{"id":131171,"date":"2023-02-15T12:16:49","date_gmt":"2023-02-15T06:46:49","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=131171"},"modified":"2023-02-15T12:16:49","modified_gmt":"2023-02-15T06:46:49","slug":"a-narrow-slit-is-illuminated-by-a-parallel-beam-of-monochromatic-light-of-wavelength-%ce%bb-equal","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/education\/a-narrow-slit-is-illuminated-by-a-parallel-beam-of-monochromatic-light-of-wavelength-%ce%bb-equal","title":{"rendered":"A narrow slit is illuminated by a parallel beam of monochromatic light of wavelength \u03bb equal&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;"},"content":{"rendered":"<h2>Question 8:A narrow slit is illuminated by a parallel beam of monochromatic light of wavelength \u03bb equal to 6000 \u00c5 and the angular width of the central maximum in the resulting diffraction pattern is measured. When the slit<br \/>\nis next illuminated by light of wavelength \u03bb\u2019, the angular width decreases by 30%. Calculate the value of the wavelength \u03bb\u2019.<\/h2>\n<h3>The correct answer is &#8211; When a narrow slit is illuminated by a parallel beam of monochromatic light, a diffraction pattern is produced consisting of a central maximum and a series of smaller secondary maxima and minima. The angular width of the central maximum can be determined using the formula:<\/h3>\n<h3>\u03b8 = \u03bb \/ a<\/h3>\n<h3>where \u03b8 is the angular width of the central maximum, \u03bb is the wavelength of the light, and a is the width of the slit.<\/h3>\n<h3>We are given that for the wavelength \u03bb = 6000 \u00c5, the angular width of the central maximum is \u03b8.<\/h3>\n<h3>When the wavelength of the light is changed to \u03bb&#8217;, the angular width of the central maximum decreases by 30%. Let \u03b8&#8217; be the new angular width of the central maximum. We can express the relationship between \u03b8 and \u03b8&#8217; as:<\/h3>\n<h3>\u03b8&#8217; = 0.7\u03b8<\/h3>\n<h3>Using the formula for \u03b8, we can write:<\/h3>\n<h3>\u03b8&#8217; = \u03bb&#8217; \/ a<\/h3>\n<h3>Equating the expressions for \u03b8&#8217; in terms of \u03b8 and in terms of \u03bb&#8217; and a, we get:<\/h3>\n<h3>0.7\u03b8 = \u03bb&#8217; \/ a<\/h3>\n<h3>Substituting the given values, we get:<\/h3>\n<h3>0.7\u03b8 = \u03bb&#8217; \/ a = \u03bb&#8217; \/ (6000 \u00c5)<\/h3>\n<h3>Solving for \u03bb&#8217;, we get:<\/h3>\n<h3>\u03bb&#8217; = 0.7\u03b8 \u00d7 6000 \u00c5 \/ a<\/h3>\n<h3>Substituting the given values for \u03b8 and a, we get:<\/h3>\n<h3>\u03bb&#8217; = 0.7 \u00d7 \u03b8 \u00d7 6000 \u00c5 \/ a = 0.7 \u00d7 \u03b8 \u00d7 6000 \u00c5 \/ (2 \u00d7 10^-4 m)<\/h3>\n<h3>where we have converted the slit width a from angstroms to meters.<\/h3>\n<h3>Substituting the given value of \u03b8 and solving, we get:<\/h3>\n<h3>\u03bb&#8217; = 0.7 \u00d7 (\u03bb \/ a) \u00d7 6000 \u00c5 \/ (2 \u00d7 10^-4 m) = 0.7 \u00d7 (6000 \u00c5 \/ 2 \u00d7 10^-4 m) \u00d7 6000 \u00c5 \/ (2 \u00d7 10^-4 m) = 7350 \u00c5<\/h3>\n<h3>Therefore, the value of the wavelength \u03bb&#8217; is 7350 \u00c5.<\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Question 8:A narrow slit is illuminated by a parallel beam of monochromatic light of wavelength \u03bb equal to 6000 \u00c5 and the angular width of the central maximum in the resulting diffraction pattern is measured. When the slit is next illuminated by light of wavelength \u03bb\u2019, the angular width decreases by 30%. Calculate the value [&hellip;]<\/p>\n","protected":false},"author":21830,"featured_media":131018,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":{"0":"post-131171","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-education"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/131171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21830"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=131171"}],"version-history":[{"count":2,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/131171\/revisions"}],"predecessor-version":[{"id":131176,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/131171\/revisions\/131176"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/131018"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=131171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=131171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=131171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}