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class="pre-content heading-holder"> <div class="page-heading"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Angle of incidence (optics)</span></h1> <div class="tagline"></div> </div> <ul id="p-associated-pages" class="minerva__tab-container"> <li class="minerva__tab selected mw-list-item"> <a class="minerva__tab-text" href="/wiki/Angle_of_incidence_(optics)" rel="" data-event-name="tabs.main">Article</a> </li> <li class="minerva__tab mw-list-item"> <a class="minerva__tab-text" href="/wiki/Talk:Angle_of_incidence_(optics)" rel="discussion" data-event-name="tabs.talk">Talk</a> </li> </ul> <nav class="page-actions-menu"> <ul id="p-views" class="page-actions-menu__list"> <li id="language-selector" class="page-actions-menu__list-item"> <a role="button" href="#p-lang" data-mw="interface" data-event-name="menu.languages" title="Language" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled 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menu__item--page-actions-edit"> <span class="minerva-icon minerva-icon--edit"></span> <span>Edit</span> </a> </li> </ul> </nav>  <div id="mw-content-subtitle"></div> </div> <div id="bodyContent" class="content"> <div id="mw-content-text" class="mw-body-content"><script>function mfTempOpenSection(id){var block=document.getElementById("mf-section-"+id);block.className+=" open-block";block.previousSibling.className+=" open-block";}</script><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><section class="mf-section-0" id="mf-section-0"> <p>The <b>angle of incidence</b>, in <a href="/wiki/Geometric_optics" class="mw-redirect" title="Geometric optics">geometric optics</a>, is the angle between a <a href="/wiki/Incident_ray" class="mw-redirect" title="Incident ray">ray incident</a> on a surface and the line perpendicular (at 90 degree angle) to the surface at the point of incidence, called the <a href="/wiki/Surface_normal" class="mw-redirect" title="Surface normal">normal</a>. The ray can be formed by any waves, such as <a href="/wiki/Light_wave" class="mw-redirect" title="Light wave">optical</a>, <a href="/wiki/Sound_wave" class="mw-redirect" title="Sound wave">acoustic</a>, <a href="/wiki/Microwave" title="Microwave">microwave</a>, and <a href="/wiki/X-ray" title="X-ray">X-ray</a>. In the figure below, the line representing a ray makes an angle θ with the normal (dotted line). The angle of incidence at which light is first totally internally reflected is known as the <a href="/wiki/Critical_angle_(optics)" class="mw-redirect" title="Critical angle (optics)">critical angle</a>. The <a href="/wiki/Angle_of_reflection" class="mw-redirect" title="Angle of reflection">angle of reflection</a> and <a href="/wiki/Angle_of_refraction" class="mw-redirect" title="Angle of refraction">angle of refraction</a> are other angles related to beams. </p><p>In <a href="/wiki/Computer_graphics" title="Computer graphics">computer graphics</a> and <a href="/wiki/Geography" title="Geography">geography</a>, the angle of incidence is also known as the <b>illumination angle</b> of a surface with a light source, such as the <a href="/wiki/Earth" title="Earth">Earth</a>'s surface and the <a href="/wiki/Sun" title="Sun">Sun</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It can also be equivalently described as the angle between the <a href="/wiki/Tangent_plane" class="mw-redirect" title="Tangent plane">tangent plane</a> of the surface and another plane at right angles to the light rays.<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> This means that the illumination angle of a certain point on Earth's surface is <a href="/wiki/Degree_(angle)" title="Degree (angle)">0°</a> if the Sun is <a href="/wiki/Zenith" title="Zenith">precisely overhead</a> and that it is <a href="/wiki/Right_angle" title="Right angle">90°</a> at <a href="/wiki/Sunset" title="Sunset">sunset</a> or <a href="/wiki/Sunrise" title="Sunrise">sunrise</a>. </p><p>Determining the angle of reflection with respect to a planar surface is trivial, but the computation for almost any other surface is significantly more difficult. </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:RefractionReflextion.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/RefractionReflextion.svg/650px-RefractionReflextion.svg.png" decoding="async" width="650" height="202" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/RefractionReflextion.svg/975px-RefractionReflextion.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/RefractionReflextion.svg/1300px-RefractionReflextion.svg.png 2x" data-file-width="2441" data-file-height="758"></a><figcaption>Refraction of light at the interface between two media</figcaption></figure> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Grazing_angle_or_glancing_angle"><span class="tocnumber">1</span> <span class="toctext">Grazing angle or glancing angle</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#See_also"><span class="tocnumber">2</span> <span class="toctext">See also</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#References"><span class="tocnumber">3</span> <span class="toctext">References</span></a></li> <li class="toclevel-1 tocsection-4"><a href="#External_links"><span class="tocnumber">4</span> <span class="toctext">External links</span></a></li> </ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Grazing_angle_or_glancing_angle">Grazing angle or glancing angle</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Angle_of_incidence_(optics)&action=edit&section=1" title="Edit section: Grazing angle or glancing angle" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Angle_of_incidence_(optics)" title="Special:EditPage/Angle of incidence (optics)">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.<br><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Angle+of+incidence%22+optics">"Angle of incidence" optics</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Angle+of+incidence%22+optics+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Angle+of+incidence%22+optics&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Angle+of+incidence%22+optics+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Angle+of+incidence%22+optics">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Angle+of+incidence%22+optics&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">January 2025</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p><span class="anchor" id="Grazing_angle"></span><span class="anchor" id="Glancing_angle"></span> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Xray_telescope_lens.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Xray_telescope_lens.svg/220px-Xray_telescope_lens.svg.png" decoding="async" width="220" height="124" class="mw-file-element" data-file-width="512" data-file-height="288"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 124px;" data-mw-src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Xray_telescope_lens.svg/220px-Xray_telescope_lens.svg.png" data-width="220" data-height="124" data-mw-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Xray_telescope_lens.svg/330px-Xray_telescope_lens.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Xray_telescope_lens.svg/440px-Xray_telescope_lens.svg.png 2x" data-class="mw-file-element"> </span></a><figcaption>Focusing X-rays with glancing reflection</figcaption></figure> <p>When dealing with a beam that is nearly parallel to a surface, it is sometimes more useful to refer to the angle between the beam and the <a href="/wiki/Surface_tangent" class="mw-redirect" title="Surface tangent">surface tangent</a>, rather than that between the beam and the <a href="/wiki/Surface_normal" class="mw-redirect" title="Surface normal">surface normal</a>. The 90-degree <a href="/wiki/Complementary_angle" class="mw-redirect" title="Complementary angle">complement</a> to the angle of incidence is called the <b>grazing angle</b> or <b>glancing angle</b>. Incidence at small grazing angles is called "grazing incidence."<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2025)">citation needed</span></a></i>]</sup> </p><p><a href="/wiki/Grazing_incidence_diffraction" title="Grazing incidence diffraction">Grazing incidence diffraction</a> is used in <a href="/wiki/X-ray_spectroscopy" title="X-ray spectroscopy">X-ray spectroscopy</a> and <a href="/wiki/Atom_optics" title="Atom optics">atom optics</a>, where significant reflection can be achieved only at small values of the grazing angle. <a href="/wiki/Ridged_mirror" title="Ridged mirror">Ridged mirrors</a> are designed to reflect atoms coming at a small grazing angle. This angle is usually measured in <a href="/wiki/Milliradian" title="Milliradian">milliradians</a>. In optics, there is <a href="/wiki/Lloyd%27s_mirror" title="Lloyd's mirror">Lloyd's mirror</a>. </p> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="See_also">See also</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Angle_of_incidence_(optics)&action=edit&section=2" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> <ul><li><a href="/wiki/Effect_of_Sun_angle_on_climate" title="Effect of Sun angle on climate">Effect of Sun angle on climate</a></li> <li><a href="/wiki/Illumination_angle" class="mw-redirect" title="Illumination angle">Illumination angle</a></li> <li><a href="/wiki/Phase_angle_(astronomy)" title="Phase angle (astronomy)">Phase angle (astronomy)</a></li> <li><a href="/wiki/Plane_of_incidence" title="Plane of incidence">Plane of incidence</a></li> <li><a href="/wiki/Reflection_(physics)" title="Reflection (physics)">Reflection (physics)</a></li> <li><a href="/wiki/Refraction" title="Refraction">Refraction</a></li> <li><a href="/wiki/Scattering_vector" class="mw-redirect" title="Scattering vector">Scattering vector</a></li> <li><a href="/wiki/Total_internal_reflection" title="Total internal reflection">Total internal reflection</a></li></ul> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="References">References</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Angle_of_incidence_(optics)&action=edit&section=3" title="Edit section: References" class="cdx-button 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.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFGodse2008" class="citation book cs1">Godse, A. P. (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=A1ka6gqKTD4C&pg=PA292"><i>Computer Graphics</i></a>. Technical Publications. p. 292. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9788189411008" title="Special:BookSources/9788189411008"><bdi>9788189411008</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computer+Graphics&rft.pages=292&rft.pub=Technical+Publications&rft.date=2008&rft.isbn=9788189411008&rft.aulast=Godse&rft.aufirst=A.+P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DA1ka6gqKTD4C%26pg%3DPA292&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAngle+of+incidence+%28optics%29" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHenglReuter2022" class="citation book cs1">Hengl, Tomislav; Reuter, Hannes I. (2022). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=iZXBeNOzOPEC&pg=PA201"><i>Geomorphometryoncepts, Software, Applications</i></a>. Developments in soil science. Vol. 33. Farha. p. 202. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780123743459" title="Special:BookSources/9780123743459"><bdi>9780123743459</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geomorphometryoncepts%2C+Software%2C+Applications&rft.series=Developments+in+soil+science&rft.pages=202&rft.pub=Farha&rft.date=2022&rft.isbn=9780123743459&rft.aulast=Hengl&rft.aufirst=Tomislav&rft.au=Reuter%2C+Hannes+I.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DiZXBeNOzOPEC%26pg%3DPA201&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAngle+of+incidence+%28optics%29" class="Z3988"></span></span> </li> </ol></div></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="External_links">External links</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Angle_of_incidence_(optics)&action=edit&section=4" title="Edit section: External links" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-4 collapsible-block" id="mf-section-4"> <ul><li><span class="citation mathworld" id="Reference-Mathworld-Angle_of_incidence"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. 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