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class="vector-toc-numb">4</span> <span>Referenties</span> </div> </a> <ul id="toc-Referenties-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="Inhoud" 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="Inhoudsopgave omschakelen" > <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">Inhoudsopgave omschakelen</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">Getal van Abbe</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="Ga naar een artikel in een andere taal. Beschikbaar in 33 talen" > <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-33" 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">33 talen</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D9%85%D9%84_%D8%A2%D8%A8%D9%8A" title="معامل آبي – Arabisch" lang="ar" hreflang="ar" data-title="معامل آبي" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Abbe_%C9%99d%C9%99di" title="Abbe ədədi – Azerbeidzjaans" lang="az" hreflang="az" data-title="Abbe ədədi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AC%E0%A7%87_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="অ্যাবে সংখ্যা – Bengaals" lang="bn" hreflang="bn" data-title="অ্যাবে সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_d%27Abbe" title="Nombre d'Abbe – Catalaans" lang="ca" hreflang="ca" data-title="Nombre d'Abbe" data-language-autonym="Català" data-language-local-name="Catalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Abbeovo_%C4%8D%C3%ADslo" title="Abbeovo číslo – Tsjechisch" lang="cs" hreflang="cs" data-title="Abbeovo číslo" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Abbe-Zahl" title="Abbe-Zahl – Duits" lang="de" hreflang="de" data-title="Abbe-Zahl" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82_%CE%86%CE%BC%CF%80%CE%B5" title="Αριθμός Άμπε – Grieks" lang="el" hreflang="el" data-title="Αριθμός Άμπε" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" 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/Abbe_number" title="Abbe number – Engels" lang="en" hreflang="en" data-title="Abbe number" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_de_Abbe" title="Número de Abbe – Spaans" lang="es" hreflang="es" data-title="Número de Abbe" data-language-autonym="Español" data-language-local-name="Spaans" 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/Abbe_arv" title="Abbe arv – Estisch" lang="et" hreflang="et" data-title="Abbe arv" data-language-autonym="Eesti" data-language-local-name="Estisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%82%D8%AF%D8%A7%D8%B1_%D8%A2%D8%A8%D9%87" title="مقدار آبه – Perzisch" lang="fa" hreflang="fa" data-title="مقدار آبه" data-language-autonym="فارسی" data-language-local-name="Perzisch" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Nombre_d%27Abbe" title="Nombre d'Abbe – Frans" lang="fr" hreflang="fr" data-title="Nombre d'Abbe" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%BAmero_de_Abbe" title="Número de Abbe – Galicisch" lang="gl" hreflang="gl" data-title="Número de Abbe" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%90%D7%91%D7%94" title="מספר אבה – Hebreeuws" lang="he" hreflang="he" data-title="מספר אבה" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan_Abbe" title="Bilangan Abbe – Indonesisch" lang="id" hreflang="id" data-title="Bilangan Abbe" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_di_Abbe" title="Numero di Abbe – Italiaans" lang="it" hreflang="it" data-title="Numero di Abbe" data-language-autonym="Italiano" data-language-local-name="Italiaans" 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/%E3%82%A2%E3%83%83%E3%83%99%E6%95%B0" title="アッベ数 – Japans" lang="ja" hreflang="ja" data-title="アッベ数" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%84%EB%B2%A0%EC%88%98" title="아베수 – Koreaans" lang="ko" hreflang="ko" data-title="아베수" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Abbetal" title="Abbetal – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Abbetal" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - 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/Abbetall" title="Abbetall – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Abbetall" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczba_Abbego" title="Liczba Abbego – Pools" lang="pl" hreflang="pl" data-title="Liczba Abbego" data-language-autonym="Polski" data-language-local-name="Pools" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero_Abbe" title="Número Abbe – Portugees" lang="pt" hreflang="pt" data-title="Número Abbe" data-language-autonym="Português" data-language-local-name="Portugees" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83rul_lui_Abbe" title="Numărul lui Abbe – Roemeens" lang="ro" hreflang="ro" data-title="Numărul lui Abbe" data-language-autonym="Română" data-language-local-name="Roemeens" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE_%D0%90%D0%B1%D0%B1%D0%B5" title="Число Аббе – Russisch" lang="ru" hreflang="ru" data-title="Число Аббе" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Abbeho_%C4%8D%C3%ADslo" title="Abbeho číslo – Slowaaks" lang="sk" hreflang="sk" data-title="Abbeho číslo" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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/Abbejevo_%C5%A1tevilo" title="Abbejevo število – Sloveens" lang="sl" hreflang="sl" data-title="Abbejevo število" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Abbetal" title="Abbetal – Zweeds" lang="sv" hreflang="sv" data-title="Abbetal" data-language-autonym="Svenska" data-language-local-name="Zweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%AA%E0%AE%BF_%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="அபி எண் – Tamil" lang="ta" hreflang="ta" data-title="அபி எண்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%AD%E0%B8%B1%E0%B8%9A%E0%B9%80%E0%B8%9A%E0%B8%AD" title="เลขอับเบอ – Thai" lang="th" hreflang="th" data-title="เลขอับเบอ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Abbe_say%C4%B1s%C4%B1" title="Abbe sayısı – Turks" lang="tr" hreflang="tr" data-title="Abbe sayısı" data-language-autonym="Türkçe" data-language-local-name="Turks" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE_%D0%90%D0%B1%D0%B1%D0%B5" title="Число Аббе – Oekraïens" lang="uk" hreflang="uk" data-title="Число Аббе" data-language-autonym="Українська" data-language-local-name="Oekraïens" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91_Abbe" title="Số Abbe – Vietnamees" lang="vi" hreflang="vi" data-title="Số Abbe" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%98%BF%E8%B4%9D%E6%95%B0" title="阿贝数 – Chinees" lang="zh" hreflang="zh" data-title="阿贝数" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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lang="nl" dir="ltr"><p>Het <b>getal van Abbe</b> is een <a href="/wiki/Dimensieloos_getal" class="mw-redirect" title="Dimensieloos getal">dimensieloos getal</a> dat een maat is voor de <a href="/wiki/Dispersie_(natuurkunde)" title="Dispersie (natuurkunde)">dispersie</a> (kleurschifting) van transparante media. Het getal is genoemd naar de Duitse fysicus <a href="/wiki/Ernst_Abbe" title="Ernst Abbe">Ernst Abbe</a> (1840-1905). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Achtergrond">Achtergrond</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Getal_van_Abbe&veaction=edit&section=1" title="Bewerk dit kopje: Achtergrond" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Getal_van_Abbe&action=edit&section=1" title="De broncode bewerken van de sectie: Achtergrond"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Optische dispersie wil zeggen dat de <a href="/wiki/Lichtbreking" title="Lichtbreking">lichtbreking</a> in een stof afhangt van de <a href="/wiki/Golflengte" title="Golflengte">golflengte</a>, en dus van de kleur. Daardoor ontstaat in <a href="/wiki/Lens_(optica)" title="Lens (optica)">lenzen</a> <a href="/wiki/Chromatische_aberratie" title="Chromatische aberratie">chromatische aberratie</a>, een afbeeldingsfout die bijvoorbeeld tot kleurige randjes langs grenzen tussen lichte en donkere delen van een beeld leidt. </p><p>Om de dispersie van een materiaal (bijvoorbeeld een glassoort) volledig te beschrijven, zou men moeten vermelden hoe de <a href="/wiki/Brekingsindex" title="Brekingsindex">brekingsindex</a> van dat materiaal afhangt van de golflengte λ, dus de volledige functie n(λ). Dat kan met de zogenaamde <a href="/w/index.php?title=Cauchyvergelijking&action=edit&redlink=1" class="new" title="Cauchyvergelijking (de pagina bestaat niet)">Cauchyvergelijking</a> en de <a href="/wiki/Sellmeiervergelijking" title="Sellmeiervergelijking">Sellmeiervergelijking</a>. Voor eenvoudige berekeningen is het echter vaak voldoende om de dispersie in het zichtbare deel van het spectrum te beschrijven met het <i>getal van Abbe</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Definitie">Definitie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Getal_van_Abbe&veaction=edit&section=2" title="Bewerk dit kopje: Definitie" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Getal_van_Abbe&action=edit&section=2" title="De broncode bewerken van de sectie: Definitie"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="float: right; margin-left: 1.5em;"> <tbody><tr> <th><a href="/wiki/Golflengte" title="Golflengte">golflengte</a> λ in nm </th> <th><a href="/wiki/Fraunhoferlijnen" title="Fraunhoferlijnen">Fraunhoferlijn</a> </th> <th>lichtbron </th> <th>kleur </th></tr> <tr> <td>  365,0146 </td> <td>  i </td> <td>  Hg </td> <td>  <a href="/wiki/Ultraviolet" title="Ultraviolet">UV</a> </td></tr> <tr> <td>  404,6561 </td> <td>  h </td> <td>  Hg </td> <td>  violet </td></tr> <tr> <td>  435,8343 </td> <td>  g </td> <td>  Hg </td> <td>  blauw </td></tr> <tr> <td>  479,9914 </td> <td>  F' </td> <td>  Cd </td> <td>  blauw </td></tr> <tr> <td>  486,1327 </td> <td>  F </td> <td>  H </td> <td>  blauw </td></tr> <tr> <td>  546,0740 </td> <td>  e </td> <td>  Hg </td> <td>  groen </td></tr> <tr> <td>  587,5618 </td> <td>  d </td> <td>  He </td> <td>  geel </td></tr> <tr> <td>  589,2938 </td> <td>  D </td> <td>  Na </td> <td>  geel </td></tr> <tr> <td>  643,8469 </td> <td>  C' </td> <td>  Cd </td> <td>  rood </td></tr> <tr> <td>  656,2725 </td> <td>  C </td> <td>  H </td> <td>  rood </td></tr> <tr> <td>  706,5188 </td> <td>  r </td> <td>  He </td> <td>  rood </td></tr> <tr> <td>  768,2 </td> <td>  A' </td> <td>  K </td> <td>  rot </td></tr> <tr> <td>  852,11 </td> <td>  s </td> <td>  Cs </td> <td>  <a href="/wiki/Infrarood" title="Infrarood">IR</a> </td></tr> <tr> <td>  1013,98 </td> <td>  t </td> <td>  Hg </td> <td>  <a href="/wiki/Infrarood" title="Infrarood">IR</a> </td></tr></tbody></table> <p>Het getal van Abbe <i>V</i> was vroeger gedefinieerd als </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {n_{\rm {d}}-1}{n_{\rm {F}}-n_{\rm {C}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> </msub> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {n_{\rm {d}}-1}{n_{\rm {F}}-n_{\rm {C}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/083920af5ab15f78fc961daf9d922b8916f356db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.076ex; height:5.509ex;" alt="{\displaystyle V={\frac {n_{\rm {d}}-1}{n_{\rm {F}}-n_{\rm {C}}}}}"></span></dd></dl> <p>waarin <i>n</i><sub>d</sub> (resp. <i>n</i><sub>e</sub>), <i>n</i><sub>F'</sub> en <i>n</i><sub>C'</sub> de brekingsindices zijn van het materiaal bij de golflengtes van de <a href="/wiki/Fraunhoferlijnen" title="Fraunhoferlijnen">Fraunhoferlijnen</a> d, F en C (587,6 nm, 486,1 nm en 656,3 nm), </p><p>en tegenwoordig als: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {n_{\rm {e}}-1}{n_{\rm {F'}}-n_{\rm {C'}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="normal">F</mi> <mo>′</mo> </msup> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="normal">C</mi> <mo>′</mo> </msup> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {n_{\rm {e}}-1}{n_{\rm {F'}}-n_{\rm {C'}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c24582ad966af1cd1474e29937d406eda443f0e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.139ex; height:5.843ex;" alt="{\displaystyle V={\frac {n_{\rm {e}}-1}{n_{\rm {F'}}-n_{\rm {C'}}}}}"></span></dd></dl> <p>waarin: <i>n</i><sub>d</sub> (resp. <i>n</i><sub>e</sub>), <i>n</i><sub>F'</sub> en <i>n</i><sub>C'</sub> de brekingsindices zijn van het materiaal bij de golflengtes van de <a href="/wiki/Fraunhoferlijnen" title="Fraunhoferlijnen">Fraunhoferlijnen</a> e, F' en C' (546,07 nm, 479,99 nm en 643,84 nm), </p><p>zoals in nevenstaande tabel. </p><p>Typische waarden lopen voor de meestgebruikte glassoorten lopen van 20 („zwaar”, dus loodhoudend, <a href="/wiki/Flintglas" title="Flintglas">flintglas</a> tot 60 voor <a href="/wiki/Kroonglas_(optisch_glas)" title="Kroonglas (optisch glas)">kroonglas</a>). De grens tussen de aanduidingen ‘flintglas’ en ‘kroonglas’ ligt bij een Abbegetal van 50. Speciale glassoorten (fluoriet-kroonglas) hebben Abbegetallen rond 85; <a href="/wiki/Magnesiumfluoride" title="Magnesiumfluoride">magnesiumfluoride</a> zelfs 95; deze soorten hebben dus een zeer geringe dispersie. </p><p>De volgende tabel geeft de standaardgolflengtes waarbij de brekingsindex normaliter wordt bepaald.<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> Zo wordt bijvoorbeeld n<sub>D</sub> gemeten bij een golflengte van 589,3 nm. </p> <div class="mw-heading mw-heading2"><h2 id="Toepassingen">Toepassingen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Getal_van_Abbe&veaction=edit&section=3" title="Bewerk dit kopje: Toepassingen" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Getal_van_Abbe&action=edit&section=3" title="De broncode bewerken van de sectie: Toepassingen"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Het getal van Abbe is vooral van belang voor het ontwerp van eenvoudige <a href="/wiki/Objectief_(optica)" title="Objectief (optica)">lenzensystemen</a> waarbij de chromatische aberratie geminimaliseerd moet worden. Zo heeft bijvoorbeeld een lenzenstelsel bestaande uit twee vlak bij elkaar geplaatste dunne lenzen voor de Fraunhoferlijnen F en C dezelfde <a href="/wiki/Brandpuntsafstand" title="Brandpuntsafstand">brandpuntsafstanden</a> als voldaan is aan </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{1}\cdot f_{1}+V_{2}\cdot f_{2}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{1}\cdot f_{1}+V_{2}\cdot f_{2}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b2bb42a2f92df7c94d015f83100d61e64cd940" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.665ex; height:2.509ex;" alt="{\displaystyle V_{1}\cdot f_{1}+V_{2}\cdot f_{2}=0}"></span></dd></dl> <p>waarin <i>V</i><sub>i</sub> de Abbegetallen en <i>f</i><sub>i</sub> de brandpuntsafstanden van de lenzen zijn. Daar een dergelijk systeem blauw en rood licht (althans twee paarsgewijs „bij elkaar passende” golflengtes) gelijk afbeeldt, is de chromatische aberratie nu gering (men ziet meestal een violette rand rond lichte objecten). Dergelijke lenzensystemen staan bekend als '<a href="/wiki/Achromaat_(optica)" title="Achromaat (optica)">achromaten</a>' en stonden aan de basis van de ontwikkeling van grote telescopen in de 19e eeuw. </p><p>Voor nauwkeuriger berekeningen en kwalitatief hoogwaardige lenzenstelsels dient de exacte dispersierelatie, dat wil zeggen het exacte verband tussen de brekingsindex en de golflengte te worden gebruikt. Toch hantert men ook daarbij het getal van Abbe om een grove voorselectie van glassoorten te maken. </p><p>In het <a href="/wiki/Infrarood" title="Infrarood">infrarode</a> en <a href="/wiki/Ultraviolet" title="Ultraviolet">ultraviolette</a> gebied is het getal van Abbe niet geschikt, daar het voor golflengtes in het zichtbaar gebied is gedefinieerd. </p> <div class="mw-heading mw-heading2"><h2 id="Referenties">Referenties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Getal_van_Abbe&veaction=edit&section=4" title="Bewerk dit kopje: Referenties" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Getal_van_Abbe&action=edit&section=4" title="De broncode bewerken van de sectie: Referenties"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">L.D. Pye, V.D. Fréchette, N.J. Kreidl: <i>Borate glasses: structure, properties, applications</i>. New York (Plenum Press), 1978; ISBN= 9780306400162</span> </li> </ol></div></div> <style data-mw-deduplicate="TemplateStyles:r67837862">.mw-parser-output .navigatie{position:relative;clear:both;overflow:auto;margin:1em auto -0.5em;padding:2px;background-color:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);text-align:center;font-size:87%}.mw-parser-output .navigatie-bewerken{margin-left:0.5em}.mw-parser-output .navigatie-bewerken .mw-ui-icon::before{background-size:0.9em}.mw-parser-output .navigatie-afb-links,.mw-parser-output .navigatie-afb-rechts{position:absolute}.mw-parser-output .navigatie-afb-rechts{right:2px}.mw-parser-output .navigatie-afb-groot{float:right;padding-left:0.5em}.mw-parser-output .navigatie-titel{background-color:#ddeef8;padding:2px 5.5em;font-weight:bold}.mw-parser-output .navigatie-inhoud{padding:0.5em}.mw-parser-output .navigatie-inhoud p:first-child{margin:0}.mw-parser-output .navigatie 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/OOjs_UI_icon_speechBubbles-ltr.svg/24px-OOjs_UI_icon_speechBubbles-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/OOjs_UI_icon_speechBubbles-ltr.svg/32px-OOjs_UI_icon_speechBubbles-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></span></span> · <span typeof="mw:File"><a href="//nl.wikipedia.org/w/index.php?title=Sjabloon:Navigatie_geometrische_optica&action=edit" title="Sjabloon bewerken"><img alt="Sjabloon bewerken" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/16px-OOjs_UI_icon_edit-ltr.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/24px-OOjs_UI_icon_edit-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/32px-OOjs_UI_icon_edit-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span></div></div> <div id="Geometrische_optica" class="navigatie-titel"><a href="/wiki/Geometrische_optica" title="Geometrische optica">Geometrische optica</a></div> <div class="navigatie-inhoud mw-collapsible-content"> <style data-mw-deduplicate="TemplateStyles:r67785531">.mw-parser-output .navigatie-tabel{margin:0 auto 0 auto;text-align:left}.mw-parser-output .navigatie-tabel .links{text-align:right}.mw-parser-output .navigatie-tabel .rechts{padding-left:0.5em}@media screen and (max-width:640px){.mw-parser-output .navigatie-tabel tr{display:grid;grid-template-columns:1fr;width:100%;margin-bottom:0.5em}.mw-parser-output .navigatie-tabel tr:last-of-type{margin-bottom:0}.mw-parser-output .navigatie-tabel .links{text-align:unset}.mw-parser-output .navigatie-tabel .rechts{padding:unset}}</style><table class="navigatie-tabel vatop" cellpadding="0" cellspacing="0" style=""><tbody><tr><td class="links" style=""><b>Basisbegrippen:</b></td><td class="rechts"><a href="/wiki/Apertuur" title="Apertuur">Apertuur</a> · <a href="/wiki/Beeld_(optica)" title="Beeld (optica)">Beeld</a> · <a href="/wiki/Beeldvlak_(optica)" title="Beeldvlak (optica)">Beeldvlak</a> · <a href="/wiki/Brandpunt_(optica)" title="Brandpunt (optica)">Brandpunt</a> · <a href="/wiki/Brandpuntsafstand" title="Brandpuntsafstand">Brandpuntsafstand</a> · <a href="/wiki/Brekingsindex" title="Brekingsindex">Brekingsindex</a> · <a href="/wiki/Catadioptrisch_systeem" title="Catadioptrisch systeem">Catadioptrisch systeem</a> · <a href="/wiki/Concaaf" title="Concaaf">Concaaf</a> · <a href="/wiki/Contrast" title="Contrast">Contrast</a> · <a href="/wiki/Convergentie_en_divergentie" title="Convergentie en divergentie">Convergentie en divergentie</a> · <a href="/wiki/Convex" title="Convex">Convex</a> · <a href="/wiki/Diafragmagetal" title="Diafragmagetal">Diafragmagetal</a> · <a href="/wiki/Dioptrie" title="Dioptrie">Dioptrie</a> · <a href="/wiki/Fresnelvergelijkingen" title="Fresnelvergelijkingen">Fresnelvergelijkingen</a> · <a class="mw-selflink selflink">Getal van Abbe</a> · <a href="/wiki/Glans" title="Glans">Glans</a> · <a href="/wiki/Hoekvergroting" title="Hoekvergroting">Hoekvergroting</a> · <a href="/wiki/Hoofdvlak" title="Hoofdvlak">Hoofdvlak</a> · <a href="/wiki/Intree-_en_uittreepupil" title="Intree- en uittreepupil">Intree- en uittreepupil</a> · <a href="/wiki/Lenzenformule" title="Lenzenformule">Lenzenformule</a> · <a href="/wiki/Lichtbreking" title="Lichtbreking">Lichtbreking</a> · <a href="/wiki/Openingshoek" title="Openingshoek">Openingshoek</a> · <a href="/wiki/Optische_as_(optica)" title="Optische as (optica)">Optische as</a> · <a href="/wiki/Parallax_(hoofdbetekenis)" class="mw-redirect" title="Parallax (hoofdbetekenis)">Parallax</a> · <a href="/wiki/Paraxiale_benadering" title="Paraxiale benadering">Paraxiale benadering</a> · <a href="/wiki/Reflectie_(straling)" title="Reflectie (straling)">Reflectie</a> · <a href="/wiki/Scheimpflug-principe" title="Scheimpflug-principe">Scheimpflug-principe</a> · <a href="/wiki/Spiegelbeeld_(reflectie)" title="Spiegelbeeld (reflectie)">Spiegelbeeld</a> · <a href="/wiki/Strehlverhouding" title="Strehlverhouding">Strehlverhouding</a> · <a href="/wiki/Totale_interne_reflectie" title="Totale interne reflectie">Totale interne reflectie</a> · <a href="/wiki/Virtueel_beeld" title="Virtueel beeld">Virtueel beeld</a> · <a href="/wiki/Wet_van_Snellius" title="Wet van Snellius">Wet van Snellius</a></td></tr><tr><td class="links"><b>Optische component:</b></td><td class="rechts"><a href="/wiki/Dunne_lens" title="Dunne lens">Dunne lens</a> · <a href="/wiki/Dikke_lens" title="Dikke lens">Dikke lens</a> · <a href="/wiki/Diafragma_(optica)" title="Diafragma (optica)">Diafragma</a> · <a href="/wiki/Flintglas" title="Flintglas">Flintglas</a> · <a href="/wiki/Fresnellens" title="Fresnellens">Fresnellens</a> · <a href="/wiki/Kroonglas_(optisch_glas)" title="Kroonglas (optisch glas)">Kroonglas</a> · <a href="/wiki/Lens_(optica)" title="Lens (optica)">Lens</a> · <a href="/wiki/Microlens_(optica)" title="Microlens (optica)">Microlens</a> · <a href="/wiki/Retroreflector" title="Retroreflector">Retroreflector</a> · <a href="/wiki/Spiegel_(optica)" title="Spiegel (optica)">Spiegel</a> · <a href="/wiki/Stralingsdeler" title="Stralingsdeler">Stralingsdeler</a></td></tr><tr><td class="links"><b>Asferische component:</b></td><td class="rechts"><a href="/wiki/Asferische_optiek" title="Asferische optiek">Asferische optiek</a> · <a href="/wiki/Cilindrische_lens" title="Cilindrische lens">Cilindrische lens</a> · <a href="/wiki/Lachspiegel" title="Lachspiegel">Lachspiegel</a> · <a href="/wiki/Paraboolreflector" title="Paraboolreflector">Paraboolreflector</a> · <a href="/wiki/Spiegeltelescoop#Schmidtcorrector" title="Spiegeltelescoop">Schmidtcorrector</a> · <a href="/wiki/Torische_lens" title="Torische lens">Torische lens</a></td></tr><tr><td class="links"><b>Lenzenstelsel:</b></td><td class="rechts"><a href="/wiki/Condensor_(optica)" title="Condensor (optica)">Condensor</a> · <a href="/wiki/Lenzenstelsel" title="Lenzenstelsel">Lenzenstelsel</a> · <a href="/wiki/Objectief_(optica)" title="Objectief (optica)">Objectief (optica)</a> · <a href="/wiki/Oculair" title="Oculair">Oculair</a> · <a href="/wiki/Retrofocus-_en_teleconstructie" title="Retrofocus- en teleconstructie">Retrofocus- en teleconstructie</a></td></tr><tr><td class="links"><b>Afbeeldingsfout:</b></td><td class="rechts"><a href="/wiki/Aberratie_(optica)" title="Aberratie (optica)">Afbeeldingsfouten</a> · <a href="/wiki/Astigmatisme_(optica)" title="Astigmatisme (optica)">Astigmatisme</a> · <a href="/wiki/Beeldveldwelving" title="Beeldveldwelving">Beeldveldwelving</a> · <a href="/wiki/Chromatische_aberratie" title="Chromatische aberratie">Chromatische aberratie</a> · <a href="/wiki/Coma_(optica)" title="Coma (optica)">Coma</a> · <a href="/wiki/Sferische_aberratie" title="Sferische aberratie">Sferische aberratie</a> · <a href="/wiki/Vertekening" title="Vertekening">Vertekening</a></td></tr><tr><td class="links"><span class="nowrap"><b>Toepassing (fotografie):</b></span></td><td class="rechts"><a href="/wiki/Fisheye-objectief" title="Fisheye-objectief">Fisheye-objectief</a> · <a href="/wiki/Fotografie" title="Fotografie">Fotografie</a> · <a href="/wiki/Groothoekobjectief" title="Groothoekobjectief">Groothoekobjectief</a> · <a href="/wiki/Macro-objectief" title="Macro-objectief">Macro-objectief</a> · <a href="/wiki/Pentaprisma" title="Pentaprisma">Pentaprisma</a> · <a href="/wiki/Standaardobjectief" title="Standaardobjectief">Standaardobjectief</a> · <a href="/wiki/Teleconverter" title="Teleconverter">Teleconverter</a> · <a href="/wiki/Teleobjectief" title="Teleobjectief">Teleobjectief</a> · <a href="/wiki/Tussenring" title="Tussenring">Tussenring</a> · <a href="/wiki/Vergrotingsapparaat" title="Vergrotingsapparaat">Vergrotingsapparaat</a> · <a href="/wiki/Vignettering" title="Vignettering">Vignettering</a> · <a href="/wiki/Voorzetlens" title="Voorzetlens">Voorzetlens</a> · <a href="/wiki/Zoomobjectief" title="Zoomobjectief">Zoomobjectief</a></td></tr><tr><td class="links"><b>(bril e.d.):</b></td><td class="rechts"><a href="/wiki/Antireflectiecoating" title="Antireflectiecoating">Antireflectiecoating</a> · <a href="/wiki/Bifocaal_brillenglas" title="Bifocaal brillenglas">Bifocaal brillenglas</a> · <a href="/wiki/Beeldschermbril" title="Beeldschermbril">Beeldschermbril</a> · <a href="/wiki/Bril_(hoofdbetekenis)" class="mw-redirect" title="Bril (hoofdbetekenis)">Bril</a> · <a href="/wiki/Contactlens" title="Contactlens">Contactlens</a> · <a href="/wiki/Intraoculaire_lens" title="Intraoculaire lens">Intraoculaire lens</a> · <a href="/wiki/Multifocaal_brillenglas" title="Multifocaal brillenglas">Multifocaal brillenglas</a> · <a href="/wiki/Nabijheidspunt" title="Nabijheidspunt">Nabijheidspunt</a> · <a href="/wiki/Oogmeting" title="Oogmeting">Oogmeting</a> · <a href="/wiki/Refractor_(optometrie)" title="Refractor (optometrie)">Refractor (optometrie)</a> · <a href="/wiki/Vertepunt" title="Vertepunt">Vertepunt</a></td></tr><tr><td class="links"><b>(microscoop):</b></td><td class="rechts"><a href="/wiki/Microscoop" title="Microscoop">Microscoop</a> · <a href="/wiki/Numerieke_apertuur" title="Numerieke apertuur">Numerieke apertuur</a> · <a href="/wiki/Olie-immersie" title="Olie-immersie">Olie-immersie</a> · <a href="/wiki/Stereomicroscoop" title="Stereomicroscoop">Stereomicroscoop</a></td></tr><tr><td class="links"><b>(projector):</b></td><td class="rechts"><a href="/wiki/Eidophor" title="Eidophor">Eidophor</a> · <a href="/wiki/Episcoop" title="Episcoop">Episcoop</a> · <a href="/wiki/Diaprojector" title="Diaprojector">Diaprojector</a> · <a href="/wiki/Filmprojector" title="Filmprojector">Filmprojector</a> · <a href="/wiki/Overheadprojector" title="Overheadprojector">Overheadprojector</a> · <a href="/wiki/Toverlantaarn" title="Toverlantaarn">Toverlantaarn</a> · <a href="/wiki/Videoprojector" title="Videoprojector">Videoprojector</a></td></tr><tr><td class="links"><span class="nowrap"><b>(telescoop e.d.):</b></span></td><td class="rechts"><a href="/wiki/Actieve_optiek" title="Actieve optiek">Actieve optiek</a> · <a href="/wiki/Astrograaf" title="Astrograaf">Astrograaf</a> · <a href="/wiki/Dobsontelescoop" title="Dobsontelescoop">Dobsontelescoop</a> · <a href="/wiki/Hollandse_kijker" title="Hollandse kijker">Hollandse kijker</a> · <a href="/wiki/Montering_(telescoop)" title="Montering (telescoop)">Montering</a> · <a href="/wiki/Newtontelescoop" title="Newtontelescoop">Newtontelescoop</a> · <a href="/wiki/Nulcorrector" title="Nulcorrector">Nulcorrector</a> · <a href="/wiki/Refractor_(telescoop)" title="Refractor (telescoop)">Refractor (telescoop)</a> · <a href="/wiki/Spiegeltelescoop" title="Spiegeltelescoop">Spiegeltelescoop (alle types)</a> · <a href="/wiki/Telescoop_(optica)" title="Telescoop (optica)">Telescoop</a> · <a href="/wiki/Verrekijker_(hoofdbetekenis)" class="mw-redirect" title="Verrekijker (hoofdbetekenis)">Verrekijker</a> · <a href="/wiki/Volgster" title="Volgster">Volgster</a></td></tr><tr><td class="links"><b>Algemene toepassing:</b></td><td class="rechts"><a href="/wiki/Achteruitkijkspiegel" title="Achteruitkijkspiegel">Achteruitkijkspiegel</a> · <a href="/wiki/Adaptieve_optiek" title="Adaptieve optiek">Adaptieve optiek</a> · <a href="/wiki/Barlowlens" title="Barlowlens">Barlowlens</a> · <a href="/wiki/Kaleidoscoop" class="mw-redirect" title="Kaleidoscoop">Kaleidoscoop</a> · <a href="/wiki/Eenrichtingsspiegel" title="Eenrichtingsspiegel">Eenrichtingsspiegel</a> · <a href="/wiki/Immersielithografie" title="Immersielithografie">Immersielithografie</a> · <a href="/wiki/Loep" title="Loep">Loep</a> · <a href="/wiki/Periscoop" title="Periscoop">Periscoop</a> · <a href="/wiki/Theodoliet" title="Theodoliet">Theodoliet</a> · <a href="/wiki/Waterpas_(landmeetkunde)" title="Waterpas (landmeetkunde)">Waterpasinstrument</a></td></tr></tbody></table> </div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Getal_van_Abbe&oldid=39247639">https://nl.wikipedia.org/w/index.php?title=Getal_van_Abbe&oldid=39247639</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorieën</a>: <ul><li><a href="/wiki/Categorie:Fysische_optica" title="Categorie:Fysische optica">Fysische optica</a></li><li><a href="/wiki/Categorie:Geometrische_optica" title="Categorie:Geometrische optica">Geometrische 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