{"id":39515,"date":"2025-06-27T08:09:38","date_gmt":"2025-06-27T08:09:38","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39515"},"modified":"2025-06-27T08:09:40","modified_gmt":"2025-06-27T08:09:40","slug":"in-youngs-double-slit-interference-experiment-the-distance-between-two-sources-is-0-1-p-mm","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/in-youngs-double-slit-interference-experiment-the-distance-between-two-sources-is-0-1-p-mm\/","title":{"rendered":"In young’s double slit interference experiment, the distance between two sources is 0.1\/p mm."},"content":{"rendered":"\n

In young’s double slit interference experiment, the distance between two sources is 0.1\/p mm. The distance of the screen from the source is 25 cm. Wavelength of light used is 5000A ?. Then what is the angular position of the first dark fringe ?”<\/p>\n\n\n\n

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

Correct Answer:<\/strong><\/h3>\n\n\n\n

To find the angular position of the first dark fringe in Young\u2019s double slit experiment, we use the condition for destructive interference:\u03b8dark=(2n\u22121)\u03bb2d\\theta_{\\text{dark}} = \\frac{(2n – 1)\\lambda}{2d}\u03b8dark\u200b=2d(2n\u22121)\u03bb\u200b<\/p>\n\n\n\n

For the first dark fringe<\/strong>, n=1n = 1n=1, so:\u03b8=\u03bb2d\\theta = \\frac{\\lambda}{2d}\u03b8=2d\u03bb\u200b<\/p>\n\n\n\n

\n\n\n\n

Given Data:<\/strong><\/h3>\n\n\n\n
    \n
  • Distance between slits d=0.1p\u00a0mm=0.1\u00d710\u22123p\u00a0md = \\frac{0.1}{p} \\text{ mm} = \\frac{0.1 \\times 10^{-3}}{p} \\text{ m}d=p0.1\u200b\u00a0mm=p0.1\u00d710\u22123\u200b\u00a0m<\/li>\n\n\n\n
  • Wavelength \u03bb=5000\u00a0A\u02da=5000\u00d710\u221210\u00a0m=5\u00d710\u22127\u00a0m\\lambda = 5000 \\text{ \u00c5} = 5000 \\times 10^{-10} \\text{ m} = 5 \\times 10^{-7} \\text{ m}\u03bb=5000\u00a0A\u02da=5000\u00d710\u221210\u00a0m=5\u00d710\u22127\u00a0m<\/li>\n<\/ul>\n\n\n\n

    Now substitute the values:\u03b8=5\u00d710\u221272\u00d70.1\u00d710\u22123p=5\u00d710\u22127\u22c5p2\u00d70.1\u00d710\u22123=5p2\u00d70.1\u00d710\u22124=5p0.2\u00d710\u22124=25p\u00d710\u22124\\theta = \\frac{5 \\times 10^{-7}}{2 \\times \\frac{0.1 \\times 10^{-3}}{p}} = \\frac{5 \\times 10^{-7} \\cdot p}{2 \\times 0.1 \\times 10^{-3}} = \\frac{5p}{2 \\times 0.1} \\times 10^{-4} = \\frac{5p}{0.2} \\times 10^{-4} = 25p \\times 10^{-4}\u03b8=2\u00d7p0.1\u00d710\u22123\u200b5\u00d710\u22127\u200b=2\u00d70.1\u00d710\u221235\u00d710\u22127\u22c5p\u200b=2\u00d70.15p\u200b\u00d710\u22124=0.25p\u200b\u00d710\u22124=25p\u00d710\u22124\u03b8=2.5p\u00d710\u22123 radians\\theta = 2.5p \\times 10^{-3} \\text{ radians}\u03b8=2.5p\u00d710\u22123 radians<\/p>\n\n\n\n

    So the angular position of the first dark fringe is 2.5p\u00d710\u221232.5p \\times 10^{-3}2.5p\u00d710\u22123 radians<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    Explanation<\/strong><\/h3>\n\n\n\n

    Young\u2019s double slit experiment demonstrates the wave nature of light through the phenomenon of interference. When coherent light passes through two closely spaced slits, it creates an interference pattern of bright and dark fringes on a screen. This pattern results from the constructive and destructive interference of light waves emanating from the slits.<\/p>\n\n\n\n

    Constructive interference leads to bright fringes where the path difference is an integer multiple of the wavelength. Destructive interference results in dark fringes where the path difference is an odd multiple of half the wavelength. For the first dark fringe, the path difference is exactly \u03bb2\\frac{\\lambda}{2}2\u03bb\u200b.<\/p>\n\n\n\n

    The angular position of a dark fringe is given by:\u03b8=(2n\u22121)\u03bb2d\\theta = \\frac{(2n – 1)\\lambda}{2d}\u03b8=2d(2n\u22121)\u03bb\u200b<\/p>\n\n\n\n

    Here, nnn is the order of the dark fringe, \u03bb\\lambda\u03bb is the wavelength of the light, and ddd is the slit separation. For the first dark fringe (n=1n = 1n=1), this simplifies to:\u03b8=\u03bb2d\\theta = \\frac{\\lambda}{2d}\u03b8=2d\u03bb\u200b<\/p>\n\n\n\n

    The problem gives the slit separation as 0.1p\\frac{0.1}{p}p0.1\u200b mm, and the wavelength as 5000 angstroms, which is in the visible range. Converting all units to SI and substituting into the formula gives a general expression for the angular position: \u03b8=2.5p\u00d710\u22123\\theta = 2.5p \\times 10^{-3}\u03b8=2.5p\u00d710\u22123 radians. This means the angular location of the first dark fringe depends directly on the variable ppp, which would be a constant or parameter defined elsewhere.<\/p>\n\n\n\n

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

    In young’s double slit interference experiment, the distance between two sources is 0.1\/p mm. The distance of the screen from the source is 25 cm. Wavelength of light used is 5000A ?. Then what is the angular position of the first dark fringe ?” The Correct Answer and Explanation is: Correct Answer: To find the […]<\/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-39515","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39515","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=39515"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39515\/revisions"}],"predecessor-version":[{"id":39517,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39515\/revisions\/39517"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39515"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39515"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39515"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}