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class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Sadržaj" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Sadržaj</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Objašnjenje" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Objašnjenje"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Objašnjenje</span> </div> </a> <button aria-controls="toc-Objašnjenje-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>Sadržaj cjeline Objašnjenje</span> </button> <ul id="toc-Objašnjenje-sublist" class="vector-toc-list"> <li id="toc-Indeks_loma" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Indeks_loma"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Indeks loma</span> </div> </a> <ul id="toc-Indeks_loma-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lom_svjetlosti_u_planparalelnoj_ploči" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lom_svjetlosti_u_planparalelnoj_ploči"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Lom svjetlosti u planparalelnoj ploči</span> </div> </a> <ul id="toc-Lom_svjetlosti_u_planparalelnoj_ploči-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lom_svjetlosti_u_prizmi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lom_svjetlosti_u_prizmi"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Lom svjetlosti u prizmi</span> </div> </a> <ul id="toc-Lom_svjetlosti_u_prizmi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Refraktometar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Refraktometar"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Refraktometar</span> </div> </a> <button aria-controls="toc-Refraktometar-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>Sadržaj cjeline Refraktometar</span> </button> <ul id="toc-Refraktometar-sublist" class="vector-toc-list"> <li id="toc-Refraktometrija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Refraktometrija"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Refraktometrija</span> </div> </a> <ul id="toc-Refraktometrija-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Refrakcija_oka" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Refrakcija_oka"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Refrakcija oka</span> </div> </a> <ul id="toc-Refrakcija_oka-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Refrakcija_u_atmosferi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Refrakcija_u_atmosferi"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Refrakcija u atmosferi</span> </div> </a> <ul id="toc-Refrakcija_u_atmosferi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vanjske_poveznice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vanjske_poveznice"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Vanjske poveznice</span> </div> </a> <ul id="toc-Vanjske_poveznice-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="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="Prikaz sadržaja stranice" > <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">Prikaz sadržaja stranice</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">Refrakcija</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="Idi na druge jezične varijante članka. Dostupan je na 89 jezika" > <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-89" 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">89 jezika</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/Ligbreking" title="Ligbreking – afrikaans" lang="af" hreflang="af" data-title="Ligbreking" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Brechung_(Physik)" title="Brechung (Physik) – švicarski njemački" lang="gsw" hreflang="gsw" data-title="Brechung (Physik)" data-language-autonym="Alemannisch" data-language-local-name="švicarski njemački" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%89%A5%E1%88%AD%E1%88%83%E1%8A%95_%E1%88%B5%E1%89%A5%E1%88%A8%E1%89%B5" title="የብርሃን ስብረት – amharski" lang="am" hreflang="am" data-title="የብርሃን ስብረት" data-language-autonym="አማርኛ" data-language-local-name="amharski" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%86%D9%83%D8%B3%D8%A7%D8%B1_(%D9%81%D9%8A%D8%B2%D9%8A%D8%A7%D8%A1)" title="انكسار (فيزياء) – arapski" lang="ar" hreflang="ar" data-title="انكسار (فيزياء)" data-language-autonym="العربية" data-language-local-name="arapski" 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/Refraici%C3%B3n" title="Refraición – asturijski" lang="ast" hreflang="ast" data-title="Refraición" data-language-autonym="Asturianu" data-language-local-name="asturijski" 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/%C4%B0%C5%9F%C4%B1%C4%9F%C4%B1n_s%C4%B1nmas%C4%B1" title="İşığın sınması – azerbajdžanski" lang="az" hreflang="az" data-title="İşığın sınması" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanski" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D0%BB%D0%B0%D0%BC%D0%BB%D0%B5%D0%BD%D0%BD%D0%B5" title="Праламленне – bjeloruski" lang="be" hreflang="be" data-title="Праламленне" data-language-autonym="Беларуская" data-language-local-name="bjeloruski" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Peml%C3%A8ngsongan" title="Pemlèngsongan – Betawi" lang="bew" hreflang="bew" data-title="Pemlèngsongan" data-language-autonym="Betawi" data-language-local-name="Betawi" class="interlanguage-link-target"><span>Betawi</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D1%87%D1%83%D0%BF%D0%B2%D0%B0%D0%BD%D0%B5" title="Пречупване – bugarski" lang="bg" hreflang="bg" data-title="Пречупване" data-language-autonym="Български" data-language-local-name="bugarski" 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%86%E0%A6%B2%E0%A7%8B%E0%A6%B0_%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%A4%E0%A6%BF%E0%A6%B8%E0%A6%B0%E0%A6%A3" title="আলোর প্রতিসরণ – bangla" lang="bn" hreflang="bn" data-title="আলোর প্রতিসরণ" data-language-autonym="বাংলা" data-language-local-name="bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Refracci%C3%B3" title="Refracció – katalonski" lang="ca" hreflang="ca" data-title="Refracció" data-language-autonym="Català" data-language-local-name="katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B4%DA%A9%D8%A7%D9%86%DB%95%D9%88%DB%95%DB%8C_%DA%95%D9%88%D9%88%D9%86%D8%A7%DA%A9%DB%8C" title="شکانەوەی ڕووناکی – soranski kurdski" lang="ckb" hreflang="ckb" data-title="شکانەوەی ڕووناکی" data-language-autonym="کوردی" data-language-local-name="soranski kurdski" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Lom_vln%C4%9Bn%C3%AD" title="Lom vlnění – češki" lang="cs" hreflang="cs" data-title="Lom vlnění" data-language-autonym="Čeština" data-language-local-name="češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A0%D0%B5%D1%84%D1%80%D0%B0%D0%BA%D1%86%D0%B8" title="Рефракци – čuvaški" lang="cv" hreflang="cv" data-title="Рефракци" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Plygiant" title="Plygiant – velški" lang="cy" hreflang="cy" data-title="Plygiant" data-language-autonym="Cymraeg" data-language-local-name="velški" 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/Refraktion" title="Refraktion – danski" lang="da" hreflang="da" data-title="Refraktion" data-language-autonym="Dansk" data-language-local-name="danski" 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/Brechung_(Physik)" title="Brechung (Physik) – njemački" lang="de" hreflang="de" data-title="Brechung (Physik)" data-language-autonym="Deutsch" data-language-local-name="njemački" 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%94%CE%B9%CE%AC%CE%B8%CE%BB%CE%B1%CF%83%CE%B7" title="Διάθλαση – grčki" lang="el" hreflang="el" data-title="Διάθλαση" data-language-autonym="Ελληνικά" data-language-local-name="grčki" 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/Refraction" title="Refraction – engleski" lang="en" hreflang="en" data-title="Refraction" data-language-autonym="English" data-language-local-name="engleski" 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/Refrakto" title="Refrakto – esperanto" lang="eo" hreflang="eo" data-title="Refrakto" 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/Refracci%C3%B3n" title="Refracción – španjolski" lang="es" hreflang="es" data-title="Refracción" data-language-autonym="Español" data-language-local-name="španjolski" 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/Refraktsioon" title="Refraktsioon – estonski" lang="et" hreflang="et" data-title="Refraktsioon" data-language-autonym="Eesti" data-language-local-name="estonski" 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/Errefrakzio" title="Errefrakzio – baskijski" lang="eu" hreflang="eu" data-title="Errefrakzio" data-language-autonym="Euskara" data-language-local-name="baskijski" 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/%D8%B4%DA%A9%D8%B3%D8%AA_(%D8%A7%D9%85%D9%88%D8%A7%D8%AC)" title="شکست (امواج) – perzijski" lang="fa" hreflang="fa" data-title="شکست (امواج)" data-language-autonym="فارسی" data-language-local-name="perzijski" 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/Taittuminen" title="Taittuminen – finski" lang="fi" hreflang="fi" data-title="Taittuminen" data-language-autonym="Suomi" data-language-local-name="finski" 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/R%C3%A9fraction" title="Réfraction – francuski" lang="fr" hreflang="fr" data-title="Réfraction" data-language-autonym="Français" data-language-local-name="francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Athraonadh" title="Athraonadh – irski" lang="ga" hreflang="ga" data-title="Athraonadh" data-language-autonym="Gaeilge" data-language-local-name="irski" 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/Refracci%C3%B3n" title="Refracción – galicijski" lang="gl" hreflang="gl" data-title="Refracción" data-language-autonym="Galego" data-language-local-name="galicijski" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%91%D7%99%D7%A8%D7%94" title="שבירה – hebrejski" lang="he" hreflang="he" data-title="שבירה" data-language-autonym="עברית" data-language-local-name="hebrejski" 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%85%E0%A4%AA%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%A4%E0%A4%A8" title="अपवर्तन – hindski" lang="hi" hreflang="hi" data-title="अपवर्तन" data-language-autonym="हिन्दी" data-language-local-name="hindski" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Refraksyon" title="Refraksyon – haićanski kreolski" lang="ht" hreflang="ht" data-title="Refraksyon" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haićanski kreolski" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/F%C3%A9nyt%C3%B6r%C3%A9s" title="Fénytörés – mađarski" lang="hu" hreflang="hu" data-title="Fénytörés" data-language-autonym="Magyar" data-language-local-name="mađarski" 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/%D4%BC%D5%B8%D6%82%D5%B5%D5%BD%D5%AB_%D5%A1%D5%B6%D5%A4%D6%80%D5%A1%D5%A4%D5%A1%D6%80%D5%B1%D5%B8%D6%82%D5%B4" title="Լույսի անդրադարձում – armenski" lang="hy" hreflang="hy" data-title="Լույսի անդրադարձում" data-language-autonym="Հայերեն" data-language-local-name="armenski" 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/Pembiasan" title="Pembiasan – indonezijski" lang="id" hreflang="id" data-title="Pembiasan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" 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/Lj%C3%B3sbrot" title="Ljósbrot – islandski" lang="is" hreflang="is" data-title="Ljósbrot" data-language-autonym="Íslenska" data-language-local-name="islandski" 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/Rifrazione" title="Rifrazione – talijanski" lang="it" hreflang="it" data-title="Rifrazione" data-language-autonym="Italiano" data-language-local-name="talijanski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%B1%88%E6%8A%98" title="屈折 – japanski" lang="ja" hreflang="ja" data-title="屈折" data-language-autonym="日本語" data-language-local-name="japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Refraksi" title="Refraksi – javanski" lang="jv" hreflang="jv" data-title="Refraksi" data-language-autonym="Jawa" data-language-local-name="javanski" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A0%D0%B5%D1%84%D1%80%D0%B0%D0%BA%D1%86%D0%B8%D1%8F" title="Рефракция – kazaški" lang="kk" hreflang="kk" data-title="Рефракция" data-language-autonym="Қазақша" data-language-local-name="kazaški" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B2%95%E0%B3%8D%E0%B2%B0%E0%B3%80%E0%B2%AD%E0%B2%B5%E0%B2%A8" title="ವಕ್ರೀಭವನ – karnatački" lang="kn" hreflang="kn" data-title="ವಕ್ರೀಭವನ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="karnatački" 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/%EA%B5%B4%EC%A0%88" title="굴절 – korejski" lang="ko" hreflang="ko" data-title="굴절" data-language-autonym="한국어" data-language-local-name="korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A0%D0%B5%D1%84%D1%80%D0%B0%D0%BA%D1%86%D0%B8%D1%8F" title="Рефракция – kirgiski" lang="ky" hreflang="ky" data-title="Рефракция" data-language-autonym="Кыргызча" data-language-local-name="kirgiski" 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/Refractio" title="Refractio – latinski" lang="la" hreflang="la" data-title="Refractio" data-language-autonym="Latina" data-language-local-name="latinski" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Liichtrefraktioun" title="Liichtrefraktioun – luksemburški" lang="lb" hreflang="lb" data-title="Liichtrefraktioun" data-language-autonym="Lëtzebuergesch" data-language-local-name="luksemburški" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Rifrazion" title="Rifrazion – Lombard" lang="lmo" hreflang="lmo" data-title="Rifrazion" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%81%E0%BA%B2%E0%BA%99%E0%BA%AB%E0%BA%B1%E0%BA%81%E0%BA%A5%E0%BA%BB%E0%BA%9A" title="ການຫັກລົບ – laoski" lang="lo" hreflang="lo" data-title="ການຫັກລົບ" data-language-autonym="ລາວ" data-language-local-name="laoski" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Bangos_l%C5%AB%C5%BEis" title="Bangos lūžis – litavski" lang="lt" hreflang="lt" data-title="Bangos lūžis" data-language-autonym="Lietuvių" data-language-local-name="litavski" 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/Gaismas_lau%C5%A1ana" title="Gaismas laušana – latvijski" lang="lv" hreflang="lv" data-title="Gaismas laušana" data-language-autonym="Latviešu" data-language-local-name="latvijski" 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%B5%D0%BA%D1%80%D1%88%D1%83%D0%B2%D0%B0%D1%9A%D0%B5_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Прекршување (физика) – makedonski" lang="mk" hreflang="mk" data-title="Прекршување (физика)" data-language-autonym="Македонски" data-language-local-name="makedonski" 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%85%E0%B4%AA%E0%B4%B5%E0%B5%BC%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%A8%E0%B4%82" title="അപവർത്തനം – malajalamski" lang="ml" hreflang="ml" data-title="അപവർത്തനം" data-language-autonym="മലയാളം" data-language-local-name="malajalamski" 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%85%E0%A4%AA%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%A4%E0%A4%A8" title="अपवर्तन – marathski" lang="mr" hreflang="mr" data-title="अपवर्तन" data-language-autonym="मराठी" data-language-local-name="marathski" 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/Pembiasan" title="Pembiasan – malajski" lang="ms" hreflang="ms" data-title="Pembiasan" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Lichtbreking" title="Lichtbreking – nizozemski" lang="nl" hreflang="nl" data-title="Lichtbreking" data-language-autonym="Nederlands" data-language-local-name="nizozemski" 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/Refraksjon" title="Refraksjon – norveški nynorsk" lang="nn" hreflang="nn" data-title="Refraksjon" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški 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/Lysbrytning" title="Lysbrytning – norveški bokmål" lang="nb" hreflang="nb" data-title="Lysbrytning" data-language-autonym="Norsk bokmål" data-language-local-name="norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Refraccion" title="Refraccion – okcitanski" lang="oc" hreflang="oc" data-title="Refraccion" data-language-autonym="Occitan" data-language-local-name="okcitanski" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Dabee_darbuu" title="Dabee darbuu – oromski" lang="om" hreflang="om" data-title="Dabee darbuu" data-language-autonym="Oromoo" data-language-local-name="oromski" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%AA%E0%A8%B5%E0%A8%B0%E0%A8%A4%E0%A8%A8_(%E0%A8%AA%E0%A9%8D%E0%A8%B0%E0%A8%95%E0%A8%BE%E0%A8%B8%E0%A8%BC)" title="ਅਪਵਰਤਨ (ਪ੍ਰਕਾਸ਼) – pandžapski" lang="pa" hreflang="pa" data-title="ਅਪਵਰਤਨ (ਪ੍ਰਕਾਸ਼)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžapski" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pcm mw-list-item"><a href="https://pcm.wikipedia.org/wiki/Refrakshion" title="Refrakshion – nigerijski pidžin" lang="pcm" hreflang="pcm" data-title="Refrakshion" data-language-autonym="Naijá" data-language-local-name="nigerijski pidžin" class="interlanguage-link-target"><span>Naijá</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Refrakcja" title="Refrakcja – poljski" lang="pl" hreflang="pl" data-title="Refrakcja" data-language-autonym="Polski" data-language-local-name="poljski" 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/Rifrassion" title="Rifrassion – Piedmontese" lang="pms" hreflang="pms" data-title="Rifrassion" 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/Refra%C3%A7%C3%A3o" title="Refração – portugalski" lang="pt" hreflang="pt" data-title="Refração" data-language-autonym="Português" data-language-local-name="portugalski" 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/Refrac%C8%9Bie" title="Refracție – rumunjski" lang="ro" hreflang="ro" data-title="Refracție" data-language-autonym="Română" data-language-local-name="rumunjski" 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%B5%D0%BB%D0%BE%D0%BC%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Преломление – ruski" lang="ru" hreflang="ru" data-title="Преломление" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9B%D0%BE%D0%BC_%D1%81%D0%B2%D1%96%D1%82%D0%BB%D0%B0" title="Лом світла – Rusyn" lang="rue" hreflang="rue" data-title="Лом світла" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%85%E0%A4%AA%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%A4%E0%A4%A8%E0%A4%AE%E0%A5%8D_(%E0%A4%AD%E0%A5%8C%E0%A4%A4%E0%A4%B5%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%9E%E0%A4%BE%E0%A4%A8%E0%A4%AE%E0%A5%8D)" title="अपवर्तनम् (भौतविज्ञानम्) – sanskrtski" lang="sa" hreflang="sa" data-title="अपवर्तनम् (भौतविज्ञानम्)" data-language-autonym="संस्कृतम्" data-language-local-name="sanskrtski" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Rifrazzioni" title="Rifrazzioni – sicilijski" lang="scn" hreflang="scn" data-title="Rifrazzioni" data-language-autonym="Sicilianu" data-language-local-name="sicilijski" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Refraction" title="Refraction – škotski" lang="sco" hreflang="sco" data-title="Refraction" data-language-autonym="Scots" data-language-local-name="škotski" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Prelamanje" title="Prelamanje – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Prelamanje" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpsko-hrvatski" 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%B7%80%E0%B6%BB%E0%B7%8A%E0%B6%AD%E0%B6%B1%E0%B6%BA" title="වර්තනය – sinhaleški" lang="si" hreflang="si" data-title="වර්තනය" data-language-autonym="සිංහල" data-language-local-name="sinhaleški" 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/Refraction" title="Refraction – Simple English" lang="en-simple" hreflang="en-simple" data-title="Refraction" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Lom_svetlobe" title="Lom svetlobe – slovenski" lang="sl" hreflang="sl" data-title="Lom svetlobe" data-language-autonym="Slovenščina" data-language-local-name="slovenski" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Rupambuko_rweChiedza" title="Rupambuko rweChiedza – shona" lang="sn" hreflang="sn" data-title="Rupambuko rweChiedza" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Prelamanje_svetlosti" title="Prelamanje svetlosti – srpski" lang="sr" hreflang="sr" data-title="Prelamanje svetlosti" data-language-autonym="Српски / srpski" data-language-local-name="srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Refraktion" title="Refraktion – švedski" lang="sv" hreflang="sv" data-title="Refraktion" data-language-autonym="Svenska" data-language-local-name="švedski" 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%92%E0%AE%B3%E0%AE%BF_%E0%AE%AE%E0%AF%81%E0%AE%B1%E0%AE%BF%E0%AE%B5%E0%AF%81" title="ஒளி முறிவு – tamilski" lang="ta" hreflang="ta" data-title="ஒளி முறிவு" data-language-autonym="தமிழ்" data-language-local-name="tamilski" 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%B5%E0%B0%95%E0%B1%8D%E0%B0%B0%E0%B1%80%E0%B0%AD%E0%B0%B5%E0%B0%A8%E0%B0%82" title="వక్రీభవనం – teluški" lang="te" hreflang="te" data-title="వక్రీభవనం" data-language-autonym="తెలుగు" data-language-local-name="teluški" 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%81%E0%B8%B2%E0%B8%A3%E0%B8%AB%E0%B8%B1%E0%B8%81%E0%B9%80%E0%B8%AB" title="การหักเห – tajlandski" lang="th" hreflang="th" data-title="การหักเห" data-language-autonym="ไทย" data-language-local-name="tajlandski" 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/K%C4%B1r%C4%B1lma_(fizik)" title="Kırılma (fizik) – turski" lang="tr" hreflang="tr" data-title="Kırılma (fizik)" data-language-autonym="Türkçe" data-language-local-name="turski" 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%97%D0%B0%D0%BB%D0%BE%D0%BC%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F" title="Заломлення – ukrajinski" lang="uk" hreflang="uk" data-title="Заломлення" data-language-autonym="Українська" data-language-local-name="ukrajinski" 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%A7%D9%86%D8%B9%D8%B7%D8%A7%D9%81" title="انعطاف – urdski" lang="ur" hreflang="ur" data-title="انعطاف" data-language-autonym="اردو" data-language-local-name="urdski" 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/Refraksiya" title="Refraksiya – uzbečki" lang="uz" hreflang="uz" data-title="Refraksiya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečki" 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/Kh%C3%BAc_x%E1%BA%A1" title="Khúc xạ – vijetnamski" lang="vi" hreflang="vi" data-title="Khúc xạ" data-language-autonym="Tiếng Việt" data-language-local-name="vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%8A%98%E5%B0%84" title="折射 – wu kineski" lang="wuu" hreflang="wuu" data-title="折射" data-language-autonym="吴语" data-language-local-name="wu kineski" 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%91%D7%A8%D7%A2%D7%9B%D7%95%D7%A0%D7%92" title="ברעכונג – jidiš" lang="yi" hreflang="yi" data-title="ברעכונג" data-language-autonym="ייִדיש" data-language-local-name="jidiš" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%8A%98%E5%B0%84" title="折射 – kineski" lang="zh" hreflang="zh" data-title="折射" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%8A%98%E5%B0%84" title="折射 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="折射" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Chiat-si%C4%81" title="Chiat-siā – min nan kineski" lang="nan" hreflang="nan" data-title="Chiat-siā" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan kineski" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%8A%98%E5%B0%84" title="折射 – kantonski" lang="yue" hreflang="yue" data-title="折射" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet 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href="/wiki/Posebno:Povezane_promjene/Refrakcija" rel="nofollow" title="Nedavne promjene na stranicama koje su povezane s navedenom stranicom [k]" accesskey="k"><span>Povezane promjene</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedija:Upload" title="Postavi datoteke [u]" accesskey="u"><span>Postavi datoteku</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:Posebne_stranice" title="Popis svih posebnih stranica [q]" accesskey="q"><span>Posebne stranice</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Refrakcija&oldid=6737235" title="Trajna poveznica na ovu verziju stranice"><span>Trajna poveznica</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Refrakcija&action=info" title="Više informacija o ovoj stranici"><span>Podatci o stranici</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Citiraj&page=Refrakcija&id=6737235&wpFormIdentifier=titleform" title="Informacije o tome kako citirati ovu stranicu"><span>Citiraj ovu stranicu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:Skra%C4%87iva%C4%8D_adresa&url=https%3A%2F%2Fhr.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DRefrakcija%26section%3D3%26veaction%3Dedit"><span>Skraćeni URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrCode&url=https%3A%2F%2Fhr.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DRefrakcija%26section%3D3%26veaction%3Dedit"><span>Preuzmi QR kôd</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"> Ispis/izvoz </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=Posebno:Zbirka&bookcmd=book_creator&referer=Refrakcija"><span>Stvori knjigu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Refrakcija&action=show-download-screen"><span>Preuzmi kao PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Refrakcija&printable=yes" title="Inačica za ispis ove stranice [p]" accesskey="p"><span>Inačica za ispis</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"> Wikimedijini projekti </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/Refraction" hreflang="en"><span>Zajednički poslužitelj</span></a></li><li id="t-wikibase" class="wb-otherproject-link 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data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</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">Izvor: Wikipedija</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="hr" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Snells_law-bs.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Snells_law-bs.svg/250px-Snells_law-bs.svg.png" decoding="async" width="250" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Snells_law-bs.svg/375px-Snells_law-bs.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Snells_law-bs.svg/500px-Snells_law-bs.svg.png 2x" data-file-width="641" data-file-height="355" /></a><figcaption>Refrakcija ili <a href="/wiki/Lom_svjetlosti" class="mw-redirect" title="Lom svjetlosti">lom svjetlosti</a> je skretanje <a href="/wiki/Svjetlost" title="Svjetlost">svjetlosnih</a> zraka pri prijelazu iz jednoga sredstva u drugo zbog razlike u brzini širenja <a href="/wiki/Val" title="Val">valova</a> u njima.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:F%C3%A9nyt%C3%B6r%C3%A9s.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/F%C3%A9nyt%C3%B6r%C3%A9s.jpg/250px-F%C3%A9nyt%C3%B6r%C3%A9s.jpg" decoding="async" width="250" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/F%C3%A9nyt%C3%B6r%C3%A9s.jpg/375px-F%C3%A9nyt%C3%B6r%C3%A9s.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/F%C3%A9nyt%C3%B6r%C3%A9s.jpg/500px-F%C3%A9nyt%C3%B6r%C3%A9s.jpg 2x" data-file-width="1712" data-file-height="1368" /></a><figcaption>Refrakcija ili lom svjetlosti.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Angle_of_incidence_Refraction_example.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Angle_of_incidence_Refraction_example.jpg/250px-Angle_of_incidence_Refraction_example.jpg" decoding="async" width="250" height="177" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Angle_of_incidence_Refraction_example.jpg/375px-Angle_of_incidence_Refraction_example.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Angle_of_incidence_Refraction_example.jpg/500px-Angle_of_incidence_Refraction_example.jpg 2x" data-file-width="858" data-file-height="609" /></a><figcaption>Zbog loma svjetlosti štap postavljen koso u vodu izgleda kao da je prelomljen.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Refrakcija_1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/a/ac/Refrakcija_1.jpg/250px-Refrakcija_1.jpg" decoding="async" width="250" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/a/ac/Refrakcija_1.jpg 1.5x" data-file-width="326" data-file-height="260" /></a><figcaption>Zbog loma svjetlosti čini nam se da je riba uzdignuta i dubina manja nego što je u stvari.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Totalna_refleksija_1.pdf" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/f/fd/Totalna_refleksija_1.pdf/page1-250px-Totalna_refleksija_1.pdf.jpg" decoding="async" width="250" height="177" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/f/fd/Totalna_refleksija_1.pdf/page1-375px-Totalna_refleksija_1.pdf.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/f/fd/Totalna_refleksija_1.pdf/page1-500px-Totalna_refleksija_1.pdf.jpg 2x" data-file-width="1754" data-file-height="1239" /></a><figcaption><a href="/wiki/Totalna_refleksija" title="Totalna refleksija">Totalna refleksija</a> nastaje kada zrake svjetlosti koje se šire iz optički gušćeg u optički rjeđe sredstvo padaju na granicu tih sredstava pod kutom većim od nekoga graničnoga kuta.</figcaption></figure> <p><b>Refrakcija</b> (srednjovj. lat. <i>refractio</i>, prema <a href="/wiki/Latinski_jezik" title="Latinski jezik">lat</a>. <i>refractus</i>: slomljen) ili <b>lom svjetlosti</b> je skretanje <a href="/wiki/Svjetlost" title="Svjetlost">svjetlosnih</a> zraka ili zraka drugog <a href="/wiki/Elektromagnetsko_zra%C4%8Denje" title="Elektromagnetsko zračenje">elektromagnetskoga zračenja</a> pri prijelazu iz jednoga sredstva u drugo zbog razlike u <a href="/wiki/Brzina" title="Brzina">brzini</a> širenja <a href="/wiki/Val" title="Val">valova</a> u različitim sredstvima. Pojam se može odnositi i na valove <a href="/wiki/Zvuk" title="Zvuk">zvuka</a>. Zakoni su refrakcije: </p> <ul><li>upadna zraka, lomljena zraka i okomica na granicu sredstava leže u istoj ravnini;</li> <li><a href="/wiki/Snelliusov_zakon" title="Snelliusov zakon">Snelliusov zakon</a>:</li></ul> <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 {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}={\frac {n_{2}}{n_{1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}={\frac {n_{2}}{n_{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/429d498749f292c242e1b7bd9e1cf219fd403736" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.724ex; height:5.843ex;" alt="{\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}={\frac {n_{2}}{n_{1}}}}"></span></dd></dl> <p>ili </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 n_{1}\cdot \sin \theta _{1}=n_{2}\cdot \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> <mo>⋅</mo> <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> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{1}\cdot \sin \theta _{1}=n_{2}\cdot \sin \theta _{2}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0916bf6a7117ef4ddf528a1345416da3814b3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.71ex; height:2.509ex;" alt="{\displaystyle n_{1}\cdot \sin \theta _{1}=n_{2}\cdot \sin \theta _{2}\ }"></span></dd></dl> <p>pri čemu su: <i>θ<sub>1</sub></i> - kut upadne zrake svjetlosti, <i>θ<sub>2</sub></i> - kut loma, <i>v</i><sub>1</sub> i <i>v</i><sub>2</sub> brzine vala, a <i>n</i><sub>1</sub> i <i>n</i><sub>2</sub> odgovarajući <a href="/wiki/Indeks_loma" title="Indeks loma">indeksi loma</a> sredstva iz kojega zrake dolaze i sredstva u koje ulaze. </p><p>Ako zrake dolaze iz <a href="/wiki/Optika" title="Optika">optički</a> <a href="/wiki/Gusto%C4%87a" title="Gustoća">gušćega</a> u optički rjeđe sredstvo, postoji granični <a href="/wiki/Kut" title="Kut">kut</a> upadne zrake za koji još vrijedi Snelliusov zakon (odbijanje valova ili <a href="/wiki/Refleksija" title="Refleksija">refleksija</a>). Kod kutova većih od graničnoga događa se <a href="/wiki/Totalna_refleksija" title="Totalna refleksija">totalna refleksija</a>.<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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Objašnjenje"><span id="Obja.C5.A1njenje"></span>Objašnjenje</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=1" title="Uredi odlomak: Objašnjenje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=1" title="Uredi kôd odjeljka Objašnjenje"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pustimo kroz usku pukotonu u tamnoj sobi mali snop <a href="/wiki/Svjetlost" title="Svjetlost">svjetlosti</a> na površinu vode u posudi. Jedan dio zraka svjetlosti <a href="/wiki/Refleksija" title="Refleksija">reflektirat</a> će se tako da kut upadanja bude jednak kutu refleksije (odbijanja). Veći dio svjetlosnog snopa ući će u vodu, ali će skrenuti s prvobitnog smjera. Kažemo da se zraka svjetlosti lomi. Kut loma <i>θ<sub>2</sub></i> bit će manji od kuta upadanja <i>θ<sub>1</sub></i>, znači da se zraka svjetlosti lomi prema okomici. Upadajuća i lomljena zraka leže u jednoj ravnini. Ako zraka svjetlosti pada okomito na površinu vode, ona će prolaziti kroz vodu bez ikakvog skretanja. </p><p>Zbog loma svjetlosti čini nam se štap, postavljen koso u vodu, kao prelomljen. Iz istoga razloga čini nam se dno rijeke, odnosno mora, uzdignuto i dubina manja nego što je u stvari. </p><p>Pokus loma svjetlosti može se izvesti pomoću zrcala koji se nalazi u vodi. Zraka svjetlosti pada na koso postavljeno zrcalo te se od njega reflektira. Na granici vode i zraka jedan se dio zrake svjetlosti reflektira u zrak, a drugi ulazi u vodu, te se lomi prema okomici. Na zrcalu u vodi zraka se svjetlosti opet reflektira, a na granici vode i zraka također će se jedan dio svjetlosti reflektirati u vodu, dok će veći dio izaći u zrak i lomiti se od okomice. Iz navedenih pokusa vidimo da se svjetlost kad koso dođe na granicu dvaju sredstava, na primjer zraka i vode, djelomično reflektira, a djelomično ulazi u sredstvo i pri tom se lomi. </p><p>Ono sredstvo u kojem je kut loma zraka svjetlosti manji od kuta upadanja zovemo optički gušće, a sredstvo u kojem je kut loma zrake svjetlosti veći od kuta upadanja zovemo optički rjeđe sredstvo. Prema tome je <a href="/wiki/Voda" title="Voda">voda</a> optički gušće, a <a href="/wiki/Zrak" title="Zrak">zrak</a> optički rjeđe sredstvo.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Indeks_loma">Indeks loma</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=2" title="Uredi odlomak: Indeks loma" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=2" title="Uredi kôd odjeljka Indeks loma"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><style data-mw-deduplicate="TemplateStyles:r7016135">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote 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"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Indeks_loma" title="Indeks loma">Indeks loma</a></div></i></div> <p><b>Indeks loma</b> (oznaka <i>n</i>) je bezdimenzionalna <a href="/wiki/Fizikalna_veli%C4%8Dina" class="mw-redirect" title="Fizikalna veličina">fizikalna veličina</a> koja opisuje međudjelovanje <a href="/wiki/Svjetlost" title="Svjetlost">svjetlosti</a> i optički prozirne tvari, a definirana je kao omjer <a href="/wiki/Brzina_svjetlosti" title="Brzina svjetlosti">brzine svjetlosti</a> u <a href="/wiki/Vakuum" title="Vakuum">vakuumu</a> <i>c</i> i brzine svjetlosti u tvari <i>v</i>, </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 n={\frac {c}{v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>v</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n={\frac {c}{v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33da8c421d52a437e59e6726572ed6d09cb6f3e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.457ex; height:4.676ex;" alt="{\displaystyle n={\frac {c}{v}}}"></span></dd></dl> <p>Posljedica je promjene brzine svjetlosti promjena pravca njezina širenja pri prelasku iz jednoga optičkog sredstva u drugo. Što je indeks loma veći, veća je promjena pravca, odnosno veći je lom svjetlosti (refrakcija). Indeks loma može se s pomoću Snelliusova zakona odrediti iz geometrijskih odnosa kutova zraka svjetlosti prema površini sredstva u kojem dolazi do loma: </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 {\frac {n_{2}}{n_{1}}}={\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n_{2}}{n_{1}}}={\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ec6112853b999321f28d2edd7457edfb353c15a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.724ex; height:5.843ex;" alt="{\displaystyle {\frac {n_{2}}{n_{1}}}={\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}}"></span></dd></dl> <p>gdje je: <i>θ<sub>1</sub></i> - upadni kut prema okomici na površinu sredstva, <i>θ<sub>1</sub></i> - kut loma, <i>n<sub>1</sub></i> - indeks loma optičkoga sredstva iz kojega svjetlost dolazi, a <i>n<sub>2</sub></i> - indeks loma optičkoga sredstva u koje svjetlost ulazi. Često se rabi relativni indeks loma, koji je jednak omjeru indeksa loma dvaju sredstava: </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 n_{r}=n_{21}={\frac {n_{2}}{n_{1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{r}=n_{21}={\frac {n_{2}}{n_{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b0ceb42711534a5162b9660b2ebc46204acbcf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.121ex; height:5.009ex;" alt="{\displaystyle n_{r}=n_{21}={\frac {n_{2}}{n_{1}}}}"></span></dd></dl> <p>Svjetlost se u nekoj tvari širi brzinom: </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 v={c \over {\sqrt {\mu _{r}\cdot \varepsilon _{r}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>⋅</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </msqrt> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={c \over {\sqrt {\mu _{r}\cdot \varepsilon _{r}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73d6769f40488ddbde9276cad8edc40a4809f490" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:13.11ex; height:5.676ex;" alt="{\displaystyle v={c \over {\sqrt {\mu _{r}\cdot \varepsilon _{r}}}}}"></span></dd></dl> <p>gdje je: <i>ε<sub>r</sub></i> - <a href="/wiki/Relativna_dielektri%C4%8Dna_permitivnost" title="Relativna dielektrična permitivnost">relativna dielektrična permitivnost</a> tvari, a <i>μ<sub>r</sub></i> - <a href="/wiki/Relativna_magnetska_permeabilnost" title="Relativna magnetska permeabilnost">relativna magnetska permeabilnost</a>. Kako za relativnu magnetsku permeabilnost u optički prozirnom sredstvu vrijedi <i>μ<sub>r</sub></i> ≈ 1, proizlazi da indeks loma ovisi samo o relativnoj dielektričnoj permitivnosti: </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 n={\sqrt {\varepsilon _{r}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n={\sqrt {\varepsilon _{r}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cebe9d49bf10f252b9c6789c6607ee4466088b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:8.486ex; height:3.009ex;" alt="{\displaystyle n={\sqrt {\varepsilon _{r}}}}"></span></dd></dl> <p>Međutim, za mnoge tvari dolazi do odstupanja od toga izraza, zbog postojanja električnih <a href="/wiki/Dipol" title="Dipol">dipola</a> u <a href="/wiki/Dielektrik" title="Dielektrik">dielektricima</a> i ovisnosti relativne dielektrične permitivnosti o frekvenciji svjetlosti.<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> <div class="mw-heading mw-heading3"><h3 id="Lom_svjetlosti_u_planparalelnoj_ploči"><span id="Lom_svjetlosti_u_planparalelnoj_plo.C4.8Di"></span>Lom svjetlosti u planparalelnoj ploči</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=3" title="Uredi odlomak: Lom svjetlosti u planparalelnoj ploči" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=3" title="Uredi kôd odjeljka Lom svjetlosti u planparalelnoj ploči"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Lom_01.pdf" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/b/b6/Lom_01.pdf/page1-250px-Lom_01.pdf.jpg" decoding="async" width="250" height="177" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/b/b6/Lom_01.pdf/page1-375px-Lom_01.pdf.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/b/b6/Lom_01.pdf/page1-500px-Lom_01.pdf.jpg 2x" data-file-width="1754" data-file-height="1239" /></a><figcaption>Lom svjetlosti u planparalelnoj ploči.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:(175)_Refraction.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/%28175%29_Refraction.jpg/250px-%28175%29_Refraction.jpg" decoding="async" width="250" height="162" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/%28175%29_Refraction.jpg/375px-%28175%29_Refraction.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/%28175%29_Refraction.jpg/500px-%28175%29_Refraction.jpg 2x" data-file-width="800" data-file-height="519" /></a><figcaption>Lom svjetlosti u akrilnoj planparalelnoj ploči.</figcaption></figure><p>Planparalelna ploča je prozirno tijelo omeđeno dvjema <a href="/wiki/Paralelnost" title="Paralelnost">paralelnim</a> <a href="/wiki/Ravnina" title="Ravnina">ravninama</a>. Zraka svjetlosti lomi se dvaput prolazeći kroz planparalelnu ploču. Za lom svjetlosti u prvoj točki loma vrijedi: </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 {\frac {\sin \alpha }{\sin \beta }}=n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sin \alpha }{\sin \beta }}=n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e41d1fa8ece6aa22c4eb3ef43024ea64cb8b3517" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.06ex; height:5.676ex;" alt="{\displaystyle {\frac {\sin \alpha }{\sin \beta }}=n}"></span></dd></dl> <p>a za lom u drugoj točki vrijedi: </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 {\frac {\sin \beta _{1}}{\sin \alpha _{1}}}={\frac {1}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sin \beta _{1}}{\sin \alpha _{1}}}={\frac {1}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d953381e04195cf14676afbc960107a255f14f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.95ex; height:5.676ex;" alt="{\displaystyle {\frac {\sin \beta _{1}}{\sin \alpha _{1}}}={\frac {1}{n}}}"></span></dd></dl> <p>Pomnožimo li međusobno obje jednadžbe, dobivamo: </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 {\frac {\sin \alpha \cdot \sin \beta _{1}}{\sin \beta \cdot \sin \alpha _{1}}}={\frac {n}{n}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mi>n</mi> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sin \alpha \cdot \sin \beta _{1}}{\sin \beta \cdot \sin \alpha _{1}}}={\frac {n}{n}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f218cff95d7cabd1a2769681d69065da94e2e580" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.465ex; height:5.843ex;" alt="{\displaystyle {\frac {\sin \alpha \cdot \sin \beta _{1}}{\sin \beta \cdot \sin \alpha _{1}}}={\frac {n}{n}}=1}"></span></dd></dl> <p>Kako su granične plohe paralelne, to mora biti <i>β = β1</i>, a stoga je <i>sin β = sin β<sub>1</sub></i>, pa je <i>sin α / sin α<sub>1</sub></i> = 1, a odatle je <i>α = α<sub>1</sub></i>. </p><p>Znači, kut upadanja zrake svjetlosti pri ulazu u planparalelnu ploču jednak je kutu loma kod izlaza zrake iz ploče. Zraka dakle izlazi u istom smjeru, samo je malo pomaknuta: </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 \xi =d\cdot {\frac {\sin(\alpha -\beta )}{\cos \beta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi =d\cdot {\frac {\sin(\alpha -\beta )}{\cos \beta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c863a3396f7715b3ecebe2b85db6ba63f17c9d8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.185ex; height:6.176ex;" alt="{\displaystyle \xi =d\cdot {\frac {\sin(\alpha -\beta )}{\cos \beta }}}"></span></dd></dl> <p>Pomak <i>ζ</i> je, dakle, to veći što je veća debljina <i>d</i> ploče. </p> <div class="mw-heading mw-heading3"><h3 id="Lom_svjetlosti_u_prizmi">Lom svjetlosti u prizmi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=4" title="Uredi odlomak: Lom svjetlosti u prizmi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=4" title="Uredi kôd odjeljka Lom svjetlosti u prizmi"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135"><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Prizma_(optika)" title="Prizma (optika)">Prizma (optika)</a></div></i></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Lom_u_prizmi.pdf" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/hr/thumb/3/38/Lom_u_prizmi.pdf/page1-250px-Lom_u_prizmi.pdf.jpg" decoding="async" width="250" height="177" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/hr/thumb/3/38/Lom_u_prizmi.pdf/page1-375px-Lom_u_prizmi.pdf.jpg 1.5x, //upload.wikimedia.org/wikipedia/hr/thumb/3/38/Lom_u_prizmi.pdf/page1-500px-Lom_u_prizmi.pdf.jpg 2x" data-file-width="1754" data-file-height="1239" /></a><figcaption>Lom svjetlosti u <a href="/wiki/Prizma_(optika)" title="Prizma (optika)">prizmi</a>.</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Prism-rainbow.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Prism-rainbow.svg/250px-Prism-rainbow.svg.png" decoding="async" width="250" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Prism-rainbow.svg/375px-Prism-rainbow.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Prism-rainbow.svg/500px-Prism-rainbow.svg.png 2x" data-file-width="400" data-file-height="300" /></a><figcaption><a href="/wiki/Disperzija_(optika)" title="Disperzija (optika)">Disperzija</a> kod <a href="/wiki/Opti%C4%8Dka_prizma" class="mw-redirect" title="Optička prizma">optičke prizme</a> uzrokuje da se bijela <a href="/wiki/Svjetlost" title="Svjetlost">svjetlost</a> razloži na <a href="/wiki/Spektar_(boja)" title="Spektar (boja)">dugine boje</a>.</figcaption></figure> <p><a href="/wiki/Opti%C4%8Dka_prizma" class="mw-redirect" title="Optička prizma">Optička prizma</a> je prozirno tijelo omeđeno s dvije ravnine koje se sijeku pod oštrim kutom koji se zove lomni kut prizme <i>ρ</i>. Zraka se lomi kod ulaza u prizmu u točki A i kod izlaza iz prizme u točki B. U točki A zraka se otklonila od prvobitnog smjera za kut <i>δ<sub>1</sub> = α<sub>1</sub> - β<sub>1</sub></i>. U točki B za kut <i>δ<sub>2</sub> = α<sub>2</sub> - β<sub>2</sub></i>, pa je ukupni otklon ili <a href="/wiki/Devijacija" class="mw-disambig" title="Devijacija">devijacija</a> zrake svjetlosti od svoga prvobitnog smjera: </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 =\delta _{1}+\delta _{2}=(\alpha _{1}-\beta _{1})+(\beta _{2}-\alpha _{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta =\delta _{1}+\delta _{2}=(\alpha _{1}-\beta _{1})+(\beta _{2}-\alpha _{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b88d361c5bc65ccde801cce1e81015262ad01b4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.223ex; height:2.843ex;" alt="{\displaystyle \delta =\delta _{1}+\delta _{2}=(\alpha _{1}-\beta _{1})+(\beta _{2}-\alpha _{2})}"></span></dd></dl> <p>Kako je zbroj kutova u trokutu 180°: </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 (90^{\circ }-\beta _{1})+(90^{\circ }-\alpha _{2})+\rho =180^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <msup> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mi>ρ</mi> <mo>=</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (90^{\circ }-\beta _{1})+(90^{\circ }-\alpha _{2})+\rho =180^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e295708654ec302f6af6ab10d4a9901e5414fb53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.492ex; height:2.843ex;" alt="{\displaystyle (90^{\circ }-\beta _{1})+(90^{\circ }-\alpha _{2})+\rho =180^{\circ }}"></span></dd></dl> <p>a odatle je: </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 \rho =\alpha _{2}+\beta _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho =\alpha _{2}+\beta _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d58a518a40b987d745af272e1b952872a8a82566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.053ex; height:2.676ex;" alt="{\displaystyle \rho =\alpha _{2}+\beta _{1}}"></span></dd></dl> <p>Uvrstimo li to u izraz za devijaciju, dobit ćemo: </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 =\alpha _{1}+\beta _{2}-\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta =\alpha _{1}+\beta _{2}-\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60a623c3610ec9cfaaf9f24b795d8e60a37fb419" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.942ex; height:2.843ex;" alt="{\displaystyle \delta =\alpha _{1}+\beta _{2}-\rho }"></span></dd></dl> <p>Devijacija će biti najmanja kada zraka svjetlosti bude simetrično prolazila kroz prizmu, to je kad bude <i>α<sub>1</sub> = β<sub>2</sub></i>. Ako je lomni kut <i>ρ</i> malen, imamo tanku prizmu, pa su i svi ostali kutovi maleni. Stoga u izrazu za indeks loma možemo sinuse zamijeniti samim kutovima, to jest: </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 n={\frac {\sin \alpha _{1}}{\sin \beta _{1}}}\approx {\frac {\alpha _{1}}{\beta _{1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n={\frac {\sin \alpha _{1}}{\sin \beta _{1}}}\approx {\frac {\alpha _{1}}{\beta _{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11616d63c63f4c735f6b3297e4f329a433d449a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.59ex; height:5.676ex;" alt="{\displaystyle n={\frac {\sin \alpha _{1}}{\sin \beta _{1}}}\approx {\frac {\alpha _{1}}{\beta _{1}}}}"></span></dd></dl> <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 n={\frac {\sin \beta _{2}}{\sin \alpha _{2}}}\approx {\frac {\beta _{2}}{\alpha _{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n={\frac {\sin \beta _{2}}{\sin \alpha _{2}}}\approx {\frac {\beta _{2}}{\alpha _{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83531aeee889a5063faba8cbf822eeebd82fe3ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.59ex; height:5.676ex;" alt="{\displaystyle n={\frac {\sin \beta _{2}}{\sin \alpha _{2}}}\approx {\frac {\beta _{2}}{\alpha _{2}}}}"></span></dd></dl> <p>pa je: </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 \alpha _{1}=n\cdot \beta _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>n</mi> <mo>⋅</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{1}=n\cdot \beta _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4c50956ffd484f5518a6b93f67c5e611f22e10a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.084ex; height:2.509ex;" alt="{\displaystyle \alpha _{1}=n\cdot \beta _{1}}"></span></dd></dl> <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 \beta _{2}=n\cdot \alpha _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mi>n</mi> <mo>⋅</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta _{2}=n\cdot \alpha _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b928b7e2587ef071f6ffa3e88287ffdbd917221" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.084ex; height:2.509ex;" alt="{\displaystyle \beta _{2}=n\cdot \alpha _{2}}"></span></dd></dl> <p>Uvrstimo li to u izraz za devijaciju: </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 =n\cdot \beta _{1}+n\cdot \alpha _{2}-\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <mi>n</mi> <mo>⋅</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>n</mi> <mo>⋅</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta =n\cdot \beta _{1}+n\cdot \alpha _{2}-\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ee159602d3cb006d472900264bac617b2624d82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.089ex; height:2.843ex;" alt="{\displaystyle \delta =n\cdot \beta _{1}+n\cdot \alpha _{2}-\rho }"></span></dd></dl> <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 =n\cdot (\alpha _{2}+\beta _{1})-\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <mi>n</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta =n\cdot (\alpha _{2}+\beta _{1})-\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fffc17805032ed8ddaad16432f95a1e1c64ed03b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.825ex; height:2.843ex;" alt="{\displaystyle \delta =n\cdot (\alpha _{2}+\beta _{1})-\rho }"></span></dd></dl> <p>ili, jer je: </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 \rho =\alpha _{2}+\beta _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho =\alpha _{2}+\beta _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d58a518a40b987d745af272e1b952872a8a82566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.053ex; height:2.676ex;" alt="{\displaystyle \rho =\alpha _{2}+\beta _{1}}"></span></dd></dl> <p>dobivamo: </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 =n\cdot \rho -\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <mi>n</mi> <mo>⋅</mo> <mi>ρ</mi> <mo>−</mo> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta =n\cdot \rho -\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cab7569017cee84727d10a5a5ce0a3d8d48614a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.465ex; height:2.843ex;" alt="{\displaystyle \delta =n\cdot \rho -\rho }"></span></dd></dl> <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 =(n-1)\cdot \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta =(n-1)\cdot \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/780d2af92f97bfaef210fd15e9c3fd32f433b97a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.235ex; height:2.843ex;" alt="{\displaystyle \delta =(n-1)\cdot \rho }"></span></dd></dl> <p>Odatle vidimo da je devijacija kod prizme to veća što je veći indeks loma i lomni kut prizme. Zraka iz prizme izlazi otklonjena prema debljem kraju za kut devijacije. </p> <div class="mw-heading mw-heading2"><h2 id="Refraktometar">Refraktometar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=5" title="Uredi odlomak: Refraktometar" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=5" title="Uredi kôd odjeljka Refraktometar"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135"><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Refraktometar" title="Refraktometar">Refraktometar</a></div></i></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Refractometer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Refractometer.jpg/250px-Refractometer.jpg" decoding="async" width="250" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Refractometer.jpg/375px-Refractometer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Refractometer.jpg/500px-Refractometer.jpg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption><a href="/wiki/Refraktometar" title="Refraktometar">Refraktometar</a>.</figcaption></figure> <p><b>Refraktometar</b> je <a href="/wiki/Mjerni_instrument" title="Mjerni instrument">mjerni instrument</a> kojim se određuje <a href="/wiki/Indeks_loma" title="Indeks loma">indeks loma</a> <a href="/wiki/Svjetlost" title="Svjetlost">svjetlosti</a>. Indeks loma može se odrediti i mjerenjem <a href="/wiki/Kut" title="Kut">kuta</a> otklona svjetlosne zrake kada ona prolazi <a href="/wiki/Prizma_(optika)" title="Prizma (optika)">prizmom</a> od <a href="/wiki/Materijal" title="Materijal">materijala</a> kojemu se želi odrediti indeks loma. Tako je indeks loma određivao <a href="/wiki/Ru%C4%91er_Bo%C5%A1kovi%C4%87" title="Ruđer Bošković">Ruđer Bošković</a> na specijalnom <i>vitrometru</i>, kod kojega se mogao mijenjati kut loma prizme. Danas se upotrebljavaju refraktometri za tekućine i čvrste tvari kod kojih se iz izmjerenoga graničnoga kuta pri totalnoj refleksiji određuje indeks loma. Na tom su načelu načinjeni Abbeov refraktometar (za određivanje indeksa loma malih količina tekućine), refraktometar s prizmom za uranjanje (za određivanje indeksa loma većih količina tekućine), Pulfrichov refraktometar (za određivanje indeksa loma tekućine i čvrstih tvari). Indeks loma plinova određuje se iz pomaka <a href="/wiki/Interferencija_valova" title="Interferencija valova">interferencijskih pruga</a> dviju <a href="/wiki/Koherencija" class="mw-disambig" title="Koherencija">koherentnih</a> zraka svjetlosti koje prolaze kroz dvije kivete od kojih jedna sadrži plin poznatog indeksa loma, a druga plin kojemu se određuje indeks loma. Na tom načelu radi <a href="/wiki/John_William_Strutt_Rayleigh" title="John William Strutt Rayleigh">Rayleighov</a> interferencijski refraktometar za plinove. Indeks loma ovisi o <a href="/wiki/Valna_duljina" title="Valna duljina">valnoj duljini</a> svjetlosti pa se mjerenja provode monokromatskom svjetlošću ili su pak u refraktometru ugrađeni kompenzatori kojima se može mjeriti indeks loma za određenu valnu duljinu svjetlosti, obično za <a href="/wiki/Natrij" title="Natrij">natrijevu</a> D-liniju, upotrebljavajući bijelu svjetlost, ili s pomoću <a href="/wiki/Opti%C4%8Dka_re%C5%A1etka" title="Optička rešetka">optičke rešetke</a> za različite valne duljine.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Refraktometrija">Refraktometrija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=6" title="Uredi odlomak: Refraktometrija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=6" title="Uredi kôd odjeljka Refraktometrija"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135"><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Refraktometrija" title="Refraktometrija">Refraktometrija</a></div></i></div> <p><b>Refraktometrija</b> je određivanje indeksa loma svjetlosti. Obavlja se refraktometrom, mjerenjem kuta pod kojim se svjetlosna zraka lomi pri prijelazu iz istraživane tekućine u staklenu prizmu poznatog indeksa loma. Budući da je indeks loma <a href="/wiki/Otopina" class="mw-redirect" title="Otopina">otopina</a> razmjeran njihovoj koncentraciji, refraktometrija služi i kao analitička tehnika za određivanje <a href="/wiki/Koncentracija" title="Koncentracija">koncentracije</a> <a href="/wiki/Vo%C4%87ni_sok" class="mw-redirect" title="Voćni sok">šećernih sokova</a>, voćnih <a href="/wiki/Sirup" title="Sirup">sirupa</a>, <a href="/wiki/Marmelada" title="Marmelada">marmelada</a>, <a href="/wiki/Masti" title="Masti">masti</a> u <a href="/wiki/Mlijeko" title="Mlijeko">mlijeku</a>, <a href="/wiki/Alkoholi" title="Alkoholi">alkohola</a> u <a href="/wiki/Alkoholno_pi%C4%87e" title="Alkoholno piće">alkoholnim pićima</a>, za određivanje čistoće <a href="/wiki/Glicerol" title="Glicerol">glicerola</a>, <a href="/wiki/Mineralna_ulja" title="Mineralna ulja">mineralnih</a> i <a href="/wiki/Eteri%C4%8Dna_ulja" title="Eterična ulja">eteričnih ulja</a>, <a href="/wiki/Vosak" title="Vosak">voskova</a>, <a href="/wiki/Masti" title="Masti">masti</a> i tako dalje. Refraktometrija je također važna metoda za određivanje konstitucije organskih spojeva.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Refrakcija_oka">Refrakcija oka</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=7" title="Uredi odlomak: Refrakcija oka" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=7" title="Uredi kôd odjeljka Refrakcija oka"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Refrakcija oka</b> je lom svjetlosnih zraka u <a href="/wiki/Dioptrija" title="Dioptrija">dioptrijskom</a> uređaju <a href="/wiki/Oko" title="Oko">oka</a> (<a href="/wiki/Ro%C5%BEnica" title="Rožnica">rožnici</a>, <a href="/wiki/O%C4%8Dna_vodica" title="Očna vodica">očnoj vodici</a>, <a href="/wiki/Le%C4%87a_(oko)" title="Leća (oko)">leći</a> i staklovini), što omogućuje stvaranje slike na <a href="/wiki/Mre%C5%BEnica_(oko)" title="Mrežnica (oko)">mrežnici</a>. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Farallon_Islands_at_inferior_mirage_no_mirage_and_superior_mirage.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Farallon_Islands_at_inferior_mirage_no_mirage_and_superior_mirage.jpg/250px-Farallon_Islands_at_inferior_mirage_no_mirage_and_superior_mirage.jpg" decoding="async" width="250" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Farallon_Islands_at_inferior_mirage_no_mirage_and_superior_mirage.jpg/375px-Farallon_Islands_at_inferior_mirage_no_mirage_and_superior_mirage.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Farallon_Islands_at_inferior_mirage_no_mirage_and_superior_mirage.jpg/500px-Farallon_Islands_at_inferior_mirage_no_mirage_and_superior_mirage.jpg 2x" data-file-width="1777" data-file-height="1389" /></a><figcaption>Slike prikazuju različite vrste <a href="/wiki/Mira%C5%BE" title="Miraž">miraža</a> koje su snimljene na istom mjestu u toku 6 minuta. Najgornji manji okvir prikazuje <b>donji miraž</b> na otocima Farallon Islands u blizini <a href="/wiki/San_Francisco,_Kalifornija" title="San Francisco, Kalifornija">San Francisca</a> (<a href="/wiki/Kalifornija" title="Kalifornija">Kalifornija</a>, <a href="/wiki/SAD" class="mw-redirect" title="SAD">SAD</a>). Drugi okvir odozgo prikazuje <a href="/wiki/Zeleni_bljesak" title="Zeleni bljesak">zeleni bljesak</a>. Dva najdolja okvira i glavni najveći okvir prikazuju <b>gornji miraž</b>. Najveći okvir ustvari se može objasniti i kao <a href="/wiki/Fatamorgana" title="Fatamorgana">fatamorgana</a>. Najgornja slika je fotografirana s <a href="/wiki/Razina_mora" class="mw-redirect" title="Razina mora">razine mora</a>, dok su ostale 4 slike s <a href="/wiki/Nadmorska_visina" title="Nadmorska visina">visine</a> od oko 20 <a href="/wiki/Metar" title="Metar">metara</a>.</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Refrakcija_u_atmosferi">Refrakcija u atmosferi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=8" title="Uredi odlomak: Refrakcija u atmosferi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=8" title="Uredi kôd odjeljka Refrakcija u atmosferi"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7016135"><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Atmosferska_refrakcija" title="Atmosferska refrakcija">Atmosferska refrakcija</a></div></i></div> <p><b>Refrakcija u atmosferi</b> nastaje zbog prolaza <a href="/wiki/Svjetlost" title="Svjetlost">svjetlosti</a> kroz slojeve zraka različite <a href="/wiki/Gusto%C4%87a" title="Gustoća">gustoće</a>, pa se svjetlosna zraka pri prijelazu iz jednoga sloja zraka u drugi lomi. Kako se <a href="/wiki/Gusto%C4%87a_zraka" title="Gustoća zraka">gustoća zraka</a> mijenja postupno, put svjetlosne zrake nije izlomljena linija nego kontinuirana <a href="/wiki/Krivulja" title="Krivulja">krivulja</a>. Pod normalnim uvjetima, to jest kada se gustoća zraka s visinom smanjuje, ta je krivulja zakrivljena pa je njezin udubljeni dio okrenut prema <a href="/wiki/Zemlja" title="Zemlja">Zemlji</a>. Budući da ljudsko oko predmete od kojih svjetlosna zraka dolazi smješta u smjeru <a href="/wiki/Tangenta" title="Tangenta">tangente</a> na put zrake, zemaljski predmeti, <a href="/wiki/Zvijezde" class="mw-redirect" title="Zvijezde">zvijezde</a>, <a href="/wiki/Mjesec" title="Mjesec">Mjesec</a> i <a href="/wiki/Sunce" title="Sunce">Sunce</a> izgledaju viši nego što zapravo jesu. Kut koji čini tangenta s pravocrtnom spojnicom oka i predmeta naziva se <b>kut refrakcije</b>. Razlikuju se <a href="/wiki/Atmosferska_refrakcija" title="Atmosferska refrakcija">astronomska refrakcija</a>, kada se promatraju <a href="/wiki/Nebesko_tijelo" class="mw-redirect" title="Nebesko tijelo">nebeska tijela</a>, i zemaljska refrakcija, kada se promatraju predmeti na Zemlji. Zbog astronomske refrakcije zvijezde se vide nad obzorom (horizontom) i onda kada se nalaze nešto ispod <a href="/wiki/Obzor" title="Obzor">obzora</a>; zbog nje je dan u umjerenim <a href="/wiki/Zemljopisna_%C5%A1irina" title="Zemljopisna širina">zemljopisnim širinama</a> duži za 8 do 13 <a href="/wiki/Minuta" title="Minuta">minuta</a>, a <a href="/wiki/Polarna_no%C4%87" title="Polarna noć">polarna noć</a> kraća za 12 dana. Zemaljskom refrakcijom vidljivi se obzor proširuje za 5 do 6%. Kod nenormalne <a href="/wiki/Stratifikacija" class="mw-disambig" title="Stratifikacija">stratifikacije</a> <a href="/wiki/Atmosfera" title="Atmosfera">atmosfere</a>, kada gustoća zraka raste s visinom, pojavljuju se u atmosferi posebne optičke pojave (na primjer <a href="/wiki/Mira%C5%BE" title="Miraž">miraž</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=9" title="Uredi odlomak: Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=9" title="Uredi kôd odjeljka Izvori"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6541845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.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"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"> <b>refrakcija</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=52225">[1]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2016.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"> Velimir Kruz: "Tehnička fizika za tehničke škole", "Školska knjiga" Zagreb, 1969.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"> <b>indeks loma</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=69487">[2]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2016.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"> <b>refraktometar</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/natuknica.aspx?ID=52226">[3]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2016.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"> <b>refraktometrija</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/natuknica.aspx?ID=52227">[4]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2016.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Vanjske_poveznice">Vanjske poveznice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Refrakcija&veaction=edit&section=10" title="Uredi odlomak: Vanjske poveznice" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Refrakcija&action=edit&section=10" title="Uredi kôd odjeljka Vanjske poveznice"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <table border="0" class="noprint" style="clear: right; border: solid var(--border-color-base, #a2a9b1) 1px; margin: 0 0 1em 1em; font-size: 90%; background: var(--background-color-neutral-subtle, #f8f9fa); color: inherit; width: 250px; padding: 4px; spacing: 0px; text-align: left; float: right;"> <tbody><tr> <td><figure class="mw-halign-none" typeof="mw:File"><span title="Logotip Zajedničkog poslužitelja"><img alt="Logotip Zajedničkog poslužitelja" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span><figcaption>Logotip Zajedničkog poslužitelja</figcaption></figure> </td> <td><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Glavna_stranica?uselang=hr">Zajednički poslužitelj</a> ima stranicu o temi <i><b><a class="external text" href="https://commons.wikimedia.org/wiki/Refraction?uselang=hr">Refrakcija</a></b></i></span> </td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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