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(D) The emergent ray just grazes the second face,so the angle of emergence $e = 90^{\circ}$.Using Snell's law at the second face: $\mu = \frac{\sin e}

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$\sin ^{-1}\left(\sqrt{2} \sin 15^{\circ}\right)$

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(D) The emergent ray just grazes the second face,so the angle of emergence $e = 90^{\circ}$.Using Snell's law at the second face: $\mu = \frac{\sin e}{\sin r_2} = \frac{\sin 90^{\circ}}{\sin r_2} = \frac{1}{\sin r_2}$.Given $\mu = \sqrt{2}$,we have $\sin r_2 = \frac{1}{\sqrt{2}}$,which gives $r_2 = 45^{\circ}$.For an equilateral prism,the prism angle $A = 60^{\circ}$.Using the relation $A = r_1 + r_2$,we find $r_1 = A - r_2 = 60^{\circ} - 45^{\circ} = 15^{\circ}$.Applying Snell's law at the first face: $\frac{\sin i}{\sin r_1} = \mu$.Therefore,$\sin i = \mu \sin r_1 = \sqrt{2} \sin 15^{\circ}$.Thus,$i = \sin ^{-1}(\sqrt{2} \sin 15^{\circ})$.

$A$ ray of light is incident on one face of an equilateral glass prism having refractive index $\sqrt{2}$. It produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is

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