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class="vector-toc-link" href="#Curcubeul_ca_fenomen_meteorologic"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Curcubeul ca fenomen meteorologic</span> </div> </a> <ul id="toc-Curcubeul_ca_fenomen_meteorologic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lumina_și_curcubeul_ca_fenomene_optice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lumina_și_curcubeul_ca_fenomene_optice"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Lumina și curcubeul ca fenomene optice</span> </div> </a> <button aria-controls="toc-Lumina_și_curcubeul_ca_fenomene_optice-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Lumina și curcubeul ca fenomene optice subsection</span> </button> <ul id="toc-Lumina_și_curcubeul_ca_fenomene_optice-sublist" class="vector-toc-list"> <li id="toc-Formarea_și_culorile_curcubeului" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formarea_și_culorile_curcubeului"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Formarea și culorile curcubeului</span> </div> </a> <ul id="toc-Formarea_și_culorile_curcubeului-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Curcubeul_principal_ca_fenomen_observabil" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Curcubeul_principal_ca_fenomen_observabil"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Curcubeul principal ca fenomen observabil</span> </div> </a> <ul id="toc-Curcubeul_principal_ca_fenomen_observabil-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Deducere_matematică" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Deducere_matematică"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Deducere matematică</span> </div> </a> <ul id="toc-Deducere_matematică-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Cronologia_explicației_fizice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cronologia_explicației_fizice"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Cronologia explicației fizice</span> </div> </a> <ul id="toc-Cronologia_explicației_fizice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Variații" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Variații"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Variații</span> </div> </a> <button aria-controls="toc-Variații-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon 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<span>Bibliografie</span> </div> </a> <ul id="toc-Bibliografie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legături_externe" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legături_externe"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Legături externe</span> </div> </a> <ul id="toc-Legături_externe-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="Cuprins" 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="Comută cuprinsul" > <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">Comută cuprinsul</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">Curcubeu</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="Mergeți la un articol în altă limbă. Disponibil în 175 limbi" > <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-175" 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">175 limbi</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/Re%C3%ABnboog" title="Reënboog – afrikaans" lang="af" hreflang="af" data-title="Reënboog" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%89%80%E1%88%B5%E1%89%B0_%E1%8B%B0%E1%88%98%E1%8A%93" title="ቀስተ ደመና – amharică" lang="am" hreflang="am" data-title="ቀስተ ደመና" data-language-autonym="አማርኛ" data-language-local-name="amharică" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ami mw-list-item"><a href="https://ami.wikipedia.org/wiki/Talakal_ni_Idek" title="Talakal ni Idek – Amis" lang="ami" hreflang="ami" data-title="Talakal ni Idek" data-language-autonym="Pangcah" data-language-local-name="Amis" class="interlanguage-link-target"><span>Pangcah</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Arco_de_Sant_Chuan" title="Arco de Sant Chuan – aragoneză" lang="an" hreflang="an" data-title="Arco de Sant Chuan" data-language-autonym="Aragonés" data-language-local-name="aragoneză" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D9%88%D8%B3_%D9%82%D8%B2%D8%AD" title="قوس قزح – arabă" lang="ar" hreflang="ar" data-title="قوس قزح" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arc mw-list-item"><a href="https://arc.wikipedia.org/wiki/%DC%A9%DC%AB%DC%AC%DC%90_%DC%95%DC%A1%DC%AA%DC%A2" title="ܩܫܬܐ ܕܡܪܢ – aramaică" lang="arc" hreflang="arc" data-title="ܩܫܬܐ ܕܡܪܢ" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="aramaică" class="interlanguage-link-target"><span>ܐܪܡܝܐ</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B9%D8%B1%D8%B3_%D8%A7%D9%84%D8%AF%D9%8A%D8%A8" title="عرس الديب – Moroccan Arabic" lang="ary" hreflang="ary" data-title="عرس الديب" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A7%B0%E0%A6%BE%E0%A6%AE%E0%A6%A7%E0%A7%87%E0%A6%A8%E0%A7%81" title="ৰামধেনু – asameză" lang="as" hreflang="as" data-title="ৰামধেনু" data-language-autonym="অসমীয়া" data-language-local-name="asameză" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Arcu_la_vieya" title="Arcu la vieya – asturiană" lang="ast" hreflang="ast" data-title="Arcu la vieya" data-language-autonym="Asturianu" data-language-local-name="asturiană" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Kurmi" title="Kurmi – aymara" lang="ay" hreflang="ay" data-title="Kurmi" data-language-autonym="Aymar aru" data-language-local-name="aymara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/G%C3%B6y_qur%C5%9Fa%C4%9F%C4%B1" title="Göy qurşağı – azeră" lang="az" hreflang="az" data-title="Göy qurşağı" data-language-autonym="Azərbaycanca" data-language-local-name="azeră" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%99%D3%99%D0%B9%D2%93%D0%BE%D1%80" title="Йәйғор – bașkiră" lang="ba" hreflang="ba" data-title="Йәйғор" data-language-autonym="Башҡортса" data-language-local-name="bașkiră" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Bianglalah" title="Bianglalah – balineză" lang="ban" hreflang="ban" data-title="Bianglalah" data-language-autonym="Basa Bali" data-language-local-name="balineză" class="interlanguage-link-target"><span>Basa Bali</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Vandar%C4%ABk%C5%A1t%C4%97" title="Vandarīkštė – Samogitian" lang="sgs" hreflang="sgs" data-title="Vandarīkštė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Hablondawani" title="Hablondawani – Central Bikol" lang="bcl" hreflang="bcl" data-title="Hablondawani" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bdr mw-list-item"><a href="https://bdr.wikipedia.org/wiki/Beruntung" title="Beruntung – West Coast Bajau" lang="bdr" hreflang="bdr" data-title="Beruntung" data-language-autonym="Bajau Sama" data-language-local-name="West Coast Bajau" class="interlanguage-link-target"><span>Bajau Sama</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%92%D1%8F%D1%81%D1%91%D0%BB%D0%BA%D0%B0" title="Вясёлка – belarusă" lang="be" hreflang="be" data-title="Вясёлка" data-language-autonym="Беларуская" data-language-local-name="belarusă" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%92%D1%8F%D1%81%D1%91%D0%BB%D0%BA%D0%B0" title="Вясёлка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Вясёлка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Bianglala" title="Bianglala – Betawi" lang="bew" hreflang="bew" data-title="Bianglala" 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%94%D1%8A%D0%B3%D0%B0" title="Дъга – bulgară" lang="bg" hreflang="bg" data-title="Дъга" data-language-autonym="Български" data-language-local-name="bulgară" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/T%C3%A9ja" title="Téja – Banjar" lang="bjn" hreflang="bjn" data-title="Téja" data-language-autonym="Banjar" data-language-local-name="Banjar" class="interlanguage-link-target"><span>Banjar</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B0%E0%A6%82%E0%A6%A7%E0%A6%A8%E0%A7%81" title="রংধনু – bengaleză" lang="bn" hreflang="bn" data-title="রংধনু" data-language-autonym="বাংলা" data-language-local-name="bengaleză" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A0%E0%BD%87%E0%BD%A0%E0%BC%8D" title="འཇའ། – tibetană" lang="bo" hreflang="bo" data-title="འཇའ།" data-language-autonym="བོད་ཡིག" data-language-local-name="tibetană" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Kanevedenn" title="Kanevedenn – bretonă" lang="br" hreflang="br" data-title="Kanevedenn" data-language-autonym="Brezhoneg" data-language-local-name="bretonă" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Duga" title="Duga – bosniacă" lang="bs" hreflang="bs" data-title="Duga" data-language-autonym="Bosanski" data-language-local-name="bosniacă" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Arc_de_Sant_Mart%C3%AD" title="Arc de Sant Martí – catalană" lang="ca" hreflang="ca" data-title="Arc de Sant Martí" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo badge-Q17437798 badge-goodarticle mw-list-item" title="articol bun"><a href="https://cdo.wikipedia.org/wiki/K%C3%AA%CC%A4%E1%B9%B3ng" title="Kê̤ṳng – Mindong" lang="cdo" hreflang="cdo" data-title="Kê̤ṳng" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D0%BB%D0%B0%D3%80%D0%B0%D0%B4" title="СтелаӀад – cecenă" lang="ce" hreflang="ce" data-title="СтелаӀад" data-language-autonym="Нохчийн" data-language-local-name="cecenă" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%8E%A4%E1%8F%85%E1%8F%89%E1%8E%B3%E1%8F%9B" title="ᎤᏅᏉᎳᏛ – cherokee" lang="chr" hreflang="chr" data-title="ᎤᏅᏉᎳᏛ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="cherokee" class="interlanguage-link-target"><span>ᏣᎳᎩ</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%BE%DB%95%D9%84%DA%A9%DB%95%D8%B2%DB%8E%DA%95%DB%8C%D9%86%DB%95" title="پەلکەزێڕینە – kurdă centrală" lang="ckb" hreflang="ckb" data-title="پەلکەزێڕینە" data-language-autonym="کوردی" data-language-local-name="kurdă centrală" 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/Duha" title="Duha – cehă" lang="cs" hreflang="cs" data-title="Duha" data-language-autonym="Čeština" data-language-local-name="cehă" 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%90%D1%81%D0%B0%D0%BC%D0%B0%D1%82_%D0%BA%C4%95%D0%BF%D0%B5%D1%80%C4%95" title="Асамат кĕперĕ – ciuvașă" lang="cv" hreflang="cv" data-title="Асамат кĕперĕ" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" 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/Enfys" title="Enfys – galeză" lang="cy" hreflang="cy" data-title="Enfys" data-language-autonym="Cymraeg" data-language-local-name="galeză" 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/Regnbue" title="Regnbue – daneză" lang="da" hreflang="da" data-title="Regnbue" data-language-autonym="Dansk" data-language-local-name="daneză" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="articol bun"><a href="https://de.wikipedia.org/wiki/Regenbogen" title="Regenbogen – germană" lang="de" hreflang="de" data-title="Regenbogen" data-language-autonym="Deutsch" data-language-local-name="germană" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Eysa_Fatma" title="Eysa Fatma – Zazaki" lang="diq" hreflang="diq" data-title="Eysa Fatma" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dsb mw-list-item"><a href="https://dsb.wikipedia.org/wiki/Tyca" title="Tyca – sorabă de jos" lang="dsb" hreflang="dsb" data-title="Tyca" data-language-autonym="Dolnoserbski" data-language-local-name="sorabă de jos" class="interlanguage-link-target"><span>Dolnoserbski</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9F%CF%85%CF%81%CE%AC%CE%BD%CE%B9%CE%BF_%CF%84%CF%8C%CE%BE%CE%BF" title="Ουράνιο τόξο – greacă" lang="el" hreflang="el" data-title="Ουράνιο τόξο" data-language-autonym="Ελληνικά" data-language-local-name="greacă" 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/Rainbow" title="Rainbow – engleză" lang="en" hreflang="en" data-title="Rainbow" data-language-autonym="English" data-language-local-name="engleză" 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/%C4%88ielarko" title="Ĉielarko – esperanto" lang="eo" hreflang="eo" data-title="Ĉielarko" 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/Arco%C3%ADris" title="Arcoíris – spaniolă" lang="es" hreflang="es" data-title="Arcoíris" data-language-autonym="Español" data-language-local-name="spaniolă" 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/Vikerkaar" title="Vikerkaar – estonă" lang="et" hreflang="et" data-title="Vikerkaar" data-language-autonym="Eesti" data-language-local-name="estonă" 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/Ostadar" title="Ostadar – bască" lang="eu" hreflang="eu" data-title="Ostadar" data-language-autonym="Euskara" data-language-local-name="bască" 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%B1%D9%86%DA%AF%DB%8C%D9%86%E2%80%8C%DA%A9%D9%85%D8%A7%D9%86" title="رنگین‌کمان – persană" lang="fa" hreflang="fa" data-title="رنگین‌کمان" data-language-autonym="فارسی" data-language-local-name="persană" 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/Sateenkaari" title="Sateenkaari – finlandeză" lang="fi" hreflang="fi" data-title="Sateenkaari" data-language-autonym="Suomi" data-language-local-name="finlandeză" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Vikahtkaar" title="Vikahtkaar – Võro" lang="vro" hreflang="vro" data-title="Vikahtkaar" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Drodrolagi" title="Drodrolagi – fijiană" lang="fj" hreflang="fj" data-title="Drodrolagi" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fijiană" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Arc-en-ciel" title="Arc-en-ciel – franceză" lang="fr" hreflang="fr" data-title="Arc-en-ciel" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Arc_di_Sant_Marc" title="Arc di Sant Marc – friulană" lang="fur" hreflang="fur" data-title="Arc di Sant Marc" data-language-autonym="Furlan" data-language-local-name="friulană" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Reinb%C3%B4ge" title="Reinbôge – frizonă occidentală" lang="fy" hreflang="fy" data-title="Reinbôge" data-language-autonym="Frysk" data-language-local-name="frizonă occidentală" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Tuar_ceatha" title="Tuar ceatha – irlandeză" lang="ga" hreflang="ga" data-title="Tuar ceatha" data-language-autonym="Gaeilge" data-language-local-name="irlandeză" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Bogha-frois" title="Bogha-frois – gaelică scoțiană" lang="gd" hreflang="gd" data-title="Bogha-frois" data-language-autonym="Gàidhlig" data-language-local-name="gaelică scoțiană" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Arco_da_vella" title="Arco da vella – galiciană" lang="gl" hreflang="gl" data-title="Arco da vella" data-language-autonym="Galego" data-language-local-name="galiciană" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Ararok%C3%A1i" title="Ararokái – guarani" lang="gn" hreflang="gn" data-title="Ararokái" data-language-autonym="Avañe'ẽ" data-language-local-name="guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gor mw-list-item"><a href="https://gor.wikipedia.org/wiki/Duhu_lo_butu" title="Duhu lo butu – gorontalo" lang="gor" hreflang="gor" data-title="Duhu lo butu" data-language-autonym="Bahasa Hulontalo" data-language-local-name="gorontalo" class="interlanguage-link-target"><span>Bahasa Hulontalo</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AE%E0%AB%87%E0%AA%98%E0%AA%A7%E0%AA%A8%E0%AB%81%E0%AA%B7" title="મેઘધનુષ – gujarati" lang="gu" hreflang="gu" data-title="મેઘધનુષ" data-language-autonym="ગુજરાતી" data-language-local-name="gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-guc mw-list-item"><a href="https://guc.wikipedia.org/wiki/Kasipoluin" title="Kasipoluin – Wayuu" lang="guc" hreflang="guc" data-title="Kasipoluin" data-language-autonym="Wayuunaiki" data-language-local-name="Wayuu" class="interlanguage-link-target"><span>Wayuunaiki</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Goal_twoaie" title="Goal twoaie – manx" lang="gv" hreflang="gv" data-title="Goal twoaie" data-language-autonym="Gaelg" data-language-local-name="manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Bakan_gizo" title="Bakan gizo – hausa" lang="ha" hreflang="ha" data-title="Bakan gizo" data-language-autonym="Hausa" data-language-local-name="hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Thi%C3%AAn-ki%C3%BBng" title="Thiên-kiûng – chineză hakka" lang="hak" hreflang="hak" data-title="Thiên-kiûng" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="chineză hakka" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A9%D7%AA_%D7%91%D7%A2%D7%A0%D7%9F" title="קשת בענן – ebraică" lang="he" hreflang="he" data-title="קשת בענן" data-language-autonym="עברית" data-language-local-name="ebraică" 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%87%E0%A4%A8%E0%A5%8D%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%A7%E0%A4%A8%E0%A5%81%E0%A4%B7" title="इन्द्रधनुष – hindi" lang="hi" hreflang="hi" data-title="इन्द्रधनुष" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Duga" title="Duga – croată" lang="hr" hreflang="hr" data-title="Duga" data-language-autonym="Hrvatski" data-language-local-name="croată" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Tu%C4%8Del" title="Tučel – sorabă de sus" lang="hsb" hreflang="hsb" data-title="Tučel" data-language-autonym="Hornjoserbsce" data-language-local-name="sorabă de sus" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Lakansy%C3%A8l" title="Lakansyèl – haitiană" lang="ht" hreflang="ht" data-title="Lakansyèl" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiană" 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/Sziv%C3%A1rv%C3%A1ny_(optika)" title="Szivárvány (optika) – maghiară" lang="hu" hreflang="hu" data-title="Szivárvány (optika)" data-language-autonym="Magyar" data-language-local-name="maghiară" 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%BE%D5%AB%D5%A1%D5%AE%D5%A1%D5%B6" title="Ծիածան – armeană" lang="hy" hreflang="hy" data-title="Ծիածան" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Iride" title="Iride – interlingua" lang="ia" hreflang="ia" data-title="Iride" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Endaraja" title="Endaraja – iban" lang="iba" hreflang="iba" data-title="Endaraja" data-language-autonym="Jaku Iban" data-language-local-name="iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pelangi" title="Pelangi – indoneziană" lang="id" hreflang="id" data-title="Pelangi" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ik mw-list-item"><a href="https://ik.wikipedia.org/wiki/Nigatchiaq" title="Nigatchiaq – inupiak" lang="ik" hreflang="ik" data-title="Nigatchiaq" data-language-autonym="Iñupiatun" data-language-local-name="inupiak" class="interlanguage-link-target"><span>Iñupiatun</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%A1%D0%B5%D0%BB%D0%B0%D3%80%D0%B0%D0%B4" title="СелаӀад – ingușă" lang="inh" hreflang="inh" data-title="СелаӀад" data-language-autonym="ГӀалгӀай" data-language-local-name="ingușă" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Pluv-arko" title="Pluv-arko – ido" lang="io" hreflang="io" data-title="Pluv-arko" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Regnbogi" title="Regnbogi – islandeză" lang="is" hreflang="is" data-title="Regnbogi" data-language-autonym="Íslenska" data-language-local-name="islandeză" 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/Arcobaleno" title="Arcobaleno – italiană" lang="it" hreflang="it" data-title="Arcobaleno" data-language-autonym="Italiano" data-language-local-name="italiană" 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/%E8%99%B9" title="虹 – japoneză" lang="ja" hreflang="ja" data-title="虹" data-language-autonym="日本語" data-language-local-name="japoneză" 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/Kluwung" title="Kluwung – javaneză" lang="jv" hreflang="jv" data-title="Kluwung" data-language-autonym="Jawa" data-language-local-name="javaneză" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AA%E1%83%98%E1%83%A1%E1%83%90%E1%83%A0%E1%83%A2%E1%83%A7%E1%83%94%E1%83%9A%E1%83%90" title="ცისარტყელა – georgiană" lang="ka" hreflang="ka" data-title="ცისარტყელა" data-language-autonym="ქართული" data-language-local-name="georgiană" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/T%C9%A9%C5%8Bga%C9%A3y%CA%8B_(Arc-en-ciel)" title="Tɩŋgaɣyʋ (Arc-en-ciel) – Kabiye" lang="kbp" hreflang="kbp" data-title="Tɩŋgaɣyʋ (Arc-en-ciel)" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kge mw-list-item"><a href="https://kge.wikipedia.org/wiki/Runih" title="Runih – Komering" lang="kge" hreflang="kge" data-title="Runih" data-language-autonym="Kumoring" data-language-local-name="Komering" class="interlanguage-link-target"><span>Kumoring</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%B5%D0%BC%D0%BF%D1%96%D1%80%D2%9B%D0%BE%D1%81%D0%B0%D2%9B" title="Кемпірқосақ – kazahă" lang="kk" hreflang="kk" data-title="Кемпірқосақ" data-language-autonym="Қазақша" data-language-local-name="kazahă" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%A5%E1%9E%93%E1%9F%92%E1%9E%91%E1%9E%92%E1%9E%93%E1%9E%BC" title="ឥន្ទធនូ – khmeră" lang="km" hreflang="km" data-title="ឥន្ទធនូ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmeră" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AE%E0%B2%B3%E0%B3%86%E0%B2%AC%E0%B2%BF%E0%B2%B2%E0%B3%8D%E0%B2%B2%E0%B3%81" title="ಮಳೆಬಿಲ್ಲು – kannada" lang="kn" hreflang="kn" data-title="ಮಳೆಬಿಲ್ಲು" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AC%B4%EC%A7%80%EA%B0%9C" title="무지개 – coreeană" lang="ko" hreflang="ko" data-title="무지개" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-koi mw-list-item"><a href="https://koi.wikipedia.org/wiki/%D0%95%D0%BD%D3%A7%D1%88%D0%BA%D0%B0" title="Енӧшка – komi-permiak" lang="koi" hreflang="koi" data-title="Енӧшка" data-language-autonym="Перем коми" data-language-local-name="komi-permiak" class="interlanguage-link-target"><span>Перем коми</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%D8%B3%DB%84%D9%86%D9%9B%D8%B2%D9%8E%D9%84" title="سۄنٛزَل – cașmiră" lang="ks" hreflang="ks" data-title="سۄنٛزَل" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="cașmiră" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Keskesor" title="Keskesor – kurdă" lang="ku" hreflang="ku" data-title="Keskesor" data-language-autonym="Kurdî" data-language-local-name="kurdă" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kv mw-list-item"><a href="https://kv.wikipedia.org/wiki/%D3%A6%D1%88%D0%BA%D0%B0%D0%BC%D3%A7%D1%88%D0%BA%D0%B0" title="Ӧшкамӧшка – komi" lang="kv" hreflang="kv" data-title="Ӧшкамӧшка" data-language-autonym="Коми" data-language-local-name="komi" class="interlanguage-link-target"><span>Коми</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D3%A9%D0%BA%D0%B6%D0%B5%D0%BB%D0%B5" title="Көкжеле – kârgâză" lang="ky" hreflang="ky" data-title="Көкжеле" data-language-autonym="Кыргызча" data-language-local-name="kârgâză" 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/Arcus_caelestis" title="Arcus caelestis – latină" lang="la" hreflang="la" data-title="Arcus caelestis" data-language-autonym="Latina" data-language-local-name="latină" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Raengerbaog" title="Raengerbaog – limburgheză" lang="li" hreflang="li" data-title="Raengerbaog" data-language-autonym="Limburgs" data-language-local-name="limburgheză" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/%C3%86rcubalen" title="Ærcubalen – liguriană" lang="lij" hreflang="lij" data-title="Ærcubalen" data-language-autonym="Ligure" data-language-local-name="liguriană" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lld mw-list-item"><a href="https://lld.wikipedia.org/wiki/Ercabuan" title="Ercabuan – Ladin" lang="lld" hreflang="lld" data-title="Ercabuan" data-language-autonym="Ladin" data-language-local-name="Ladin" class="interlanguage-link-target"><span>Ladin</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Arcobalen" title="Arcobalen – Lombard" lang="lmo" hreflang="lmo" data-title="Arcobalen" 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%AE%E0%BA%B8%E0%BB%89%E0%BA%87" title="ຮຸ້ງ – laoțiană" lang="lo" hreflang="lo" data-title="ຮຸ້ງ" data-language-autonym="ລາວ" data-language-local-name="laoțiană" 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/Vaivoryk%C5%A1t%C4%97" title="Vaivorykštė – lituaniană" lang="lt" hreflang="lt" data-title="Vaivorykštė" data-language-autonym="Lietuvių" data-language-local-name="lituaniană" 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/Varav%C4%ABksne" title="Varavīksne – letonă" lang="lv" hreflang="lv" data-title="Varavīksne" data-language-autonym="Latviešu" data-language-local-name="letonă" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%87%E0%A4%A8%E0%A5%8D%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%A7%E0%A4%A8%E0%A5%81%E0%A4%B7" title="इन्द्रधनुष – maithili" lang="mai" hreflang="mai" data-title="इन्द्रधनुष" data-language-autonym="मैथिली" data-language-local-name="maithili" class="interlanguage-link-target"><span>मैथिली</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Avana" title="Avana – malgașă" lang="mg" hreflang="mg" data-title="Avana" data-language-autonym="Malagasy" data-language-local-name="malgașă" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%A8%D0%BE%D0%BD%D0%B0%D0%BD%D0%BF%D1%8B%D0%BB" title="Шонанпыл – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Шонанпыл" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mi mw-list-item"><a href="https://mi.wikipedia.org/wiki/K%C5%8Dpere" title="Kōpere – maori" lang="mi" hreflang="mi" data-title="Kōpere" data-language-autonym="Māori" data-language-local-name="maori" class="interlanguage-link-target"><span>Māori</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%92%D0%B8%D0%BD%D0%BE%D0%B6%D0%B8%D1%82%D0%BE" title="Виножито – macedoneană" lang="mk" hreflang="mk" data-title="Виножито" data-language-autonym="Македонски" data-language-local-name="macedoneană" 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%AE%E0%B4%B4%E0%B4%B5%E0%B4%BF%E0%B4%B2%E0%B5%8D%E0%B4%B2%E0%B5%8D" title="മഴവില്ല് – malayalam" lang="ml" hreflang="ml" data-title="മഴവില്ല്" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A1%D0%BE%D0%BB%D0%BE%D0%BD%D0%B3%D0%BE" title="Солонго – mongolă" lang="mn" hreflang="mn" data-title="Солонго" data-language-autonym="Монгол" data-language-local-name="mongolă" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mnw mw-list-item"><a href="https://mnw.wikipedia.org/wiki/%E1%80%93%E1%80%99%E1%81%9A%E1%80%BA%E1%80%9E%E1%80%AF%E1%81%9A%E1%80%BA%E1%80%8D%E1%80%AC%E1%80%BA" title="ဓမၚ်သုၚ်ဍာ် – Mon" lang="mnw" hreflang="mnw" data-title="ဓမၚ်သုၚ်ဍာ်" data-language-autonym="ဘာသာမန်" data-language-local-name="Mon" class="interlanguage-link-target"><span>ဘာသာမန်</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%87%E0%A4%82%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%A7%E0%A4%A8%E0%A5%81%E0%A4%B7%E0%A5%8D%E0%A4%AF" title="इंद्रधनुष्य – marathi" lang="mr" hreflang="mr" data-title="इंद्रधनुष्य" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-mrj mw-list-item"><a href="https://mrj.wikipedia.org/wiki/%D0%A8%D0%B0%D0%BD%D0%B0%D0%B2%D3%B9%D0%BB" title="Шанавӹл – Western Mari" lang="mrj" hreflang="mrj" data-title="Шанавӹл" data-language-autonym="Кырык мары" data-language-local-name="Western Mari" class="interlanguage-link-target"><span>Кырык мары</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pelangi" title="Pelangi – malaeză" lang="ms" hreflang="ms" data-title="Pelangi" data-language-autonym="Bahasa Melayu" data-language-local-name="malaeză" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%80%E1%80%BA%E1%80%90%E1%80%B6" title="သက်တံ – birmană" lang="my" hreflang="my" data-title="သက်တံ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmană" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%9F%D0%B8%D0%B7%D0%B5%D0%BC%D0%B5%D1%87%D0%B8%D1%80%D1%8C%D0%BA%D0%B5" title="Пиземечирьке – erzya" lang="myv" hreflang="myv" data-title="Пиземечирьке" data-language-autonym="Эрзянь" data-language-local-name="erzya" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-nah mw-list-item"><a href="https://nah.wikipedia.org/wiki/Cozamalotl" title="Cozamalotl – Nahuatl" lang="nah" hreflang="nah" data-title="Cozamalotl" data-language-autonym="Nāhuatl" data-language-local-name="Nahuatl" class="interlanguage-link-target"><span>Nāhuatl</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%87%E0%A4%A8%E0%A5%8D%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A5%87%E0%A4%A3%E0%A5%80" title="इन्द्रेणी – nepaleză" lang="ne" hreflang="ne" data-title="इन्द्रेणी" data-language-autonym="नेपाली" data-language-local-name="nepaleză" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BE%E0%A4%AF%E0%A5%87%E0%A4%B2%E0%A4%BE%E0%A4%AE%E0%A4%BE" title="लायेलामा – newari" lang="new" hreflang="new" data-title="लायेलामा" data-language-autonym="नेपाल भाषा" data-language-local-name="newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Regenboog_(optica)" title="Regenboog (optica) – neerlandeză" lang="nl" hreflang="nl" data-title="Regenboog (optica)" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" 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/Regnboge" title="Regnboge – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Regnboge" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană 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/Regnbue" title="Regnbue – norvegiană bokmål" lang="nb" hreflang="nb" data-title="Regnbue" data-language-autonym="Norsk bokmål" data-language-local-name="norvegiană 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/Arc_de_Sant_Martin" title="Arc de Sant Martin – occitană" lang="oc" hreflang="oc" data-title="Arc de Sant Martin" data-language-autonym="Occitan" data-language-local-name="occitană" 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/Sabbata_Waqaa" title="Sabbata Waqaa – oromo" lang="om" hreflang="om" data-title="Sabbata Waqaa" data-language-autonym="Oromoo" data-language-local-name="oromo" 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%B8%E0%A8%A4%E0%A8%B0%E0%A9%B0%E0%A8%97%E0%A9%80_%E0%A8%AA%E0%A9%80%E0%A8%82%E0%A8%98" title="ਸਤਰੰਗੀ ਪੀਂਘ – punjabi" lang="pa" hreflang="pa" data-title="ਸਤਰੰਗੀ ਪੀਂਘ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pam mw-list-item"><a href="https://pam.wikipedia.org/wiki/Pinanari" title="Pinanari – pampanga" lang="pam" hreflang="pam" data-title="Pinanari" data-language-autonym="Kapampangan" data-language-local-name="pampanga" class="interlanguage-link-target"><span>Kapampangan</span></a></li><li class="interlanguage-link interwiki-pdc mw-list-item"><a href="https://pdc.wikipedia.org/wiki/Reggebogge" title="Reggebogge – Pennsylvania German" lang="pdc" hreflang="pdc" data-title="Reggebogge" data-language-autonym="Deitsch" data-language-local-name="Pennsylvania German" class="interlanguage-link-target"><span>Deitsch</span></a></li><li class="interlanguage-link interwiki-pl badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://pl.wikipedia.org/wiki/T%C4%99cza" title="Tęcza – poloneză" lang="pl" hreflang="pl" data-title="Tęcza" data-language-autonym="Polski" data-language-local-name="poloneză" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B3%D8%AA_%D8%B1%D9%86%DA%AF%DB%8C_%D9%BE%DB%8C%D9%86%DA%AF%DA%BE" title="ست رنگی پینگھ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ست رنگی پینگھ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B4%D9%86%D9%87_%D8%B2%D8%B1%D8%BA%D9%88%D9%86%D9%87" title="شنه زرغونه – paștună" lang="ps" hreflang="ps" data-title="شنه زرغونه" data-language-autonym="پښتو" data-language-local-name="paștună" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Arco-%C3%ADris" title="Arco-íris – portugheză" lang="pt" hreflang="pt" data-title="Arco-íris" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-pwn mw-list-item"><a href="https://pwn.wikipedia.org/wiki/quljivangraw" title="quljivangraw – Paiwan" lang="pwn" hreflang="pwn" data-title="quljivangraw" data-language-autonym="Pinayuanan" data-language-local-name="Paiwan" class="interlanguage-link-target"><span>Pinayuanan</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/K%27uychi" title="K'uychi – quechua" lang="qu" hreflang="qu" data-title="K'uychi" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/Curcubeu" title="Curcubeu – aromână" lang="rup" hreflang="rup" data-title="Curcubeu" data-language-autonym="Armãneashti" data-language-local-name="aromână" class="interlanguage-link-target"><span>Armãneashti</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%83%D0%B3%D0%B0" title="Радуга – rusă" lang="ru" hreflang="ru" data-title="Радуга" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9A%D1%83%D1%81%D1%82%D1%83%D0%BA" title="Кустук – sakha" lang="sah" hreflang="sah" data-title="Кустук" data-language-autonym="Саха тыла" data-language-local-name="sakha" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%9E%E1%B1%A4%E1%B1%B4%E1%B1%9F%E1%B1%B9_%E1%B1%9F%E1%B1%9C" title="ᱞᱤᱴᱟᱹ ᱟᱜ – santali" lang="sat" hreflang="sat" data-title="ᱞᱤᱴᱟᱹ ᱟᱜ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="santali" class="interlanguage-link-target"><span>ᱥᱟᱱᱛᱟᱲᱤ</span></a></li><li class="interlanguage-link interwiki-scn badge-Q17437796 badge-featuredarticle mw-list-item" title="articol de calitate"><a href="https://scn.wikipedia.org/wiki/Arcu_di_Nuv%C3%A8" title="Arcu di Nuvè – siciliană" lang="scn" hreflang="scn" data-title="Arcu di Nuvè" data-language-autonym="Sicilianu" data-language-local-name="siciliană" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D9%86%DA%8A%D9%84%D9%BA" title="انڊلٺ – sindhi" lang="sd" hreflang="sd" data-title="انڊلٺ" data-language-autonym="سنڌي" data-language-local-name="sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Duga" title="Duga – sârbo-croată" lang="sh" hreflang="sh" data-title="Duga" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="sârbo-croată" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Tislit_n_un%E1%BA%93a%E1%B9%9B" title="Tislit n unẓaṛ – tachelhit" lang="shi" hreflang="shi" data-title="Tislit n unẓaṛ" data-language-autonym="Taclḥit" data-language-local-name="tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AF%E0%B7%9A%E0%B6%AF%E0%B7%94%E0%B6%B1%E0%B7%8A%E0%B6%B1" title="දේදුන්න – singhaleză" lang="si" hreflang="si" data-title="දේදුන්න" data-language-autonym="සිංහල" data-language-local-name="singhaleză" 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/Rainbow" title="Rainbow – Simple English" lang="en-simple" hreflang="en-simple" data-title="Rainbow" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/D%C3%BAha" title="Dúha – slovacă" lang="sk" hreflang="sk" data-title="Dúha" data-language-autonym="Slovenčina" data-language-local-name="slovacă" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Mavrica" title="Mavrica – slovenă" lang="sl" hreflang="sl" data-title="Mavrica" data-language-autonym="Slovenščina" data-language-local-name="slovenă" 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/Murarabungu" title="Murarabungu – shona" lang="sn" hreflang="sn" data-title="Murarabungu" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Qaansa_Roobaad" title="Qaansa Roobaad – somaleză" lang="so" hreflang="so" data-title="Qaansa Roobaad" data-language-autonym="Soomaaliga" data-language-local-name="somaleză" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Ylberi" title="Ylberi – albaneză" lang="sq" hreflang="sq" data-title="Ylberi" data-language-autonym="Shqip" data-language-local-name="albaneză" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D1%83%D0%B3%D0%B0" title="Дуга – sârbă" lang="sr" hreflang="sr" data-title="Дуга" data-language-autonym="Српски / srpski" data-language-local-name="sârbă" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Rienbooge" title="Rienbooge – Saterland Frisian" lang="stq" hreflang="stq" data-title="Rienbooge" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Kuwung-kuwung" title="Kuwung-kuwung – sundaneză" lang="su" hreflang="su" data-title="Kuwung-kuwung" data-language-autonym="Sunda" data-language-local-name="sundaneză" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Regnb%C3%A5ge" title="Regnbåge – suedeză" lang="sv" hreflang="sv" data-title="Regnbåge" data-language-autonym="Svenska" data-language-local-name="suedeză" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Upinde_wa_mvua" title="Upinde wa mvua – swahili" lang="sw" hreflang="sw" data-title="Upinde wa mvua" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Dynga" title="Dynga – Silesian" lang="szl" hreflang="szl" data-title="Dynga" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-szy mw-list-item"><a href="https://szy.wikipedia.org/wiki/bihkac_ni_Edek" title="bihkac ni Edek – Sakizaya" lang="szy" hreflang="szy" data-title="bihkac ni Edek" data-language-autonym="Sakizaya" data-language-local-name="Sakizaya" class="interlanguage-link-target"><span>Sakizaya</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%BE%E0%AE%A9%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AF%8D" title="வானவில் – tamilă" lang="ta" hreflang="ta" data-title="வானவில்" data-language-autonym="தமிழ்" data-language-local-name="tamilă" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tay mw-list-item"><a href="https://tay.wikipedia.org/wiki/hongu%27_utux" title="hongu' utux – Tayal" lang="tay" hreflang="tay" data-title="hongu' utux" data-language-autonym="Tayal" data-language-local-name="Tayal" class="interlanguage-link-target"><span>Tayal</span></a></li><li class="interlanguage-link interwiki-tcy mw-list-item"><a href="https://tcy.wikipedia.org/wiki/%E0%B2%85%E0%B2%9C%E0%B3%8D%E0%B2%9C%E0%B2%AC%E0%B2%BF%E0%B2%B0%E0%B3%81" title="ಅಜ್ಜಬಿರು – Tulu" lang="tcy" hreflang="tcy" data-title="ಅಜ್ಜಬಿರು" data-language-autonym="ತುಳು" data-language-local-name="Tulu" class="interlanguage-link-target"><span>ತುಳು</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%87%E0%B0%82%E0%B0%A6%E0%B1%8D%E0%B0%B0%E0%B0%A7%E0%B0%A8%E0%B1%81%E0%B0%B8%E0%B1%8D%E0%B0%B8%E0%B1%81" title="ఇంద్రధనుస్సు – telugu" lang="te" hreflang="te" data-title="ఇంద్రధనుస్సు" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A2%D0%B8%D1%80%D1%83%D0%BA%D0%B0%D0%BC%D0%BE%D0%BD" title="Тирукамон – tadjică" lang="tg" hreflang="tg" data-title="Тирукамон" data-language-autonym="Тоҷикӣ" data-language-local-name="tadjică" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B8%E0%B9%89%E0%B8%87%E0%B8%81%E0%B8%B4%E0%B8%99%E0%B8%99%E0%B9%89%E0%B8%B3" title="รุ้งกินน้ำ – thailandeză" lang="th" hreflang="th" data-title="รุ้งกินน้ำ" data-language-autonym="ไทย" data-language-local-name="thailandeză" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Bahaghari" title="Bahaghari – tagalog" lang="tl" hreflang="tl" data-title="Bahaghari" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/G%C3%B6kku%C5%9Fa%C4%9F%C4%B1" title="Gökkuşağı – turcă" lang="tr" hreflang="tr" data-title="Gökkuşağı" data-language-autonym="Türkçe" data-language-local-name="turcă" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-trv mw-list-item"><a href="https://trv.wikipedia.org/wiki/Hakaw_utux" title="Hakaw utux – taroko" lang="trv" hreflang="trv" data-title="Hakaw utux" data-language-autonym="Seediq" data-language-local-name="taroko" class="interlanguage-link-target"><span>Seediq</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Kwangalatilo" title="Kwangalatilo – tsonga" lang="ts" hreflang="ts" data-title="Kwangalatilo" data-language-autonym="Xitsonga" data-language-local-name="tsonga" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BB%D0%B0%D0%B2%D0%B0%D1%82_%D0%BA%D2%AF%D0%BF%D0%B5%D1%80%D0%B5" title="Салават күпере – tătară" lang="tt" hreflang="tt" data-title="Салават күпере" data-language-autonym="Татарча / tatarça" data-language-local-name="tătară" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B5%D1%81%D0%B5%D0%BB%D0%BA%D0%B0" title="Веселка – ucraineană" lang="uk" hreflang="uk" data-title="Веселка" data-language-autonym="Українська" data-language-local-name="ucraineană" 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%AF%DA%BE%D9%86%DA%A9" title="دھنک – urdu" lang="ur" hreflang="ur" data-title="دھنک" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kamalak" title="Kamalak – uzbecă" lang="uz" hreflang="uz" data-title="Kamalak" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecă" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Arconb%C3%A8" title="Arconbè – venetă" lang="vec" hreflang="vec" data-title="Arconbè" data-language-autonym="Vèneto" data-language-local-name="venetă" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Jumalanbembel%27" title="Jumalanbembel' – Veps" lang="vep" hreflang="vep" data-title="Jumalanbembel'" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/C%E1%BA%A7u_v%E1%BB%93ng" title="Cầu vồng – vietnameză" lang="vi" hreflang="vi" data-title="Cầu vồng" data-language-autonym="Tiếng Việt" data-language-local-name="vietnameză" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Airdi%C3%A8" title="Airdiè – valonă" lang="wa" hreflang="wa" data-title="Airdiè" data-language-autonym="Walon" data-language-local-name="valonă" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Balangaw" title="Balangaw – waray" lang="war" hreflang="war" data-title="Balangaw" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%B1%9F" title="鱟 – chineză wu" lang="wuu" hreflang="wuu" data-title="鱟" data-language-autonym="吴语" data-language-local-name="chineză wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A8%D7%A2%D7%92%D7%A0%D7%91%D7%95%D7%99%D7%92%D7%9F" title="רעגנבויגן – idiș" lang="yi" hreflang="yi" data-title="רעגנבויגן" data-language-autonym="ייִדיש" data-language-local-name="idiș" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Saihoengz" title="Saihoengz – zhuang" lang="za" hreflang="za" data-title="Saihoengz" data-language-autonym="Vahcuengh" data-language-local-name="zhuang" class="interlanguage-link-target"><span>Vahcuengh</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BD%A9%E8%99%B9" title="彩虹 – chineză" lang="zh" hreflang="zh" data-title="彩虹" data-language-autonym="中文" data-language-local-name="chineză" 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/%E8%9E%AE%E8%9D%80" title="螮蝀 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="螮蝀" 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/Kh%C4%93ng" title="Khēng – chineză min nan" lang="nan" hreflang="nan" data-title="Khēng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="chineză min nan" 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/%E8%99%B9" title="虹 – cantoneză" lang="yue" hreflang="yue" data-title="虹" data-language-autonym="粵語" data-language-local-name="cantoneză" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1052#sitelinks-wikipedia" title="Modifică legăturile interlinguale" class="wbc-editpage">Modifică 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class="cdx-message cdx-message--block cdx-message--warning mw-revision"><span class="cdx-message__icon"></span><div class="cdx-message__content"><div id="mw-revision-info"><div id="viewingold-warning" class="plainlinks" style="background: #FFC; border: 1px solid #C88; color: #000000; font-weight: bold; margin: 2em 0 .5em; padding: .5em 1em; vertical-align: middle; clear: both;">Aceasta este o <a class="external text" href="https://ro.wikipedia.org/w/index.php?title=Curcubeu&action=history">versiune arhivată</a> a paginii, în urma modificării de către <span id="mw-revision-name"><a href="/wiki/Utilizator:Gdaniel111" class="mw-userlink" title="Utilizator:Gdaniel111" data-mw-revid="16567135"><bdi>Gdaniel111</bdi></a> <span class="mw-usertoollinks">(<a href="/wiki/Discu%C8%9Bie_Utilizator:Gdaniel111" class="mw-usertoollinks-talk" title="Discuție Utilizator:Gdaniel111">discuție</a> | <a href="/wiki/Special:Contribu%C8%9Bii/Gdaniel111" class="mw-usertoollinks-contribs" 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Diferențele față de <a class="external text" href="https://ro.wikipedia.org/wiki/Curcubeu">versiunea curentă</a> pot fi semnificative.</div> <div id="viewingold-plain" style="display:none;">Versiune creată de <a href="/wiki/Utilizator:Gdaniel111" class="mw-userlink" title="Utilizator:Gdaniel111" data-mw-revid="16567135"><bdi>Gdaniel111</bdi></a> <span class="mw-usertoollinks">(<a href="/wiki/Discu%C8%9Bie_Utilizator:Gdaniel111" class="mw-usertoollinks-talk" title="Discuție Utilizator:Gdaniel111">discuție</a> | <a href="/wiki/Special:Contribu%C8%9Bii/Gdaniel111" class="mw-usertoollinks-contribs" title="Special:Contribuții/Gdaniel111">contribuții</a>)</span> la 14 octombrie 2024 16:45</div></div><div id="mw-revision-nav">(<a href="/w/index.php?title=Curcubeu&diff=prev&oldid=16567135" title="Curcubeu">dif</a>) <a href="/w/index.php?title=Curcubeu&direction=prev&oldid=16567135" title="Curcubeu">← Versiunea anterioară</a> | afișează versiunea curentă (dif) | Versiunea următoare → (dif)</div></div></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ro" dir="ltr"><div role="note" class="dezambiguizare">Pentru alte sensuri, vedeți <a href="/wiki/Curcubeu_(dezambiguizare)" class="mw-disambig" title="Curcubeu (dezambiguizare)">Curcubeu (dezambiguizare)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Ring-billed_gull_and_a_rainbow_(52910).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Ring-billed_gull_and_a_rainbow_%2852910%29.jpg/290px-Ring-billed_gull_and_a_rainbow_%2852910%29.jpg" decoding="async" width="290" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Ring-billed_gull_and_a_rainbow_%2852910%29.jpg/435px-Ring-billed_gull_and_a_rainbow_%2852910%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Ring-billed_gull_and_a_rainbow_%2852910%29.jpg/580px-Ring-billed_gull_and_a_rainbow_%2852910%29.jpg 2x" data-file-width="4608" data-file-height="3456" /></a><figcaption>Un pescăruș zboară pe lângă un curcubeu deasupra cascadei Horseshoe</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Cetate_Fagaras.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Cetate_Fagaras.jpg/290px-Cetate_Fagaras.jpg" decoding="async" width="290" height="193" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Cetate_Fagaras.jpg/435px-Cetate_Fagaras.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Cetate_Fagaras.jpg/580px-Cetate_Fagaras.jpg 2x" data-file-width="5165" data-file-height="3442" /></a><figcaption>Curcubeu deasupra <a href="/wiki/Cetatea_F%C4%83g%C4%83ra%C8%99ului" title="Cetatea Făgărașului">Cetății Făgărașului</a></figcaption></figure> <p><b>Curcubeul</b> este un fenomen <a href="/wiki/Optic%C4%83" title="Optică">optic</a> și <a href="/wiki/Meteorologie" title="Meteorologie">meteorologic</a> atmosferic care se manifestă prin apariția pe cer a unui <a href="/wiki/Spectru" class="mw-disambig" title="Spectru">spectru</a> de forma unui arc <a href="/wiki/Culoare" title="Culoare">colorat</a> atunci când <a href="/wiki/Lumin%C4%83" title="Lumină">lumina</a> <a href="/wiki/Soare" title="Soare">soarelui</a> se refractă în picăturile de <a href="/wiki/Ap%C4%83" title="Apă">apă</a> din <a href="/wiki/Atmosfer%C4%83" title="Atmosferă">atmosferă</a>. De cele mai multe ori curcubeul <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> se observă după <a href="/wiki/Ploaie" title="Ploaie">ploaie</a>, când soarele este apropiat de <a href="/wiki/Orizont" title="Orizont">orizont</a>. </p><p>În condiții bune de lumină, în fața peretelui de ploaie, un curcubeu secundar este vizibil deasupra curcubeului principal. Acesta este mai slab din cauza dublei <a href="/wiki/Reflexia_luminii" title="Reflexia luminii">reflexii</a> a luminii în picăturile de apă și are o secvență de culori opusă. </p><p>Există mai multe fenomene fizice care stau la baza producerii curcubeului sau care îl pot influența: </p> <ul><li><a href="/wiki/Tensiune_superficial%C4%83" title="Tensiune superficială">Tensiunea superficială</a> face ca picăturile de apă, mai ales cele foarte mici, să fie aproape perfect sferice.</li> <li><a href="/wiki/Refrac%C8%9Bie" title="Refracție">Refracția</a> și <a href="/wiki/Reflexie" class="mw-disambig" title="Reflexie">reflexia</a> luminii explică de ce lumina curcubeului are altă direcție decât lumina de la soare.</li> <li><a href="/wiki/Dispersia_luminii" title="Dispersia luminii">Dispersia luminii</a>, adică dependența <a href="/wiki/Indice_de_refrac%C8%9Bie" title="Indice de refracție">indicelui de refracție</a> al apei de <a href="/wiki/Lungime_de_und%C4%83" title="Lungime de undă">lungimea de undă</a> a luminii, explică de ce curcubeiele sunt colorate și nu doar albe.</li> <li><a href="/wiki/Difrac%C8%9Bie" title="Difracție">Difracția</a> luminii devine semnificativă atunci când picăturile de apă sunt extrem de mici, de ordinul micronilor, deci comparabile cu lungimea de undă (aproximativ 0,5 μm). În acest caz culorile curcubeului se estompează.</li> <li>Dacă picăturile sunt mari și nu se află într-un echilibru care să le asigure forma sferică, efectul de curcubeu fie este redus, fie nu apare.</li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Curcubeul_ca_fenomen_meteorologic">Curcubeul ca fenomen meteorologic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=1" title="Modifică secțiunea: Curcubeul ca fenomen meteorologic" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=1" title="Edit section's source code: Curcubeul ca fenomen meteorologic"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Curcubeiele naturale apar, de obicei, atunci când cerul se înseninează rapid după o ploaie, iar soarele se află la o <a href="/wiki/Altitudine" title="Altitudine">altitudine</a> mică. Din acest motiv, curcubeiele sunt observate de obicei pe cerul vestic, dimineața, și pe cel estic, <a href="/wiki/Sear%C4%83" title="Seară">seara</a>. Totodată, fenomenul nu se poate forma <a href="/wiki/Var%C4%83" title="Vară">vara</a>, la prânz, deoarece soarele se află la punctul maxim pe cer. Cele mai spectaculoase apariții ale curcubeului au loc atunci când jumătate din cer este încă întunecat cu nori de ploaie, iar observatorul se află într-un punct cu cer senin în direcția <a href="/wiki/Soare" title="Soare">Soarelui</a>. Rezultatul este un curcubeu luminos care contrastează cu fundalul întunecat. Se pot observa curcubeie destul de des într-un jet de apă, în special în fântâni si cascade. În cazuri speciale, se pot observa mici curcubeie la capătul valurilor mării. </p> <div class="mw-heading mw-heading2"><h2 id="Lumina_și_curcubeul_ca_fenomene_optice"><span id="Lumina_.C8.99i_curcubeul_ca_fenomene_optice"></span>Lumina și curcubeul ca fenomene optice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=2" title="Modifică secțiunea: Lumina și curcubeul ca fenomene optice" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=2" title="Edit section's source code: Lumina și curcubeul ca fenomene optice"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lumina soarelui reprezintă o mică parte din <a href="/wiki/Spectru_electromagnetic" title="Spectru electromagnetic">spectrul electromagnetic</a>. Atunci când soarele este pe cer, toate părțile spectrului vizibil ajung la suprafața pământului, iar amestecul lor este perceput ca o lumină de zi albicioasă. În cazul în care soarele se află la o înălțime mică pe cer (spre exemplu la <a href="/wiki/R%C4%83s%C4%83rit" title="Răsărit">răsărit</a>), partea cu unde scurte a spectrului solar (definită prin culorile de tip albastru) este mai dispensată în <a href="/wiki/Atmosfer%C4%83" title="Atmosferă">atmosfera</a>, rezultând culoarea roșie a cerului. </p> <div class="mw-heading mw-heading3"><h3 id="Formarea_și_culorile_curcubeului"><span id="Formarea_.C8.99i_culorile_curcubeului"></span>Formarea și culorile curcubeului</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=3" title="Modifică secțiunea: Formarea și culorile curcubeului" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=3" title="Edit section's source code: Formarea și culorile curcubeului"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Frameless"><a href="/wiki/Fi%C8%99ier:Spectru-ROGVAIV.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d7/Spectru-ROGVAIV.png" decoding="async" width="135" height="214" class="mw-file-element" data-file-width="135" data-file-height="214" /></a><figcaption></figcaption></figure> <p>Culorile curcubeului sunt produse prin <a href="/wiki/Dispersia_luminii" title="Dispersia luminii">dispersia</a> luminii solare în picăturile de apă, unde aceasta este descompusă în funcție de lungimea de undă, precum într-o <a href="/wiki/Prism%C4%83_(optic%C4%83)" title="Prismă (optică)">prismă</a> (fenomen pentru prima oară descoperit de <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>). În curcubeu, datorită <a href="/wiki/Interferen%C8%9B%C4%83" title="Interferență">amestecării</a> parțiale a razelor de lumină prin reflexia internă la diferite puncte de pe suprafața sferică a picăturii, culorile apar mai puțin clar separate în comparație cu un spectru luminos produs, spre exemplu, cu ajutorul unui <a href="/wiki/Spectroscop" title="Spectroscop">spectroscop</a> cu prisme. </p><p>Numărul de culori pe care <a href="/wiki/Ochi" title="Ochi">ochiul uman</a> este capabil să le distingă este aproximativ 100. Datorită subiectivității situației, numărul exact de culori principale este o alegere oarecum arbitrară. Așadar, Newton, împărțea inițial spectrul în cinci culori principale: roșu, galben, verde, albastru și violet. Mai târziu a inclus portocaliu și indigo, oferind șapte noi culori (o analogie la filozofia sofiștilor greci, care credeau că există o legătură între culori, notele muzicale si obiectele cunoscute din sistemul solar). De reținut este faptul că, ceea ce Newton considera atunci ca <i>albastru</i> ar fi considerat astăzi drept <i>cian</i> și ceea ce Newton a numit <i>indigo</i> ar fi considerat astăzi <i>albastru</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Curcubeul_principal_ca_fenomen_observabil">Curcubeul principal ca fenomen observabil</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=4" title="Modifică secțiunea: Curcubeul principal ca fenomen observabil" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=4" title="Edit section's source code: Curcubeul principal ca fenomen observabil"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Rainbow_single_reflection.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Rainbow_single_reflection.svg/220px-Rainbow_single_reflection.svg.png" decoding="async" width="220" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Rainbow_single_reflection.svg/330px-Rainbow_single_reflection.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Rainbow_single_reflection.svg/440px-Rainbow_single_reflection.svg.png 2x" data-file-width="340" data-file-height="260" /></a><figcaption>Incidental Rays = razele de la soare Outgoing rays = razele reflectate</figcaption></figure> <p>Pentru observarea curcubeului, observatorul trebuie în primul rând să aibă peretele de apă în fața sa și soarele în spatele său. Atunci când lumina soarelui întâlnește o <a href="/wiki/Pic%C4%83tur%C4%83" title="Picătură">picătură</a> de ploaie, o parte din lumină este reflectată, iar restul se refractă in picătură. Când această lumină atinge partea din spate a picăturii de ploaie, o parte din ea este reflectată în interior și o parte este refractată, ieșind din picătură (Bineînțeles, o parte din razele de lumină deja aflate în picătura de <a href="/wiki/Ap%C4%83" title="Apă">apă</a> se pot reflecta încă odată pe suprafața interioară a picăturii. Aceste fenomene nu sunt relevante pentru formarea curcubeului principal). Pe scurt, se produce un <a href="/wiki/Con" title="Con">con</a> de lumină, la rândul lui format din mai multe conuri de diferite unghiuri pentru fiecare culoare.  În cazul <i>curcubeului principal</i> cu reflexie internă unică, conul de lumină roșu exterior (cel mai puțin deviat) are un <a href="/wiki/Unghi" title="Unghi">unghi</a> de aproximativ <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 2\times 42}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>×</mo> <mn>42</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\times 42}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a88ca075b2aa01350b83131855af37ba03dba646" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.328ex; height:2.176ex;" alt="{\displaystyle 2\times 42}"></span>°, iar conul albastru/violet interior (mai deviat) are un unghi de aproximativ <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 2\times 40.2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>×</mo> <mn>40.2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\times 40.2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ad6cee8189f214518e408e53a255aedc5b4b4d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.137ex; height:2.176ex;" alt="{\displaystyle 2\times 40.2}"></span>°<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>. Aceste diferențe pleacă de la un indice de refracție diferit (se formează de fapt mai multe curcubeie, unul pentru fiecare culoare). În esența, lumina se reflectă pe intervalul <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 40.2^{\circ }\rightarrow 42^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>40.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">→</mo> <msup> <mn>42</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 40.2^{\circ }\rightarrow 42^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97348b19a64dace979945a848f93765eda5e7c95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.182ex; height:2.343ex;" alt="{\displaystyle 40.2^{\circ }\rightarrow 42^{\circ }}"></span>, cu intensitate maxima la <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 42^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>42</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 42^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c79219283c9274e4ad3864c7d9e886ce8177a1dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.379ex; height:2.343ex;" alt="{\displaystyle 42^{\circ }}"></span><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>. Acest interval este independent de dimensiunea picăturii, dar depinde de <a href="/wiki/Indice_de_refrac%C8%9Bie" title="Indice de refracție">indicele de refracție</a> al acestuia. Spre exemplu, raza unui potențial curcubeu format pe <a href="/wiki/Titan_(satelit)" title="Titan (satelit)">Titan</a>, este de aproximativ <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 49^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>49</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 49^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/814a97db7ce0baf15516115b0b9d98b718262d6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.379ex; height:2.343ex;" alt="{\displaystyle 49^{\circ }}"></span>, datorită concentrației mare de <a href="/wiki/Metan" title="Metan">metan</a>. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Reprezentare_geometrica_a_razei_de_lumina..png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Reprezentare_geometrica_a_razei_de_lumina..png/320px-Reprezentare_geometrica_a_razei_de_lumina..png" decoding="async" width="320" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Reprezentare_geometrica_a_razei_de_lumina..png/480px-Reprezentare_geometrica_a_razei_de_lumina..png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Reprezentare_geometrica_a_razei_de_lumina..png/640px-Reprezentare_geometrica_a_razei_de_lumina..png 2x" data-file-width="1043" data-file-height="725" /></a><figcaption></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Deducere_matematică"><span id="Deducere_matematic.C4.83"></span>Deducere matematică</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=5" title="Modifică secțiunea: Deducere matematică" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=5" title="Edit section's source code: Deducere matematică"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Figura din dreapta descrie o rază de lumină ce intră într-o picătură de ploaie la punctul <i>A.</i> Linia <i>AB</i> arată traiectoria părții de lumină ce intră în picătură (se observă faptul că lumina este refractată spre linia <i>AO</i>). Legea Refracției (sau Legea lui Snell) arată că:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \alpha =k\cdot \sin \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mi>k</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \alpha =k\cdot \sin \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41ce0ba73e5bcbf1e0341b19ea3a5cda1ab0a610" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.294ex; height:2.509ex;" alt="{\displaystyle \sin \alpha =k\cdot \sin \beta }"></span>Unde <b>α</b> este <i>unghiul de incidență</i>, <b>β</b> este <i>unghiul de refracție</i> și <b>k</b> este indicele de refracție al picăturii (pentru apa dulce este <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 4/3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4/3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2f29a3dad63994c875d297399d10029b43eda57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.487ex; height:2.843ex;" alt="{\displaystyle 4/3}"></span>). De aici reiese <b>(ecuația 1)</b>:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta \approx \arcsin({\dfrac {3}{4}}\sin \alpha )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>≈</mo> <mi>arcsin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta \approx \arcsin({\dfrac {3}{4}}\sin \alpha )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd82ebc1d23a12f14f554f2da92afe838caa30f0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.318ex; height:5.176ex;" alt="{\displaystyle \beta \approx \arcsin({\dfrac {3}{4}}\sin \alpha )}"></span> Linia <i>BC</i> semnifică partea reflectată a razei (la <i>C</i> se observă că o parte se reflectă înapoi în picătură, această parte nu e semnificativă <i>curcubeului principal</i>). Unghiul <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c00b43fd534dda488ddee0f510c751881645c6ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.221ex; height:2.843ex;" alt="{\displaystyle D(\alpha )}"></span> este <i>unghiul de deviație</i>. Acesta este important pentru calculul următor deoarece: <b>(ecuația 2)</b><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha )=180^{\circ }-r_{\text{curcubeu}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>curcubeu</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha )=180^{\circ }-r_{\text{curcubeu}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c3ef7e48345801907815aee59404c7b6d0c116b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.473ex; height:2.843ex;" alt="{\displaystyle D(\alpha )=180^{\circ }-r_{\text{curcubeu}}}"></span>Considerând două raze solare paralele (prima intrând în peretele de apă și a doua plecând de la observator), ecuația de mai sus e adevărata datorita <i>egalității unghiurilor alterne-interne</i>). Din desen observăm <b>(ecuația 3)</b>:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha )=(\alpha -\beta )+(\pi -2\beta )+(\alpha -\beta )=\pi +2\alpha -4\beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mi>π</mi> <mo>−</mo> <mn>2</mn> <mi>β</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>π</mi> <mo>+</mo> <mn>2</mn> <mi>α</mi> <mo>−</mo> <mn>4</mn> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha )=(\alpha -\beta )+(\pi -2\beta )+(\alpha -\beta )=\pi +2\alpha -4\beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86d8091accf09df55e043abca9b1d80781d87bfb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:52.671ex; height:2.843ex;" alt="{\displaystyle D(\alpha )=(\alpha -\beta )+(\pi -2\beta )+(\alpha -\beta )=\pi +2\alpha -4\beta }"></span>Din <b>(ecuația 1)</b> și <b>(ecuația 2)</b> reiese:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha )=\pi +2\alpha -4\arcsin({\dfrac {3}{4}}\sin \alpha )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>π</mi> <mo>+</mo> <mn>2</mn> <mi>α</mi> <mo>−</mo> <mn>4</mn> <mi>arcsin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha )=\pi +2\alpha -4\arcsin({\dfrac {3}{4}}\sin \alpha )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8750ff26e494ac4a49ac6a338a8bf830feb72088" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:34.419ex; height:5.176ex;" alt="{\displaystyle D(\alpha )=\pi +2\alpha -4\arcsin({\dfrac {3}{4}}\sin \alpha )}"></span> Prin <a href="/wiki/Diferen%C8%9Bial%C4%83" class="mw-redirect" title="Diferențială">diferențiere</a> și utilizând <i>metoda intervalului închis</i> și <a href="/wiki/Teorema_lui_Rolle" title="Teorema lui Rolle">teorema lui Rolle</a> se determină minimul. Minimul este important deoarece atunci razele de lumină au deviația minimă, rezultând concentrația de lumină maximă.<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha )^{\prime }=2-4\left[1-\left({\frac {3}{4}}\sin \alpha \right)^{2}\right]^{-{\dfrac {1}{2}}}\left({\dfrac {3}{4}}\cos \alpha \right)=2-{\frac {3\cos \alpha }{\sqrt {1-{\dfrac {9}{16}}\sin ^{2}\alpha }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <mi>α</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mo>−</mo> <mn>4</mn> <msup> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>9</mn> <mn>16</mn> </mfrac> </mstyle> </mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha )^{\prime }=2-4\left[1-\left({\frac {3}{4}}\sin \alpha \right)^{2}\right]^{-{\dfrac {1}{2}}}\left({\dfrac {3}{4}}\cos \alpha \right)=2-{\frac {3\cos \alpha }{\sqrt {1-{\dfrac {9}{16}}\sin ^{2}\alpha }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9585af37d8acf83ae524303225df861ee80a279b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:70.76ex; height:12.843ex;" alt="{\displaystyle D(\alpha )^{\prime }=2-4\left[1-\left({\frac {3}{4}}\sin \alpha \right)^{2}\right]^{-{\dfrac {1}{2}}}\left({\dfrac {3}{4}}\cos \alpha \right)=2-{\frac {3\cos \alpha }{\sqrt {1-{\dfrac {9}{16}}\sin ^{2}\alpha }}}}"></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c00b43fd534dda488ddee0f510c751881645c6ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.221ex; height:2.843ex;" alt="{\displaystyle D(\alpha )}"></span> este 0 (punct critic) când:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2={\frac {3\cos \alpha }{\sqrt {1-{\dfrac {9}{16}}\sin ^{2}\alpha }}}\Leftrightarrow {\frac {9}{4}}\cos ^{2}\alpha =1-{\frac {9}{16}}\sin ^{2}\alpha \Leftrightarrow \cos \alpha ={\sqrt {\frac {7}{16}}}\Leftrightarrow \alpha =\arccos {\sqrt {\frac {7}{16}}}\approx 59.4^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>9</mn> <mn>16</mn> </mfrac> </mstyle> </mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </msqrt> </mfrac> </mrow> <mo stretchy="false">⇔</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>9</mn> <mn>4</mn> </mfrac> </mrow> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>9</mn> <mn>16</mn> </mfrac> </mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> <mo stretchy="false">⇔</mo> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>7</mn> <mn>16</mn> </mfrac> </msqrt> </mrow> <mo stretchy="false">⇔</mo> <mi>α</mi> <mo>=</mo> <mi>arccos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>7</mn> <mn>16</mn> </mfrac> </msqrt> </mrow> <mo>≈</mo> <msup> <mn>59.4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2={\frac {3\cos \alpha }{\sqrt {1-{\dfrac {9}{16}}\sin ^{2}\alpha }}}\Leftrightarrow {\frac {9}{4}}\cos ^{2}\alpha =1-{\frac {9}{16}}\sin ^{2}\alpha \Leftrightarrow \cos \alpha ={\sqrt {\frac {7}{16}}}\Leftrightarrow \alpha =\arccos {\sqrt {\frac {7}{16}}}\approx 59.4^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f23e5f923e82be3191f0d30efeb0b79b9626b03" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:94.99ex; height:9.843ex;" alt="{\displaystyle 2={\frac {3\cos \alpha }{\sqrt {1-{\dfrac {9}{16}}\sin ^{2}\alpha }}}\Leftrightarrow {\frac {9}{4}}\cos ^{2}\alpha =1-{\frac {9}{16}}\sin ^{2}\alpha \Leftrightarrow \cos \alpha ={\sqrt {\frac {7}{16}}}\Leftrightarrow \alpha =\arccos {\sqrt {\frac {7}{16}}}\approx 59.4^{\circ }}"></span>În concluzie, minimul local este <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(59.4^{\circ })\approx 138^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <msup> <mn>59.4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo>≈</mo> <msup> <mn>138</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(59.4^{\circ })\approx 138^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac6d9a0bd25a7d37b5cde94ea800bedf1c07869" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.562ex; height:2.843ex;" alt="{\displaystyle D(59.4^{\circ })\approx 138^{\circ }}"></span> Pentru a afla minimul global, se verifică valorile la capete. În cazul acesta <i>0</i> si <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 \pi /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi /2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b44e3d874a0b229fded7ffce67a0677dd5b8b67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.657ex; height:2.843ex;" alt="{\displaystyle \pi /2}"></span>. Se observă că:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(59^{\circ })<D(0)\quad \And \quad D(59^{\circ })<D({\dfrac {\pi }{2}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <msup> <mn>59</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo><</mo> <mi>D</mi> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi mathvariant="normal">&</mi> <mspace width="1em" /> <mi>D</mi> <mo stretchy="false">(</mo> <msup> <mn>59</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo><</mo> <mi>D</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(59^{\circ })<D(0)\quad \And \quad D(59^{\circ })<D({\dfrac {\pi }{2}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c62b7833b9a6a2b93e797f6a112e82d0d2f03f7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:37.673ex; height:4.676ex;" alt="{\displaystyle D(59^{\circ })<D(0)\quad \And \quad D(59^{\circ })<D({\dfrac {\pi }{2}})}"></span>În concluzie <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(59.4^{\circ })\approx 138^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <msup> <mn>59.4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo>≈</mo> <msup> <mn>138</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(59.4^{\circ })\approx 138^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac6d9a0bd25a7d37b5cde94ea800bedf1c07869" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.562ex; height:2.843ex;" alt="{\displaystyle D(59.4^{\circ })\approx 138^{\circ }}"></span>este minim global. Pentru a obține <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 r_{\text{curcubeu}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>curcubeu</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{curcubeu}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc97ba0efead24cfa3ee462eed927a5e64188f00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.771ex; height:2.009ex;" alt="{\displaystyle r_{\text{curcubeu}}}"></span>înlocuim în <b>(ecuația 2)</b>:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{\text{curcubeu}}\approx 180^{\circ }-138^{\circ }\approx 42^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>curcubeu</mtext> </mrow> </msub> <mo>≈</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <msup> <mn>138</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>≈</mo> <msup> <mn>42</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{curcubeu}}\approx 180^{\circ }-138^{\circ }\approx 42^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1451d9c5dbbaa9a8fe5cd563ee9947df825ce8ff" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:29.271ex; height:2.676ex;" alt="{\displaystyle r_{\text{curcubeu}}\approx 180^{\circ }-138^{\circ }\approx 42^{\circ }}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Cronologia_explicației_fizice"><span id="Cronologia_explica.C8.9Biei_fizice"></span>Cronologia explicației fizice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=6" title="Modifică secțiunea: Cronologia explicației fizice" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=6" title="Edit section's source code: Cronologia explicației fizice"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Descartes_Rainbow.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Descartes_Rainbow.png/200px-Descartes_Rainbow.png" decoding="async" width="200" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Descartes_Rainbow.png/300px-Descartes_Rainbow.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Descartes_Rainbow.png/400px-Descartes_Rainbow.png 2x" data-file-width="4823" data-file-height="4251" /></a><figcaption>Experimentul optic a lui Descartes.</figcaption></figure> <p>Explicația fizică a curcubeului prezentată mai sus se bazează, în principal, pe lucrările lui <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> publicate în secolul 17. Ele sunt descrise în apendicele <i>Les Météores</i> din tratatul său filosofic <i>Discours de la méthode</i> (Discurs asupra metodei)<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>. Fenomenul <a href="/wiki/Dispersia_luminii" title="Dispersia luminii">dispersiei</a> nu era cunoscut pe vremea lui Descartes, motiv pentru care modul în care acesta a explicat culorile în lucrarea sa este ușor eronat (de reținut ca derivarea matematica a lui Descartes este corectă). </p><p>În 1700, <a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a> a scris o lucrare despre curcubeu<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>, iar în 1704, teoria luminii a lui Isaac Newton a adus în discuție dispersia, făcând astfel inteligibilă splendoarea culorilor. </p><p>Pe vremea lui Newton, nu se știa sigur dacă lumina avea caracter ondulatoriu sau corpuscular. Această enigmă l-a determinat pe <a href="/wiki/Thomas_Young" title="Thomas Young">Thomas Young</a> să realizeze <a href="/wiki/Experimentul_celor_dou%C4%83_fante" title="Experimentul celor două fante">Experimentul celor două fante</a>. El a demonstrat astfel natura ondulatorie a luminii, iar ulterior a reușit să rezolve enigma luând în considerare fenomenul de interferență. </p><p>Descrierile fizice moderne se bazează în principal pe teoria dezvoltată de <a href="/w/index.php?title=Gustav_Mie&action=edit&redlink=1" class="new" title="Gustav Mie — pagină inexistentă">Gustav Mie</a><sup><small>⁠(<a href="https://www.wikidata.org/wiki/Q67020" class="extiw" title="d:Q67020"><span title="Gustav Mie la Wikidata">d</span></a>)</small></sup> în 1908 și denumită după el dispersia Mie. </p> <div class="mw-heading mw-heading2"><h2 id="Variații"><span id="Varia.C8.9Bii"></span>Variații</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=7" title="Modifică secțiunea: Variații" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=7" title="Edit section's source code: Variații"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Double-alaskan-rainbow.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Double-alaskan-rainbow.jpg/250px-Double-alaskan-rainbow.jpg" decoding="async" width="250" height="131" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Double-alaskan-rainbow.jpg/375px-Double-alaskan-rainbow.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Double-alaskan-rainbow.jpg/500px-Double-alaskan-rainbow.jpg 2x" data-file-width="1919" data-file-height="1008" /></a><figcaption>Curcubeu dublu în <a href="/wiki/Alaska" title="Alaska">Alaska</a> </figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Curcubeul_dublu">Curcubeul dublu</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=8" title="Modifică secțiunea: Curcubeul dublu" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=8" title="Edit section's source code: Curcubeul dublu"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Termenul de curcubeu dublu este folosit atunci când arcul format de razele dublu reflectate din picătura de apă, este vizibil lângă curcubeul principal. Acesta este întotdeauna format, ba chiar exista teoretic o infinitate de curcubeie pe lângă cel principal. În practică, datorită slabei concentrații de lumină după prima reflexie, și datorită răspândirii mai mari pe suprafața cerului, curcubeul secundar poate fi observat doar în cazuri speciale. Acesta are ordinea culorilor inversată deoarece, dacă la curcubeul principal unghiul arcului scădea de la rosu la albastru, in cazul acesta creste de la rosu la albastru. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fi%C8%99ier:Curcubeu_Dublu_fotografiat_la_Vatra_Dornei.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Curcubeu_Dublu_fotografiat_la_Vatra_Dornei.jpg/250px-Curcubeu_Dublu_fotografiat_la_Vatra_Dornei.jpg" decoding="async" width="250" height="130" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Curcubeu_Dublu_fotografiat_la_Vatra_Dornei.jpg/375px-Curcubeu_Dublu_fotografiat_la_Vatra_Dornei.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Curcubeu_Dublu_fotografiat_la_Vatra_Dornei.jpg/500px-Curcubeu_Dublu_fotografiat_la_Vatra_Dornei.jpg 2x" data-file-width="4000" data-file-height="2082" /></a><figcaption>Curcubeu Dublu fotografiat la Vatra Dornei</figcaption></figure> <p>Dacă urmărim imaginea de mai sus in care e explicată formarea curcubeului principal (vezi. <i>Derivare Matematică</i>), ne putem imagina un nou drum a razei, in care aceasta se refractă in <b>A</b>, se reflectă in <b>B</b>, se reflectă in <b>C</b> si se refractă afară din picătură la un punct <b>D</b>, (daca respectam proporțiile desenului, acesta va fi intre A si C). Observăm ca in punctul C se schimbă cu adevărat drumul razei. Pentru a afla <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c00b43fd534dda488ddee0f510c751881645c6ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.221ex; height:2.843ex;" alt="{\displaystyle D(\alpha )}"></span> (care nu este mai mult decât rotația razei in jurul picăturii) urmărim desenul si observam ca la A raza se rotește cu <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 -\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\alpha -\beta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b564213b22ab6461e8cc9c1a9b6fe39efae0936" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.469ex; height:2.843ex;" alt="{\displaystyle (\alpha -\beta )}"></span>, la B si la C cu <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 (\pi -2\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>π</mi> <mo>−</mo> <mn>2</mn> <mi>β</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\pi -2\beta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cb7880354bddf3c420bdfad895faee77a66e0fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.476ex; height:2.843ex;" alt="{\displaystyle (\pi -2\beta )}"></span> iar la D din nou cu <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 -\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\alpha -\beta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b564213b22ab6461e8cc9c1a9b6fe39efae0936" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.469ex; height:2.843ex;" alt="{\displaystyle (\alpha -\beta )}"></span>. De aici rezulta ca <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="{\textstyle D(\alpha )=2\alpha -6\beta +2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mi>α</mi> <mo>−</mo> <mn>6</mn> <mi>β</mi> <mo>+</mo> <mn>2</mn> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle D(\alpha )=2\alpha -6\beta +2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e04f3f36006824c208239612e2e31b3b1e7cde5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.639ex; height:2.843ex;" alt="{\textstyle D(\alpha )=2\alpha -6\beta +2\pi }"></span>. Înlocuim pe <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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> cu <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="{\textstyle \arcsin \left({\frac {\sin(\alpha )}{k}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>arcsin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> <mi>k</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \arcsin \left({\frac {\sin(\alpha )}{k}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e723fbc25f4b2d28fdc032111eed36ccbf14699" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.924ex; height:4.843ex;" alt="{\textstyle \arcsin \left({\frac {\sin(\alpha )}{k}}\right)}"></span> si pe <b>k</b> cu <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 {\dfrac {4}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dfrac {4}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fada482459a064c710ef2434753cfce4814a097a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\dfrac {4}{3}}}"></span> iar apoi derivam: </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Frameless"><a href="/wiki/Fi%C8%99ier:Curcubeu_dublu.png" class="mw-file-description" title="Drumul razei de lumina in formarea curcubeului dublu."><img alt="Drumul razei de lumina in formarea curcubeului dublu." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Curcubeu_dublu.png/220px-Curcubeu_dublu.png" decoding="async" width="220" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Curcubeu_dublu.png/330px-Curcubeu_dublu.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Curcubeu_dublu.png/440px-Curcubeu_dublu.png 2x" data-file-width="1313" data-file-height="898" /></a><figcaption>Drumul razei de lumina in formarea curcubeului dublu.</figcaption></figure> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha _{1})^{\prime }=2-{\frac {3\cdot 6\cos \alpha }{4{\sqrt {1-{\sin ^{2}\alpha }\cdot {\dfrac {9}{16}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mo>⋅</mo> <mn>6</mn> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>α</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>9</mn> <mn>16</mn> </mfrac> </mstyle> </mrow> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha _{1})^{\prime }=2-{\frac {3\cdot 6\cos \alpha }{4{\sqrt {1-{\sin ^{2}\alpha }\cdot {\dfrac {9}{16}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/842f74cb873637e5a4c576cea7a4078dc875b5e8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:33.011ex; height:9.343ex;" alt="{\displaystyle D(\alpha _{1})^{\prime }=2-{\frac {3\cdot 6\cos \alpha }{4{\sqrt {1-{\sin ^{2}\alpha }\cdot {\dfrac {9}{16}}}}}}}"></span>Egalam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha _{1})^{\prime }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha _{1})^{\prime }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9b46319930543acdcd2410fe062b8ac4fc11064" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.96ex; height:3.009ex;" alt="{\displaystyle D(\alpha _{1})^{\prime }}"></span>cu 0 pentru a afla minimul </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D(\alpha _{1})^{\prime }=0\Leftrightarrow 9\cdot 9\cos ^{2}(\alpha _{1})=16-\sin ^{2}(\alpha _{1})\Leftrightarrow \cos(\alpha _{1})={\sqrt {\dfrac {7}{72}}}\Leftrightarrow \alpha _{1}=\arccos {\sqrt {\dfrac {7}{72}}}=1.254\ radiani}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo stretchy="false">⇔</mo> <mn>9</mn> <mo>⋅</mo> <mn>9</mn> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mn>16</mn> <mo>−</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">⇔</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>7</mn> <mn>72</mn> </mfrac> </mstyle> </msqrt> </mrow> <mo stretchy="false">⇔</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>arccos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>7</mn> <mn>72</mn> </mfrac> </mstyle> </msqrt> </mrow> <mo>=</mo> <mn>1.254</mn> <mtext> </mtext> <mi>r</mi> <mi>a</mi> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>n</mi> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D(\alpha _{1})^{\prime }=0\Leftrightarrow 9\cdot 9\cos ^{2}(\alpha _{1})=16-\sin ^{2}(\alpha _{1})\Leftrightarrow \cos(\alpha _{1})={\sqrt {\dfrac {7}{72}}}\Leftrightarrow \alpha _{1}=\arccos {\sqrt {\dfrac {7}{72}}}=1.254\ radiani}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49bf1b8ed7177db92a30c1ffe014cfb82cd157a9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:101.971ex; height:6.176ex;" alt="{\displaystyle D(\alpha _{1})^{\prime }=0\Leftrightarrow 9\cdot 9\cos ^{2}(\alpha _{1})=16-\sin ^{2}(\alpha _{1})\Leftrightarrow \cos(\alpha _{1})={\sqrt {\dfrac {7}{72}}}\Leftrightarrow \alpha _{1}=\arccos {\sqrt {\dfrac {7}{72}}}=1.254\ radiani}"></span>De mai sus rezultă faptul ca rotația in jurul picăturii e de <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="{\textstyle D(\alpha _{1})\approx 231^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>≈</mo> <msup> <mn>231</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle D(\alpha _{1})\approx 231^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9997e5b1e9e5cebc6d12e29564f888da10a429be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.915ex; height:2.843ex;" alt="{\textstyle D(\alpha _{1})\approx 231^{\circ }}"></span> ce înseamna o rotație opusă de <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="{\textstyle 360^{\circ }-231^{\circ }=129^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <msup> <mn>231</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <msup> <mn>129</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle 360^{\circ }-231^{\circ }=129^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fce3f7fe646484d16c4760db06827bc93dd2a55f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.564ex; height:2.343ex;" alt="{\textstyle 360^{\circ }-231^{\circ }=129^{\circ }}"></span> (vezi imaginea din stânga). De aici rezultă ca unghiul curcubeului secundar e de <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="{\textstyle 180^{\circ }-129^{\circ }=51^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>−</mo> <msup> <mn>129</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>=</mo> <msup> <mn>51</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle 180^{\circ }-129^{\circ }=51^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21d3aa9c1060f04fea8d6b88f45288cb8ce14eaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:18.401ex; height:2.343ex;" alt="{\textstyle 180^{\circ }-129^{\circ }=51^{\circ }}"></span>. In general, acesta va fi <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="{\textstyle D(\alpha _{1})-\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>D</mi> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle D(\alpha _{1})-\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6802d16a76a8a315e5bcb989a26c45b6cee22a59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.448ex; height:2.843ex;" alt="{\textstyle D(\alpha _{1})-\pi }"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=9" title="Modifică secțiunea: Note" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=9" title="Edit section's source code: Note"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text"><span class="plainlinks">„<a rel="nofollow" class="external text" href="http://dexonline.ro/definitie/curcubeu">curcubeu</a>” la <a href="/wiki/DEX_online" title="DEX online">DEX online</a></span></span> </li> <li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="reference-text"><cite class="citation web">EarthSky. <a rel="nofollow" class="external text" href="https://earthsky.org/earth/what-gives-rainbows-their-curved-shape">„Why rainbows are curved”</a><span class="reference-accessdate">. Accesat în <time datetime="2021-05-14">14 mai 2021</time></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Why+rainbows+are+curved&rft.au=EarthSky&rft_id=https%3A%2F%2Fearthsky.org%2Fearth%2Fwhat-gives-rainbows-their-curved-shape&rfr_id=info%3Asid%2Fro.wikipedia.org%3ACurcubeu" class="Z3988"><span style="display:none;"> </span></span><style data-mw-deduplicate="TemplateStyles:r16236537">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"„""”""«""»"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style></span> </li> <li id="cite_note-3"><b><a href="#cite_ref-3">^</a></b> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://eo.ucar.edu/rainbows/">„About Rainbows”</a>. eo.ucar.edu<span class="reference-accessdate">. Accesat în <time datetime="2021-05-14">14 mai 2021</time></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=About+Rainbows&rft.pub=eo.ucar.edu&rft_id=https%3A%2F%2Feo.ucar.edu%2Frainbows%2F&rfr_id=info%3Asid%2Fro.wikipedia.org%3ACurcubeu" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text"><cite class="citation web">Tremblay, Jean-Marie (<time datetime="2005-02-02">2 februarie 2005</time>). <a rel="nofollow" class="external text" href="http://classiques.uqac.ca/classiques/Descartes/meteores/meteores.html">„Les classiques des sciences sociales: René Descartes, Les Météores (1637)”</a>. texte<span class="reference-accessdate">. Accesat în <time datetime="2021-05-14">14 mai 2021</time></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Les+classiques+des+sciences+sociales%3A+Ren%C3%A9+Descartes%2C+Les+M%C3%A9t%C3%A9ores+%281637%29&rft.pub=texte&rft.date=2005-02-02&rft.aulast=Tremblay&rft.aufirst=Jean-Marie&rft_id=http%3A%2F%2Fclassiques.uqac.ca%2Fclassiques%2FDescartes%2Fmeteores%2Fmeteores.html&rfr_id=info%3Asid%2Fro.wikipedia.org%3ACurcubeu" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"><cite class="citation"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1098/rstl.1700.0058">„III. De iride, sive de arcu cælesti, dissertatio geometrica, quo methodo directâ iridis utriusq; diameter, data ratione refractionis, obtinertur: Cum solutione inversi problematis, sive inventione rationis istius ex data arcus diametro. Per Edm. Halley Reg. Soc. Soc”</a>, <i>Philosophical Transactions of the Royal Society of London</i>, <b>22</b> (267), pp. 714–725, <time datetime="1701-12-31">31 decembrie 1701</time>, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstl.1700.0058">10.1098/rstl.1700.0058</a>, <a href="/wiki/International_Standard_Serial_Number" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0261-0523">0261-0523</a><span class="reference-accessdate">, accesat în <time datetime="2021-05-14">14 mai 2021</time></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London&rft.atitle=III.+De+iride%2C+sive+de+arcu+c%C3%A6lesti%2C+dissertatio+geometrica%2C+quo+methodo+direct%C3%A2+iridis+utriusq%3B+diameter%2C+data+ratione+refractionis%2C+obtinertur%3A+Cum+solutione+inversi+problematis%2C+sive+inventione+rationis+istius+ex+data+arcus+diametro.+Per+Edm.+Halley+Reg.+Soc.+Soc&rft.volume=22&rft.issue=267&rft.pages=714-725&rft.date=1701-12-31&rft_id=info%3Adoi%2F10.1098%2Frstl.1700.0058&rft.issn=0261-0523&rft_id=http%3A%2F%2Fdx.doi.org%2F10.1098%2Frstl.1700.0058&rfr_id=info%3Asid%2Fro.wikipedia.org%3ACurcubeu" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografie">Bibliografie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=10" title="Modifică secțiunea: Bibliografie" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=10" title="Edit section's source code: Bibliografie"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Alexandre Costa, Beatriz García, Ricardo Moreno - NASE - <a rel="nofollow" class="external text" href="http://sac.csic.es/astrosecundaria/ro/cursos/formato/materiales/conferencias/T5_w_ro.pdf">"Spectrul solar și petele solare</a>"</li></ul> <div class="mw-heading mw-heading2"><h2 id="Legături_externe"><span id="Leg.C4.83turi_externe"></span>Legături externe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Curcubeu&veaction=edit&section=11" title="Modifică secțiunea: Legături externe" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Curcubeu&action=edit&section=11" title="Edit section's source code: Legături externe"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint" style="clear: right; border: solid #aaa 1px; margin: 0 0 1em 1em; font-size: 90%; background: #f9f9f9; width: 230px; padding: 2px; spacing: 2px; text-align: center; float: right;"> <div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Wiktionary-logo.svg" class="mw-file-description" title="Wikţionar"><img alt="Wikţionar" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/30px-Wiktionary-logo.svg.png" decoding="async" width="30" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/45px-Wiktionary-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/60px-Wiktionary-logo.svg.png 2x" data-file-width="370" data-file-height="350" /></a><figcaption>Wikţionar</figcaption></figure></div> <div style="margin-left: 35px; line-height:normal;">Caută „<b><a href="https://ro.wiktionary.org/wiki/curcubeu" class="extiw" title="wikt:curcubeu">curcubeu</a></b>” în <a href="/wiki/Wik%C8%9Bionar" title="Wikționar">Wikționar</a>, dicționarul liber.</div> </div> <ul><li><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Commons-logo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Materiale media legate de <span class="plainlinks"><b><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Rainbows?uselang=ro">curcubeu</a></b></span> la <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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