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JEE Main & Advanced Physics Wave Optics / तरंग प्रकाशिकी Question Bank Critical Thinking

  • question_answer
    In Young?s double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelengthl. In another experiment with the same set up the two slits are of equal amplitude A and wavelength l but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is [IIT-JEE 1986; RPMT 2002]

    A)            1 : 2                                          

    B)            2 : 1

    C)            4 : 1                                          

    D)            1 : 1

    Correct Answer: B

    Solution :

               Resultant intensity \[I={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \varphi \] At central position with coherent source (and \[{{I}_{1}}={{I}_{2}}={{I}_{0}}\]  \[{{I}_{con}}=4{{I}_{0}}\]            ... (i) In case of incoherent at a given point, f varies randomly with time so (cos f)av = 0 \ \[{{I}_{In\,coh}}={{I}_{1}}+{{I}_{2}}=2{{I}_{0}}\]   ... (ii) Hence \[\frac{{{I}_{coh}}}{{{I}_{Incoh}}}=\frac{2}{1}\].


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