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

Answer: 90.00

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 $B$
$\theta +60^{\circ }+\alpha =180^{\circ }$
$30^{\circ }+60^{\circ }+\alpha =180^{\circ }$
$\alpha =90^{\circ }$