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JEE Main & Advanced Physics Ray Optics Question Bank Self Evaluation Test - Ray Optics and Optical Instruments

  • question_answer
    In a vessel, as shown in Fig. point P is just visible when no liquid is filled in vessel through a telescope in the air. When liquid is filled in the vessel completely, point Q is visible without moving the vessel or telescope. Find the refractive index of the liquid.

    A) \[\frac{\sqrt{14}}{3}\]

    B) \[\frac{\sqrt{85}}{5}\]

    C) \[\sqrt{2}\]        

    D) \[\sqrt{3}\]

    Correct Answer: B

    Solution :

    [b] From similar triangles APB and CBD, point P will be just visible if CD = 4 R \[\mu \sin i=1\times \sin r\] \[\mu \sin \left( \angle CDQ \right)=1\times \sin \left( \angle CDB \right)\] \[\mu \times \frac{R}{R\sqrt{17}}=1\times \frac{2R}{R\sqrt{20}}\Rightarrow \mu =\frac{2\sqrt{17}}{\sqrt{20}}=\frac{\sqrt{85}}{5}\]


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