{"id":628285,"date":"2023-06-23T16:41:33","date_gmt":"2023-06-23T11:11:33","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=628285"},"modified":"2024-07-05T13:00:01","modified_gmt":"2024-07-05T07:30:01","slug":"refraction-formula-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula","title":{"rendered":"Refraction Formula\u00a0"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#Introduction\" title=\"Introduction\">Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#Formula_for_Refraction\" title=\"Formula for Refraction\">Formula for Refraction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#What_is_Refraction_Formula_mathematically\" title=\"What is Refraction Formula mathematically?\">What is Refraction Formula mathematically?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#Solved_Examples_on_Refraction_Formula\" title=\"Solved Examples on Refraction Formula\">Solved Examples on Refraction Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#FAQs_on_Refraction_Formula\" title=\"FAQs on Refraction Formula\">FAQs on Refraction Formula<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#What_is_the_general_formula_for_refraction\" title=\"What is the general formula for refraction? \">What is the general formula for refraction? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#What_are_the_2_laws_of_refraction\" title=\"What are the 2 laws of refraction? \">What are the 2 laws of refraction? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#What_is_the_relationship_between_the_angles_of_incidence_and_refraction\" title=\"What is the relationship between the angles of incidence and refraction? \">What is the relationship between the angles of incidence and refraction? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#What_is_the_mathematical_expression_of_Snells_law\" title=\"What is the mathematical expression of Snell&#039;s law? \">What is the mathematical expression of Snell&#039;s law? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#What_is_Snells_law\" title=\"What is Snell&#039;s law? \">What is Snell&#039;s law? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/refraction-formula\/#What_is_refraction_in_physics\" title=\"What is refraction in physics? \">What is refraction in physics? <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">The <strong>refractive index (n)<\/strong> of a medium is a measure of how much light slows down when passing through it, compared to the speed of light in a vacuum. It is a dimensionless quantity. <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">It expresses the relationship that when light passes from one medium to another, its direction changes due to the change in speed. The amount of bending, or refraction, depends on the refractive indices of the two mediums and the angles of incidence and refraction. <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The <strong>refraction formula<\/strong> is widely used in optics and is crucial in understanding the behavior of light as it interacts with different mediums, such as when light passes from air to water or from air to a glass lens. <\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Formula_for_Refraction\"><\/span>Formula for Refraction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">The refraction formula describes the relationship between the angles of incidence and refraction when light passes through a boundary between two different transparent mediums. It is known as Snell&#8217;s law of refraction and is given by the formula:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><strong>n1 x sin(\u03b81) = n2 x sin(\u03b82) <\/strong><\/p>\n<p><span data-contrast=\"auto\">where:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">n1 is the refractive index of the medium the incident ray is coming from,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">n2 is the refractive index of the medium the refracted ray enters,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">\u03b81 is the angle of incidence (measured between the incident ray and the normal to the boundary),<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">\u03b82 is the angle of refraction (measured between the refracted ray and the normal to the boundary).<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Refraction_Formula_mathematically\"><\/span>What is Refraction Formula mathematically?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"none\">Consider a ray of light travelling from medium 1 to medium 2. Let the angle of incidence be <\/span><i><span data-contrast=\"none\">i <\/span><\/i><span data-contrast=\"none\">and the angle of refraction be r. Let the speed of light in medium 1 be v<\/span><span data-contrast=\"none\">1<\/span><span data-contrast=\"none\"> and that in medium 2 be v<\/span><span data-contrast=\"none\">2<\/span><span data-contrast=\"none\">. Let n<\/span><span data-contrast=\"none\">21<\/span><span data-contrast=\"none\"> be the refractive index of medium 2 with respect to medium 1.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559737&quot;:72,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-medium wp-image-628286 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163743-300x205.png\" alt=\"\" width=\"300\" height=\"205\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163743-300x205.png?v=1687518575 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163743.png?v=1687518575 405w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><span data-contrast=\"none\">Light travelling from medium 1 to medium 2<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span data-contrast=\"none\">Then, according to Snell&#8217;s law,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628287 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163757.png\" alt=\"\" width=\"272\" height=\"53\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">Also, by definition of refractive index,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628288 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163808.png\" alt=\"\" width=\"216\" height=\"51\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">Thus, from statement (i) and (ii),<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628289 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163820.png\" alt=\"\" width=\"192\" height=\"53\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">Let n<\/span><span data-contrast=\"none\">1<\/span><span data-contrast=\"none\"> and n<\/span><span data-contrast=\"none\">2 <\/span><span data-contrast=\"none\">be the absolute refractive indices of medium 1 and medium 2 respectively. If the velocity of light in vacuum is <\/span><i><span data-contrast=\"none\">c, <\/span><\/i><span data-contrast=\"none\">then,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559737&quot;:144,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:360}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628290 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163848.png\" alt=\"\" width=\"185\" height=\"203\" \/><\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628291 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163858.png\" alt=\"\" width=\"227\" height=\"60\" \/><\/span><\/p>\n<p><span data-contrast=\"none\">From statements (iii) and (iv), Snell&#8217;s law can be expressed as<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:2,&quot;335551620&quot;:2,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <img loading=\"lazy\" class=\"size-full wp-image-628292 aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/06\/Screenshot-2023-06-23-163912.png\" alt=\"\" width=\"232\" height=\"75\" \/><\/span><\/p>\n<p><span data-contrast=\"auto\">Remember that the refractive index does not have a unit as it is just a ratio of similar quantities.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Examples_on_Refraction_Formula\"><\/span>Solved Examples on Refraction Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Example 1: A light ray travels from water (refractive index = 1.33) into diamond (refractive index = 2.42). If the angle of incidence is 40 degrees, calculate the angle of refraction. <\/strong><\/p>\n<p><strong>Solution: <\/strong><\/p>\n<p><span data-contrast=\"none\">Given:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">n\u2081 (refractive index of water) = 1.33<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">n\u2082 (refractive index of diamond) = 2.42<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u03b8\u2081 (angle of incidence) = 40 degrees<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Using Snell&#8217;s law we can write,<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">n\u2081 x sin(\u03b8\u2081) = n\u2082 x sin(\u03b8\u2082)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Substituting the given values:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">1.33 x sin(40) = 2.42 x sin(\u03b8\u2082)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">sin(\u03b8\u2082) = (1.33 x sin(40)) \/ 2.42<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">sin(\u03b8\u2082) \u2248 0.706<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Taking the inverse sine (arcsine) of both sides:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u03b8\u2082 = arcsine(0.706)<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Using a calculator:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">\u03b8\u2082 \u2248 44.1 degrees<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, the angle of refraction is approximately 44.1 degrees.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><strong>Example 2: Light enters from air to glass having a refractive index of 1.50. What is the speed of light in glass? (The speed of light in vacuum = 3  \u00d7 108  m\/s). <\/strong><\/p>\n<p><strong>Answer:<\/strong> <span data-contrast=\"none\">To calculate the speed of light in glass, we can use the formula:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Speed of light in medium = Speed of light in vacuum \/ Refractive index of the medium<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Given: Speed of light in vacuum (c) = 3 \u00d7 10<\/span><span data-contrast=\"none\">8 <\/span><span data-contrast=\"none\">m\/s Refractive index of glass (n) = 1.50<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Substituting the values into the formula:<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Speed of light in glass = (3 \u00d7 10<\/span><span data-contrast=\"none\">8<\/span><span data-contrast=\"none\"> m\/s) \/ 1.50<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Speed of light in glass \u2248 2 \u00d7 10<\/span><span data-contrast=\"none\">8<\/span><span data-contrast=\"none\"> m\/s<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Therefore, the speed of light in glass is approximately 2 \u00d7 10<\/span><span data-contrast=\"none\">8<\/span><span data-contrast=\"none\"> m\/s.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:0,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_Refraction_Formula\"><\/span>FAQs on Refraction Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_general_formula_for_refraction\"><\/span>What is the general formula for refraction? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe general formula for refraction is known as Snell's law. It relates the angles of incidence and refraction of a light ray passing through the boundary between two different transparent mediums. Snell's law is expressed as:  n1 x sin(\u03b81) = n2 x sin(\u03b82)  where:  n1 is the refractive index of the medium the incident ray is coming from,  n2 is the refractive index of the medium the refracted ray enters,  \u03b81 is the angle of incidence (measured between the incident ray and the normal to the boundary),  \u03b82 is the angle of refraction (measured between the refracted ray and the normal to the boundary).  The refractive index (n) of a medium is a measure of how much light slows down when passing through it, compared to the speed of light in a vacuum. It is a dimensionless quantity. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_the_2_laws_of_refraction\"><\/span>What are the 2 laws of refraction? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tLaws of refraction are:  The incident ray, the refracted ray, and the normal at the point of incidence lie on the same plane.  The refractive index of a refractive medium with respect to the incident medium is equal to the ratio of the sine of the incident angle to the sine of the refractive angle. This is also known as Snell's law. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_relationship_between_the_angles_of_incidence_and_refraction\"><\/span>What is the relationship between the angles of incidence and refraction? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe relationship between the angles of incidence and refraction is given by Snell's law. It states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_mathematical_expression_of_Snells_law\"><\/span>What is the mathematical expression of Snell&#039;s law? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tSnell's law is expressed as: n\u2081 x sin(\u03b8\u2081) = n\u2082 x sin(\u03b8\u2082), where n\u2081 and n\u2082 are the refractive indices of the incident and refracting media, respectively, and \u03b8\u2081 and \u03b8\u2082 are the angles of incidence and refraction, respectively. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_Snells_law\"><\/span>What is Snell&#039;s law? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tSnell's law, also known as Snell-Descartes law, is a fundamental principle in optics that describes the behavior of light as it passes from one medium to another. It relates the angles of incidence and refraction to the refractive indices of the two media involved. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_refraction_in_physics\"><\/span>What is refraction in physics? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tRefraction in physics refers to the bending or change in direction of a wave as it passes from one medium to another, caused by a change in its speed. It occurs due to the difference in the optical density or refractive index of the two mediums. Refraction is responsible for phenomena such as the bending of light in lenses, the formation of rainbows, and the apparent displacement of objects in water. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the general formula for refraction? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The general formula for refraction is known as Snell's law. It relates the angles of incidence and refraction of a light ray passing through the boundary between two different transparent mediums. Snell's law is expressed as:  n1 x sin(\u03b81) = n2 x sin(\u03b82)  where:  n1 is the refractive index of the medium the incident ray is coming from,  n2 is the refractive index of the medium the refracted ray enters,  \u03b81 is the angle of incidence (measured between the incident ray and the normal to the boundary),  \u03b82 is the angle of refraction (measured between the refracted ray and the normal to the boundary).  The refractive index (n) of a medium is a measure of how much light slows down when passing through it, compared to the speed of light in a vacuum. It is a dimensionless quantity.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the 2 laws of refraction? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Laws of refraction are:  The incident ray, the refracted ray, and the normal at the point of incidence lie on the same plane.  The refractive index of a refractive medium with respect to the incident medium is equal to the ratio of the sine of the incident angle to the sine of the refractive angle. This is also known as Snell's law.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the relationship between the angles of incidence and refraction? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The relationship between the angles of incidence and refraction is given by Snell's law. It states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the mathematical expression of Snell's law? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Snell's law is expressed as: n\u2081 x sin(\u03b8\u2081) = n\u2082 x sin(\u03b8\u2082), where n\u2081 and n\u2082 are the refractive indices of the incident and refracting media, respectively, and \u03b8\u2081 and \u03b8\u2082 are the angles of incidence and refraction, respectively.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is Snell's law? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Snell's law, also known as Snell-Descartes law, is a fundamental principle in optics that describes the behavior of light as it passes from one medium to another. It relates the angles of incidence and refraction to the refractive indices of the two media involved.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is refraction in physics? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Refraction in physics refers to the bending or change in direction of a wave as it passes from one medium to another, caused by a change in its speed. It occurs due to the difference in the optical density or refractive index of the two mediums. Refraction is responsible for phenomena such as the bending of light in lenses, the formation of rainbows, and the apparent displacement of objects in water.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Introduction The refractive index (n) of a medium is a measure of how much light slows down when passing through [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Refraction Formula\u00a0","_yoast_wpseo_title":"Refraction Formula with Examples - Infinity learn","_yoast_wpseo_metadesc":"Discover the refraction formula and its role in understanding light bending. Easy explanation for students and quick reference for solving physics problems.","custom_permalink":"formulas\/refraction-formula"},"categories":[8438,8521],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Refraction Formula with Examples - Infinity learn<\/title>\n<meta name=\"description\" content=\"Discover the refraction formula and its role in understanding light bending. 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