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NEET Physics Wave Optics / तरंग प्रकाशिकी NEET PYQ-Wave Optics

  • question_answer
    In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths \[{{\lambda }_{1}}=12000{\AA}\] and \[{{\lambda }_{2}}=10000{\AA}\]. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?                                                                                                                                          [NEET 2013]

    A)  8 mm    

    B)        6 mm

    C)  4 mm        

    D)    3 mm

    Correct Answer: B

    Solution :

    Given \[{{\lambda }_{1}}=12000{\AA}\] and \[{{\lambda }_{2}}=10000{\AA},\]
    \[D=2\,cm\] and \[d=2\,mm=2\times {{10}^{-3}}cm\].
    We have \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{h}_{1}}}{{{h}_{2}}}\]
                \[=\frac{12000}{10000}=\frac{6}{5}\]
    as         \[x=\frac{{{u}_{1}}{{\lambda }_{1}}D}{d}=\frac{5\times 12000\times {{10}^{-10}}\times 2}{2\times {{10}^{-3}}}\]
    \[=5\times 1.2\times {{10}^{4}}\times {{10}^{-10}}\times {{10}^{3}}=6mm\]


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