{"id":1479,"date":"2020-03-22T18:21:55","date_gmt":"2020-03-22T18:21:55","guid":{"rendered":"http:\/\/lousodrome.net\/blog\/light\/?p=1479"},"modified":"2020-03-22T18:21:57","modified_gmt":"2020-03-22T18:21:57","slug":"from-maxwells-equations-to-fresnels-equations","status":"publish","type":"post","link":"https:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/","title":{"rendered":"From Maxwell&#8217;s equations to Fresnel&#8217;s equations"},"content":{"rendered":"\n<p>This <a href=\"https:\/\/www.youtube.com\/playlist?list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p\">series of short videos<\/a> shows how to derive <a href=\"https:\/\/en.wikipedia.org\/wiki\/Maxwell%27s_equations\">Maxwell&#8217;s equations<\/a> all the way to <a href=\"https:\/\/en.wikipedia.org\/wiki\/Fresnel_equations\">Fresnel&#8217;s equations<\/a>. Each one is about 10 to 15mn long.<\/p>\n\n\n\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/_FS6csrxBPU\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\" width=\"560\" height=\"315\" frameborder=\"0\"><\/iframe><\/p>\n\n\n\n<p>The first four videos show how to use boundary conditions to deduce the relationship between the electromagnetic field on both sides of a surface (or interface between two different media).<br><\/p>\n\n\n\n<ul><li><a href=\"https:\/\/www.youtube.com\/watch?v=_FS6csrxBPU&amp;list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p\">Electromagnetic Boundary Conditions Explained<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=vlNUGyDzJ90&amp;list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p&amp;index=2\">Normal Electric Field Boundary Conditions<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=BMUz8AjYzOc&amp;list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p&amp;index=3\">Tangential Magnetic Field Boundary Conditions<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=7NdMcBmjpuo&amp;list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p&amp;index=4\">Normal Magnetic Field Boundary Conditions<\/a><\/li><\/ul>\n\n\n\n<p>The next four videos use the previous results to obtain the Fresnel equations, for S-polarized and P-polarized cases.<\/p>\n\n\n\n<ul><li><a href=\"https:\/\/www.youtube.com\/watch?v=86eU7TKTr5U&amp;list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p&amp;index=5\">Wave Impedance Explained<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=fB3upo0TM6k&amp;list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p&amp;index=6\">Fresnel Equations at Normal Incidence<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=DRo2ItvLHNo&amp;list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p&amp;index=7\">Fresnels Equations at an Angle<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=OgjZj60yt04&amp;list=PLQms29D1RqeKnVqHdrQbHr7uvA7Q3401p&amp;index=8\">Fresnels Equations for p-Polarized Waves<\/a><\/li><\/ul>\n\n\n\n<p>The rest of the series then dives into other topics like thin film interference.<\/p>\n\n\n\n<p>The series assumes the viewer to be already familiar with the Maxwell equations, so it can be helpful to first see the explanation by Grant Sanderson of <a href=\"https:\/\/www.youtube.com\/watch?v=rB83DpBJQsE\">3Blue1Brown on Maxwell&#8217;s equations<\/a>.<\/p>\n\n\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/rB83DpBJQsE\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\" width=\"560\" height=\"315\" frameborder=\"0\"><\/iframe><\/p>","protected":false},"excerpt":{"rendered":"<p>This series of short videos shows how to derive Maxwell&#8217;s equations all the way to Fresnel&#8217;s equations. Each one is about 10 to 15mn long. The first four videos show how to use boundary conditions to deduce the relationship between &hellip; <a href=\"https:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[17,20],"tags":[911,910,888,112,371,909,29,75,76,666,46],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.13 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>From Maxwell&#039;s equations to Fresnel&#039;s equations &ndash; Light is beautiful<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"From Maxwell&#039;s equations to Fresnel&#039;s equations &ndash; Light is beautiful\" \/>\n<meta property=\"og:description\" content=\"This series of short videos shows how to derive Maxwell&#8217;s equations all the way to Fresnel&#8217;s equations. Each one is about 10 to 15mn long. The first four videos show how to use boundary conditions to deduce the relationship between &hellip; Continue reading &rarr;\" \/>\n<meta property=\"og:url\" content=\"http:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/\" \/>\n<meta property=\"og:site_name\" content=\"Light is beautiful\" \/>\n<meta property=\"article:published_time\" content=\"2020-03-22T18:21:55+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-03-22T18:21:57+00:00\" \/>\n<meta name=\"author\" content=\"Julien Guertault\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@Zavie\" \/>\n<meta name=\"twitter:site\" content=\"@Zavie\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Julien Guertault\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/\"},\"author\":{\"name\":\"Julien Guertault\",\"@id\":\"https:\/\/lousodrome.net\/blog\/light\/#\/schema\/person\/a16a2a69d73eca763ffdf125c49eaa2f\"},\"headline\":\"From Maxwell&#8217;s equations to Fresnel&#8217;s equations\",\"datePublished\":\"2020-03-22T18:21:55+00:00\",\"dateModified\":\"2020-03-22T18:21:57+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/\"},\"wordCount\":161,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/lousodrome.net\/blog\/light\/#\/schema\/person\/a16a2a69d73eca763ffdf125c49eaa2f\"},\"keywords\":[\"3Blue1Brown\",\"electromagnetism\",\"equation\",\"Fresnel\",\"math\",\"Maxwell\",\"physics\",\"reflection\",\"refraction\",\"tutorial\",\"video\"],\"articleSection\":[\"Rendering\",\"Science\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/\",\"url\":\"http:\/\/lousodrome.net\/blog\/light\/2020\/03\/22\/from-maxwells-equations-to-fresnels-equations\/\",\"name\":\"From Maxwell's equations to Fresnel's equations &ndash; 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