{"id":46044,"date":"2025-07-01T18:03:13","date_gmt":"2025-07-01T18:03:13","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=46044"},"modified":"2025-07-01T18:17:18","modified_gmt":"2025-07-01T18:17:18","slug":"unpolarized-light-passes-through-two-polaroid-sheets","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/unpolarized-light-passes-through-two-polaroid-sheets\/","title":{"rendered":"Unpolarized light passes through two Polaroid sheets."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Unpolarized light passes through two Polaroid sheets. The transmission axis of the analyzer makes an angle of 42.8\u00b0 with the axis of the polarizer. (a) What fraction of the original unpolarized light is transmitted through the analyzer? (Enter your answer to at least three decimal places.) (b) What fraction of the original light is absorbed by the analyze<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is a classic problem of light passing through polarizers. The fraction of light transmitted through the analyzer can be found using <strong>Malus&#8217; law<\/strong>, which states that: I=I0cos\u20612\u03b8I = I_0 \\cos^2 \\thetaI=I0\u200bcos2\u03b8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>III is the intensity of light after passing through the analyzer.<\/li>\n\n\n\n<li>I0I_0I0\u200b is the intensity of the light before passing through the analyzer.<\/li>\n\n\n\n<li>\u03b8\\theta\u03b8 is the angle between the transmission axis of the polarizer and analyzer.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Part (a) Fraction of light transmitted through the analyzer<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Step 1: Use Malus&#8217; Law<\/strong><br>The light is initially unpolarized, so after passing through the first Polaroid (the polarizer), it becomes polarized. The transmission axis of the analyzer makes an angle of 42.8\u221842.8^\\circ42.8\u2218 with the axis of the polarizer. We use Malus&#8217; law to find the fraction of light transmitted.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">I=I0cos\u20612(42.8\u2218)I = I_0 \\cos^2(42.8^\\circ)I=I0\u200bcos2(42.8\u2218)<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>Step 2: Calculate cos\u2061(42.8\u2218)\\cos(42.8^\\circ)cos(42.8\u2218)<\/strong><br>Using a calculator:<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">cos\u2061(42.8\u2218)\u22480.743\\cos(42.8^\\circ) \\approx 0.743cos(42.8\u2218)\u22480.743<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, I=I0\u00d7(0.743)2=I0\u00d70.552I = I_0 \\times (0.743)^2 = I_0 \\times 0.552I=I0\u200b\u00d7(0.743)2=I0\u200b\u00d70.552<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the fraction of the original unpolarized light transmitted through the analyzer is approximately: 0.552\\boxed{0.552}0.552\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part (b) Fraction of light absorbed by the analyzer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The light absorbed by the analyzer is simply the fraction that does not pass through. Therefore, the fraction of light absorbed is: Absorbed&nbsp;fraction=1\u2212Transmitted&nbsp;fraction=1\u22120.552=0.448\\text{Absorbed fraction} = 1 &#8211; \\text{Transmitted fraction} = 1 &#8211; 0.552 = 0.448Absorbed&nbsp;fraction=1\u2212Transmitted&nbsp;fraction=1\u22120.552=0.448<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, the fraction of light absorbed by the analyzer is approximately: 0.448\\boxed{0.448}0.448\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The fraction of the original unpolarized light transmitted through the analyzer is 0.5520.5520.552.<\/li>\n\n\n\n<li>The fraction of the original light absorbed by the analyzer is 0.4480.4480.448.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-89.jpeg\" alt=\"\" class=\"wp-image-46059\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-89.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-89-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-89-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-89-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Unpolarized light passes through two Polaroid sheets. The transmission axis of the analyzer makes an angle of 42.8\u00b0 with the axis of the polarizer. (a) What fraction of the original unpolarized light is transmitted through the analyzer? (Enter your answer to at least three decimal places.) (b) What fraction of the original light is absorbed [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-46044","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46044","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=46044"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46044\/revisions"}],"predecessor-version":[{"id":46060,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46044\/revisions\/46060"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=46044"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=46044"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=46044"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}