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Haryana PMT Haryana PMT Solved Paper-2006

  • question_answer
    The first diffraction minimum due to single slit   diffraction is \[\theta \], for a light of wavelength \[5000\overset{\text{o}}{\mathop{\text{A}}}\,\]. If the width of the slit is \[1\times {{10}^{-4}},\] then the value of \[\text{ }\!\!\theta\!\!\text{ }\] is :

    A) \[30{}^\circ \]                                   

    B) \[45{}^\circ \]

    C) \[60{}^\circ \]

    D) \[15{}^\circ \]

    Correct Answer: A

    Solution :

                    The distance of first diffraction minimum from the central principal maximum                 \[x=\frac{D\lambda }{d}\]                 \[\frac{x}{D}=\frac{\lambda }{d}\] or            \[d=\frac{\lambda }{\sin \theta }\] \[\Rightarrow \]               \[\sin \theta =\frac{\lambda }{d}=\frac{5000\times {{10}^{-8}}}{1\times {{10}^{-4}}}\]                 \[\sin \theta =0.5=\sin 30\]                 \[\theta ={{30}^{o}}\]


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