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A prism of angle A and refractive index 2 is surrounded on all sides by medium of refractive index $\sqrt{3}$ . A ray is incident on side PQ at an angle of incidence i $(0 < i < 90 °)$ as shown. The refracted ray is then incident on side PR of prism. The minimum angle A of prism for which ray incident on side PQ does not emerge out of prism from side PR (for any value of i) is

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$30 °$

$45 °$

$60 °$

$120 °$

answer is D.

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Detailed Solution

For no ray to emerge out of side PR

$A > 2 C \Rightarrow \sin \frac{A}{2} > s i n C \Rightarrow s i n \frac{A}{2} > \frac{\sqrt{3}}{2} o r A > 120 °$

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