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KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    A glass plate 0.40 micron thick is illuminated by a beam of white light normal to the plate. The refractive index of glass is 1.50 and the limits of the visible spectrum are \[{{\lambda }_{V}}=4000\ \overset{\text{o}}{\mathop{\text{A}}}\,\] and \[{{\lambda }_{\operatorname{R}}}=7000\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The wavelengths that get intensified in the reflected beam are

    A) \[4800\,\overset{\text{o}}{\mathop{\text{A}}}\,\] and \[5200\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[4800\,\overset{\text{o}}{\mathop{\text{A}}}\,\]and \[6700\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C)  only

    D) \[5200\,\overset{\text{o}}{\mathop{\text{A}}}\,\] only

    Correct Answer: C

    Solution :

    for intensified reflected beam
    \[2\mu t=(2n-1)\frac{\lambda }{2};n=1,2,...\]
    Or         \[\lambda =\frac{4\mu t}{(2n-1)}=\frac{4\times 1.5\times 0.40\times {{10}^{-6}}}{(2n-1)}\]         
    \[=\frac{2.4\times {{10}^{-6}}}{(2n-1)}\]
    For \[n=3,\]
    \[\lambda =4800\,\overset{\text{o}}{\mathop{\text{A}}}\,\] (only wavelength between \[4000\,\overset{\text{o}}{\mathop{\text{A}}}\,\] to \[7000\,\overset{\text{o}}{\mathop{\text{A}}}\,\])


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