{"id":194482,"date":"2025-02-24T06:44:02","date_gmt":"2025-02-24T06:44:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=194482"},"modified":"2025-02-24T06:44:04","modified_gmt":"2025-02-24T06:44:04","slug":"making-use-of-the-ideas-of-equal-transit-times-between-corresponding-points-and-the-orthogonality-of-rays-and-wavefronts-derive-the-law-of-reflection-and-snells-law","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/24\/making-use-of-the-ideas-of-equal-transit-times-between-corresponding-points-and-the-orthogonality-of-rays-and-wavefronts-derive-the-law-of-reflection-and-snells-law\/","title":{"rendered":"Making use of the ideas of equal transit times between corresponding points and the orthogonality of rays and wavefronts, derive the Law of Reflection and Snell\u2019s Law"},"content":{"rendered":"\n

Making use of the ideas of equal transit times between corresponding points and the orthogonality of rays and wavefronts, derive the Law of Reflection and Snell\u2019s Law. The ray diagram of Fig. P.4.32<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Derivation of the Law of Reflection and Snell\u2019s Law<\/strong><\/h3>\n\n\n\n

Using Fermat\u2019s principle, which states that light travels the path that requires the least time, we derive the Law of Reflection<\/strong> and Snell\u2019s Law<\/strong> using wavefronts and rays.<\/p>\n\n\n\n

1. Law of Reflection<\/strong><\/h4>\n\n\n\n

Consider a plane wavefront approaching a reflecting surface at an angle. The wavefront meets the surface at points A<\/strong> and B<\/strong>. If the wavefront is to maintain equal transit times between corresponding points, the new wavefront after reflection must form such that the angles are equal.<\/p>\n\n\n\n

From the diagram:<\/p>\n\n\n\n

    \n
  • The incident wavefront meets the surface at A<\/strong> first and then at B<\/strong>.<\/li>\n\n\n\n
  • The reflected wavefront must maintain equal distances traveled for light from A and B to form a coherent front.<\/li>\n<\/ul>\n\n\n\n

    By considering the orthogonality<\/strong> of rays (perpendicular to wavefronts), we see:<\/p>\n\n\n\n

      \n
    • The angle of incidence \u03b8i<\/strong> is equal to the angle of reflection \u03b8r<\/strong>, as the path lengths remain equal.<\/li>\n<\/ul>\n\n\n\n

      Thus, \u03b8i = \u03b8r<\/strong>, proving the Law of Reflection.<\/p>\n\n\n\n

      2. Snell\u2019s Law<\/strong><\/h4>\n\n\n\n

      When light travels between two media with refractive indices n\u2081<\/strong> and n\u2082<\/strong>, the wavefront changes speed. Let the wavefront strike the interface at A<\/strong> and B<\/strong> with speed v\u2081<\/strong> in medium 1 and v\u2082<\/strong> in medium 2.<\/p>\n\n\n\n

      Using equal transit time principles:<\/p>\n\n\n\n

        \n
      • Distance traveled in medium 1: v\u2081t<\/strong>.<\/li>\n\n\n\n
      • Distance traveled in medium 2: v\u2082t<\/strong>.<\/li>\n\n\n\n
      • The wavefront must remain continuous, so the path difference forms a new refracted wavefront.<\/li>\n<\/ul>\n\n\n\n

        From the geometry:
        [
        \\frac{\\sin \u03b8_1}{v_1} = \\frac{\\sin \u03b8_2}{v_2}
        ]
        Since ( v = \\frac{c}{n} ), we obtain Snell\u2019s Law:
        [
        n_1 \\sin \u03b8_1 = n_2 \\sin \u03b8_2
        ]
        which describes the bending of light.<\/p>\n\n\n\n

        Now, I will generate the image illustrating this concept.<\/p>\n\n\n\n

        Here is the generated diagram illustrating the derivation of the Law of Reflection and Snell\u2019s Law using wavefronts and rays. Let me know if you need any modifications or further clarifications!<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Making use of the ideas of equal transit times between corresponding points and the orthogonality of rays and wavefronts, derive the Law of Reflection and Snell\u2019s Law. The ray diagram of Fig. P.4.32 The Correct Answer and Explanation is : Derivation of the Law of Reflection and Snell\u2019s Law Using Fermat\u2019s principle, which states that […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-194482","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194482","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=194482"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194482\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}