A ray incident at a point at an angle of incidence 60° enters a glass sphere of $μ = \sqrt{3}$ and is reflected and refracted at the farther surface of the sphere. The angle between the reflected and refracted rays at this surface is:

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50°

90°

60°

40°

answer is B.

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Detailed Solution

$\begin{aligned} μ = \frac{\sin i}{\sin r} \\ ∴ \sin r = \frac{\sin i}{μ} \\ = \frac{\sin 60^{\circ}}{\sqrt{3}} = \frac{1}{2} \\ ∴ r = 30^{\circ} \\ PC = QC \\ ∴ ∠ CPQ = ∠ PQC = ∠ r = 30^{\circ} \end{aligned}$

Angle between reflected ray QR and refracted ray QS at the other face is $180^{o}$ –r– $60^{o}$ or $90^{o}$ (as r= $30^{o}$ ).

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