Question

If one face of a prism of prism angle $30^{\circ }$ and $\mu =\sqrt{2}$ is silvered, the incident ray retraces its initial path. The angle of incidence is

• A. $60^{\circ }$
• B. $30^{\circ }$
• C. $45^{\circ }$
• D. $90^{\circ }$

Answer 1

Answer: (C)

It is clear from the figure that the ray will retrace the path when the refracted ray $QR$ is incident normally on the polished surface $AC$. Thus angle of refraction, $r=30^{\circ }$.

$\mu =\frac{\sin i}{\sin r}$
$\therefore \sin i=\mu \sin r$
$\sin i=\sqrt{2}\times \sin 30^{\circ }=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}$
$\therefore i=45^{\circ }$