, sae's the photaegrapher can see whit will be photaegraphed. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Hou_prisms_wirks">Hou prisms wirks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism&veaction=edit&section=1" title="Eedit section: Hou prisms wirks" class="mw-editsection-visualeditor"><span>eedit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prism&action=edit&section=1" title="Edit section's source code: Hou prisms wirks"><span>eedit soorce</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure 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/330px-Light_dispersion_conceptual_waves.gif" decoding="async" width="330" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Light_dispersion_conceptual_waves.gif/495px-Light_dispersion_conceptual_waves.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/f/f5/Light_dispersion_conceptual_waves.gif 2x" data-file-width="640" data-file-height="480" /></a><figcaption>A triangular prism, skailin licht; waves shawn for tae shaw the different wavelenths o licht. (Click tae view animation)</figcaption></figure> <p>Licht cheenges <a href="/w/index.php?title=Speed&action=edit&redlink=1" class="new" title="Speed (page disna exeest)">speed</a> as it gangs frae ae medium til anither ane (for ensaumple, frae air intil the gless o the prism). This speed cheenge bends the licht and gang intil the new medium at anither angle (Huygens principle). Hou muckle the licht's path bends lippens til the angle that the incident beam o licht maks wi the surface, and on the ratio atween the <a href="/wiki/Refractive_index" title="Refractive index">refractive indices</a> o the twa media (Snell's law). The refractive index o a lot o materials (the likes o gless) varies wi the <a href="/w/index.php?title=Wavelenth&action=edit&redlink=1" class="new" title="Wavelenth (page disna exeest)">wavelenth</a> or color o the licht uised, a phenomenon kent as <i>dispersion</i>. This gars different colors o licht bend different and win ootower the prism at different angles, makkin a effect like a rainbowe. This can be uised tae sinder a beam o white licht intil its constituent spectrum o colors. A similar sinderin happens wi iridescent materials, siclike as a saip bubble. Prisms will aften skail licht ower a faur bigger frequency baundwidth as diffraction grates, makkin thaim uissfu for braid-spectrum spectroscopy. Forby, prisms disna hae the same iesues that comes frae spectral orders bein taen ower ither, that aa grates haes. </p><p>Prisms is uised for the internal reflection at the surfaces insteid o for skailin whiles. If licht inby the prism hits ane o the surfaces at a steep eneuch angle, total internal reflection occurs and <i>aa</i> o the licht is reflectit. This maks a prism a uissfu substitute for a keekin-gless in some situations. </p> <div class="mw-heading mw-heading3"><h3 id="Deviation_angle_and_dispersion">Deviation angle and dispersion</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism&veaction=edit&section=2" title="Eedit section: Deviation angle and dispersion" class="mw-editsection-visualeditor"><span>eedit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prism&action=edit&section=2" title="Edit section's source code: Deviation angle and dispersion"><span>eedit soorce</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Prism_ray_trace.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Prism_ray_trace.svg/400px-Prism_ray_trace.svg.png" decoding="async" width="400" height="224" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Prism_ray_trace.svg/600px-Prism_ray_trace.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Prism_ray_trace.svg/800px-Prism_ray_trace.svg.png 2x" data-file-width="395" data-file-height="221" /></a><figcaption>A ray trace throu a prism wi apex angle α. Regions 0, 1, and 2 haes <a href="/wiki/Refractive_index" title="Refractive index">indices o refraction</a> <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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63584d203ecb012a7bcb90f422408bbfe4018956" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{0}}"></span>, <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_{1}}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee784b70e772f55ede5e6e0bdc929994bff63413" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{1}}"></span>, 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 n_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/840e456e3058bc0be28e5cf653b170cdbfcc3be4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.449ex; height:2.009ex;" alt="{\displaystyle n_{2}}"></span>, and primed angles <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 \theta '}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>θ</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta '}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c02a68dba2972e9cf4faf9656f58da0df8be6ae9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.775ex; height:2.509ex;" alt="{\displaystyle \theta '}"></span> shaws the ray's angle efter bendin.</figcaption></figure> <p>Ray angle deviation and dispersion throu a prism can be determined wi tracin a sample ray throu the element and uisin Snell's law at ilka interface. For the prism shawn at the richt, the indicatit angles is gien wi </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 {\begin{aligned}\theta '_{0}&=\,{\text{arcsin}}{\Big (}{\frac {n_{0}}{n_{1}}}\,\sin \theta _{0}{\Big )}\\\theta _{1}&=\alpha -\theta '_{0}\\\theta '_{1}&=\,{\text{arcsin}}{\Big (}{\frac {n_{1}}{n_{2}}}\,\sin \theta _{1}{\Big )}\\\theta _{2}&=\theta '_{1}-\alpha \end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msubsup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mo>′</mo> </msubsup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>arcsin</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>α</mi> <mo>−</mo> <msubsup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mo>′</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>arcsin</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> <mo>−</mo> <mi>α</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\theta '_{0}&=\,{\text{arcsin}}{\Big (}{\frac {n_{0}}{n_{1}}}\,\sin \theta _{0}{\Big )}\\\theta _{1}&=\alpha -\theta '_{0}\\\theta '_{1}&=\,{\text{arcsin}}{\Big (}{\frac {n_{1}}{n_{2}}}\,\sin \theta _{1}{\Big )}\\\theta _{2}&=\theta '_{1}-\alpha \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b47df09014426f71ad7fec995231e23aa88bdf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.671ex; margin-bottom: -0.334ex; width:24.566ex; height:17.009ex;" alt="{\displaystyle {\begin{aligned}\theta '_{0}&=\,{\text{arcsin}}{\Big (}{\frac {n_{0}}{n_{1}}}\,\sin \theta _{0}{\Big )}\\\theta _{1}&=\alpha -\theta '_{0}\\\theta '_{1}&=\,{\text{arcsin}}{\Big (}{\frac {n_{1}}{n_{2}}}\,\sin \theta _{1}{\Big )}\\\theta _{2}&=\theta '_{1}-\alpha \end{aligned}}}"></span>.</dd></dl> <p>Aa angles is positive in the direction shawn in the pictur. For a prism in air <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_{0}=n_{2}\simeq 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≃</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{0}=n_{2}\simeq 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5025a1f8eef9343d25dd12d6cde1d0f20b30a2bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.257ex; height:2.509ex;" alt="{\displaystyle n_{0}=n_{2}\simeq 1}"></span>. Definin <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=n_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=n_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0f667fc1c95ec04b27bcd5f38d4718ca996dc54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.942ex; height:2.009ex;" alt="{\displaystyle n=n_{1}}"></span>, the deviation angle <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 \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }"></span> is gien wi </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 \delta =\theta _{0}+\theta _{2}=\theta _{0}+{\text{arcsin}}{\Big (}n\,\sin {\Big [}\alpha -{\text{arcsin}}{\Big (}{\frac {1}{n}}\,\sin \theta _{0}{\Big )}{\Big ]}{\Big )}-\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>arcsin</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mi>n</mi> <mspace width="thinmathspace" /> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">[</mo> </mrow> </mrow> <mi>α</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>arcsin</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mo>−</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta =\theta _{0}+\theta _{2}=\theta _{0}+{\text{arcsin}}{\Big (}n\,\sin {\Big [}\alpha -{\text{arcsin}}{\Big (}{\frac {1}{n}}\,\sin \theta _{0}{\Big )}{\Big ]}{\Big )}-\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddf51998a7666af6f7008837323d1cb036ed2974" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:61.491ex; height:5.176ex;" alt="{\displaystyle \delta =\theta _{0}+\theta _{2}=\theta _{0}+{\text{arcsin}}{\Big (}n\,\sin {\Big [}\alpha -{\text{arcsin}}{\Big (}{\frac {1}{n}}\,\sin \theta _{0}{\Big )}{\Big ]}{\Big )}-\alpha }"></span></dd></dl> <p>If baith the angle o incidence <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 \theta _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18b67de6bf25dba7a24e66967ff6319858798734" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.145ex; height:2.509ex;" alt="{\displaystyle \theta _{0}}"></span> and prism apex angle <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> is wee, <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 \sin \theta \approx \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mo>≈</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta \approx \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a604432d08fc1bd289e40ba08eed0c7ec697ea3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.522ex; height:2.176ex;" alt="{\displaystyle \sin \theta \approx \theta }"></span> 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 {\text{arcsin}}x\approx x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>arcsin</mtext> </mrow> <mi>x</mi> <mo>≈</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{arcsin}}x\approx x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf3ce790fab0b884544b99b8d236deafbcabec55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.72ex; height:2.176ex;" alt="{\displaystyle {\text{arcsin}}x\approx x}"></span> if the angles is expressed in radians. This lats the nonlinear equation in the deviation angle <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 \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }"></span> be approximatit 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 \delta \approx \theta _{0}-\alpha +{\Big (}n\,{\Big [}{\Big (}\alpha -{\frac {1}{n}}\,\theta _{0}{\Big )}{\Big ]}{\Big )}=\theta _{0}-\alpha +n\alpha -\theta _{0}=(n-1)\alpha \ .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>≈</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>α</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mi>n</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">[</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mi>α</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mo>=</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>α</mi> <mo>+</mo> <mi>n</mi> <mi>α</mi> <mo>−</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mi>α</mi> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta \approx \theta _{0}-\alpha +{\Big (}n\,{\Big [}{\Big (}\alpha -{\frac {1}{n}}\,\theta _{0}{\Big )}{\Big ]}{\Big )}=\theta _{0}-\alpha +n\alpha -\theta _{0}=(n-1)\alpha \ .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a1eb504ee193523ee68f4f88f7ed9e8b27e9510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:65.378ex; height:5.176ex;" alt="{\displaystyle \delta \approx \theta _{0}-\alpha +{\Big (}n\,{\Big [}{\Big (}\alpha -{\frac {1}{n}}\,\theta _{0}{\Big )}{\Big ]}{\Big )}=\theta _{0}-\alpha +n\alpha -\theta _{0}=(n-1)\alpha \ .}"></span></dd></dl> <p>The deviation angle lippens til the wavelenth throu <i>n</i>, sae for a thin prism the deviation angle varies wi wavelenth accordin tae </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 \delta (\lambda )\approx [n(\lambda )-1]\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mo>≈</mo> <mo stretchy="false">[</mo> <mi>n</mi> <mo stretchy="false">(</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> <mo stretchy="false">]</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta (\lambda )\approx [n(\lambda )-1]\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8c3977ee1555ef58a7d504a3986069f805ca082" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.655ex; height:2.843ex;" alt="{\displaystyle \delta (\lambda )\approx [n(\lambda )-1]\alpha }"></span>.</dd></dl> <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=Prism&veaction=edit&section=3" title="Eedit section: History" class="mw-editsection-visualeditor"><span>eedit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prism&action=edit&section=3" title="Edit section's source code: History"><span>eedit soorce</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:Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg/170px-Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg" decoding="async" width="170" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg/255px-Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg/340px-Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg 2x" data-file-width="2309" data-file-height="2818" /></a><figcaption>A triangular prism, skailin licht</figcaption></figure> <p>Like a wheen basic geometric terms, the wird <i>prism</i> (<a href="/w/index.php?title=Ancient_Greek_leid&action=edit&redlink=1" class="new" title="Ancient Greek leid (page disna exeest)">Ancient Greek</a>: <span lang="grc">πρίσμα</span>, <small>romanised: </small><i lang="grc-Latn" title="Ancient Greek-leid romanisation">prisma</i>, <small><a href="/w/index.php?title=Literal_translation&action=edit&redlink=1" class="new" title="Literal translation (page disna exeest)">lit.</a> </small>'something sawed') wis first uised in Euclid's <a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements"><i>Elements</i></a>. Euclid defined the term in Beuk XI as "a haurd figure hauden-inaboot by twa opposite, equal and parallel planes, while the lave is parallelograms", houaniver the nine propositions that cam efter that uised the term haed ensaumples o triangular-based prisms (i.e. wi sides that wisna parallelograms).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> This inconsistency resultit in raivelment amang later geometricians.<sup id="cite_ref-Malton1774_2-0" class="reference"><a href="#cite_note-Malton1774-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Elliot1845_3-0" class="reference"><a href="#cite_note-Elliot1845-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> haed seen licht sindert intil the colors o the rainbowe wi gless or watter,<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> tho the soorce o the color wisna kent. <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>'s 1666 experiment o bendin white licht throu a prism shawed that aa the colors aaready existit in the licht, wi different color "<a href="/w/index.php?title=Photon&action=edit&redlink=1" class="new" title="Photon (page disna exeest)">corpuscles</a>" skailin oot and muvin at different speeds throu the prism. It wis later that <a href="/w/index.php?title=Thomas_Young_(scientist)&action=edit&redlink=1" class="new" title="Thomas Young (scientist) (page disna exeest)">Young</a> and <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">Fresnel</a> pat Newton's particle theory and Huygens' wave theory thegither for tae explain hou color comes frae the spectrum o licht. </p><p>Newton wan at his conclusion wi passin the reid color frae ae prism throu a seicont ane and fand the color haedna cheenged. Frae this, he concludit that the colors maun aaready be present in the licht comin in, tharefore the prism didna mak colors, but juist sindert colors that's aaready thare. Forby, he uised a lens and a seicont prism tae recompose the spectrum back intae white licht. This experiment haes come tae be a classic example o the methodology introduced in the scientific revolution. The results o the experiment transformed the field o metaphysics a lot, and this led tae <a href="/wiki/John_Locke" title="John Locke">John Locke</a>'s primary vs secondary quality distinction.<sup class="Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needit" title="Wikipedia:Citation needit"><span title="This claim needs references tae reliable soorces. (April 2015)">citation needit</span></a></i>]</sup> </p><p>Newton spak aboot prism dispersion in a lot o detail in his beuk <i>Opticks</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> He introduced the uiss o mair as the ae prism tae guvern dispersion and aa.<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> Newton's description o his experiments on prism dispersion wis qualitative. A quantitative description o multiple-prism dispersion wisna nott until multiple prism laser beam expanders wis introduced in the 1980s.<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> </p> <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=Prism&veaction=edit&section=4" title="Eedit section: References" class="mw-editsection-visualeditor"><span>eedit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prism&action=edit&section=4" title="Edit section's source code: References"><span>eedit soorce</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://data.perseus.org/citations/urn:cts:greekLit:tlg1799.tlg001.perseus-eng1:11.def.13">Elements</a>: book 11, Def 13 and Prop 28, 29, 39; and book 12, Prop 3, 4, 5, 7, 8, 10</span> </li> <li id="cite_note-Malton1774-2"><span class="mw-cite-backlink"><a href="#cite_ref-Malton1774_2-0">↑</a></span> <span class="reference-text"><cite id="CITEREFThomas_Malton1774" class="citation book cs1">Thomas Malton (1774). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-3tLfuCB97AC&pg=PA360"><i>A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ...</i></a> (in Inglis). author, and sold. pp. 360–.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Royal+Road+to+Geometry%3A+Or%2C+an+Easy+and+Familiar+Introduction+to+the+Mathematics.+...+By+Thomas+Malton.+...&rft.pages=360-&rft.pub=author%2C+and+sold&rft.date=1774&rft.au=Thomas+Malton&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-3tLfuCB97AC%26pg%3DPA360&rfr_id=info%3Asid%2Fsco.wikipedia.org%3APrism" class="Z3988"></span><style data-mw-deduplicate="TemplateStyles:r809032">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),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 a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style></span> </li> <li id="cite_note-Elliot1845-3"><span class="mw-cite-backlink"><a href="#cite_ref-Elliot1845_3-0">↑</a></span> <span class="reference-text"><cite id="CITEREFJames_Elliot1845" class="citation book cs1">James Elliot (1845). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qilLAAAAYAAJ&pg=PA3"><i>Key to the Complete Treatise on Practical Geometry and Mensuration: Containing Full Demonstrations of the Rules ...</i></a> (in Inglis). Longman, Brown, Green, and Longmans. pp. 3–.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Key+to+the+Complete+Treatise+on+Practical+Geometry+and+Mensuration%3A+Containing+Full+Demonstrations+of+the+Rules+...&rft.pages=3-&rft.pub=Longman%2C+Brown%2C+Green%2C+and+Longmans&rft.date=1845&rft.au=James+Elliot&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DqilLAAAAYAAJ%26pg%3DPA3&rfr_id=info%3Asid%2Fsco.wikipedia.org%3APrism" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r809032"></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><cite id="CITEREFJames_Gleick2004" class="citation book cs1">James Gleick (8 Juin 2004). <i>Isaac Newton</i> (in Inglis). Vintage. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1400032954" title="Special:BookSources/1400032954"><bdi>1400032954</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Isaac+Newton&rft.pub=Vintage&rft.date=2004-06-08&rft.isbn=1400032954&rft.au=James+Gleick&rfr_id=info%3Asid%2Fsco.wikipedia.org%3APrism" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r809032"></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><cite id="CITEREFIsaac_Newton1704" class="citation book cs1">Isaac Newton (1704). <i><a href="/w/index.php?title=Opticks&action=edit&redlink=1" class="new" title="Opticks (page disna exeest)">Opticks</a></i> (in Inglis). London: Royal Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-60205-2" title="Special:BookSources/0-486-60205-2"><bdi>0-486-60205-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Opticks&rft.place=London&rft.pub=Royal+Society&rft.date=1704&rft.isbn=0-486-60205-2&rft.au=Isaac+Newton&rfr_id=info%3Asid%2Fsco.wikipedia.org%3APrism" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r809032"></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.juliantrubin.com/bigten/lightexperiments.html">"The Discovery of the Spectrum of Light"</a> (in Inglis)<span class="reference-accessdate">. Retrieved <span class="nowrap">20 Februar</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Discovery+of+the+Spectrum+of+Light&rft_id=http%3A%2F%2Fwww.juliantrubin.com%2Fbigten%2Flightexperiments.html&rfr_id=info%3Asid%2Fsco.wikipedia.org%3APrism" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r809032"></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><cite id="CITEREFF._J._Duarte_and_J._A._Piper1982" class="citation journal cs1"><a href="/w/index.php?title=F._J._Duarte&action=edit&redlink=1" class="new" title="F. J. Duarte (page disna exeest)">F. J. Duarte</a> and J. A. Piper (1982). "Dispersion theory of multiple-prism beam expanders for pulsed dye lasers". <i>Opt. Commun.</i> (in Inglis). <b>43</b> (5): 303–307. <a href="/w/index.php?title=Bibcode_(identifier)&action=edit&redlink=1" class="new" title="Bibcode (identifier) (page disna exeest)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1982OptCo..43..303D">1982OptCo..43..303D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0030-4018%2882%2990216-4">10.1016/0030-4018(82)90216-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Opt.+Commun.&rft.atitle=Dispersion+theory+of+multiple-prism+beam+expanders+for+pulsed+dye+lasers&rft.volume=43&rft.issue=5&rft.pages=303-307&rft.date=1982&rft_id=info%3Adoi%2F10.1016%2F0030-4018%2882%2990216-4&rft_id=info%3Abibcode%2F1982OptCo..43..303D&rft.au=F.+J.+Duarte+and+J.+A.+Piper&rfr_id=info%3Asid%2Fsco.wikipedia.org%3APrism" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r809032"></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Prism&veaction=edit&section=5" title="Eedit section: Further reading" class="mw-editsection-visualeditor"><span>eedit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prism&action=edit&section=5" title="Edit section's source code: Further reading"><span>eedit soorce</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFHecht,_Eugene2001" class="citation book cs1">Hecht, Eugene (2001). <i>Optics</i> (4th ed.). Pearson Education. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8053-8566-5" title="Special:BookSources/0-8053-8566-5"><bdi>0-8053-8566-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Optics&rft.edition=4th&rft.pub=Pearson+Education&rft.date=2001&rft.isbn=0-8053-8566-5&rft.au=Hecht%2C+Eugene&rfr_id=info%3Asid%2Fsco.wikipedia.org%3APrism" class="Z3988"></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r809032"></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=Prism&veaction=edit&section=6" title="Eedit section: External links" class="mw-editsection-visualeditor"><span>eedit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Prism&action=edit&section=6" title="Edit section's source code: External links"><span>eedit soorce</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/18px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span> <cite class="citation encyclopaedia cs1"><span class="cs1-ws-icon" title="Wikisource:1911 Encyclopædia Britannica/Prism"><a class="external text" href="https://sco.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Prism">"Prism" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" class="mw-redirect" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. <b>22</b> (11th ed.). 1911. p. 361.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Prism&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=361&rft.edition=11th&rft.date=1911&rfr_id=info%3Asid%2Fsco.wikipedia.org%3APrism" class="Z3988"></span> <span class="cs1-hidden-error error citation-comment">Cite has empty unkent parameters: <code class="cs1-code">|HIDE_PARAMETER15=</code>, <code class="cs1-code">|HIDE_PARAMETER13=</code>, <code class="cs1-code">|HIDE_PARAMETER14c=</code>, <code class="cs1-code">|HIDE_PARAMETER14=</code>, <code class="cs1-code">|HIDE_PARAMETER9=</code>, <code class="cs1-code">|HIDE_PARAMETER3=</code>, <code class="cs1-code">|HIDE_PARAMETER1=</code>, <code class="cs1-code">|HIDE_PARAMETER4=</code>, <code class="cs1-code">|HIDE_PARAMETER2=</code>, <code class="cs1-code">|HIDE_PARAMETER8=</code>, 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