KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    A ray hits the y-axis making an angle \[\theta \] with y-axis as shown in the figure. The variation of refractive index with x-coordinate is \[\mu ={{\mu }_{0}}\left( 1-\frac{x}{d} \right)\] for \[0\le x\le d,\]\[\left( 1-\frac{1}{{{\mu }_{0}}} \right)\] and \[\text{ }\mu \text{=}{{\mu }_{0}}\] for x < 0, where d is a positive constant. The maximum x-coordinate of the path traced by the ray is -

    A) \[d\,\,(1-\sin \theta )\]

    B) \[d\,\,(1-\cos \theta )\]

    C) \[d\,\,\sin \,\,\theta \]

    D) \[d\,\,\cos \,\,\theta \]

    Correct Answer: B

    Solution :

    Snell?s law \[={{\mu }_{0}}\sin \,\,(90{}^\circ -\theta )\]
    \[={{\mu }_{0}}\left( 1-\frac{x}{d} \right)\,\,\sin 90{}^\circ \]\[\Rightarrow \left( 1-\frac{x}{d} \right)=\cos \theta \]\[\Rightarrow x=d\,\,(1-cos\theta )\]

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