Question

A light ray enters a solid glass sphere of refractive index $\mu=\sqrt{3}$ at an angle of incidence $60^{\circ} .$ The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is___

Answer 1

By Snell's law at $A$ :
$1 \times \sin 60^{\circ}=\sqrt{3} \times \sin \theta$
$\frac{\sqrt{3}}{2}=\sqrt{3} \sin \theta$
$\sin \theta=\frac{1}{2} \Rightarrow \theta=30^{\circ}$
So at $B$
$\theta+60^{\circ}+\alpha=180^{\circ}$
$30^{\circ}+60^{\circ}+\alpha=180^{\circ}$
$\alpha=90^{\circ}$