{"id":175702,"date":"2016-01-29T03:00:00","date_gmt":"2016-01-29T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=eb7c18567eb01475925e7e15ed289119"},"modified":"2016-01-29T03:00:00","modified_gmt":"2016-01-29T00:00:00","slug":"is-n-sin-%ce%b8-conserved-along-the-light-path","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=175702","title":{"rendered":"Is n sin \u03b8 conserved along the light path?"},"content":{"rendered":"<p>Snell\u2019s law states that the quantity ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/2\/025301\/ejpaa12c8ieqn3.gif] {$nmathrm{sin}theta $} is<br \/>\nunchanged in refraction of light passing from one medium to another. We inquire whether this is true<br \/>\nin the general case where the speed of light varies continuously within a medium. It turns out to be<br \/>\nan instructive exercise in application of Snell\u2019s law and Fermat\u2019s principle. It also provides good<br \/>\npedagogical problems in calculus of variations to deal with the subtleties of a variable domain of<br \/>\nintegration and inclusion of constraints. The final result of these exercises is that, contrary to<br \/>\nan initial expectation, the answer to the question in the title is negative.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Snell\u2019s law states that the quantity ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/37\/2\/025301\/ejpaa12c8ieqn3.gif] {$nmathrm{sin}theta $} is<br \/>\nunchanged in refraction of light passing from one medium to another. We inquire whether this is true<br \/>\nin th&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-175702","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/175702","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=175702"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/175702\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=175702"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=175702"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=175702"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}