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KVPY Sample Paper KVPY Stream-SX Model Paper-12

  • question_answer
    In figure, the optical fiber is  \[l=2m\] long and has a diameter of \[d=20\mu m.\]If a ray of light is incident on  one end of the fiber at angle \[{{\theta }_{1}}=40{}^\circ ,\]the number of reflections it makes before emerging from the other end is close to (refractive index of fiber is 1.31 and \[\sin 40{}^\circ =0.64)\]

    A) 66000

    B) 55000

    C) 45000

    D) 57000

    Correct Answer: D

    Solution :

    \[I\,\,\sin 40=1.31\,\sin \,\theta \]
    \[\Rightarrow \]\[\sin \theta =\frac{0.64}{1.31}\simeq \frac{1}{2}\]\[\Rightarrow \] \[\theta =30{}^\circ \]
    \[x=\frac{D}{1/\sqrt{3}}20\sqrt{3}\times {{10}^{-6}}m\]
    No. of reflections \[=\frac{20}{20\sqrt{3}\times 10-6}\simeq 57000.\]


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