Question

If one face of prism is silvered having prism angle $30{}^{\circ }$ and $\mu =\sqrt{2}.$ What will be the angle of incidence, so that the incident ray retraces its path?

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

Answer 1

Answer: (D)

The ray retraces its path after reflection from the silvered face $AC$. Therefore, $\angle ARQ=90^{\circ }$. As is clear from the figure, the angle of reflection $RQN$ at face $AB$ is $30^{\circ }$.

Therefore, by Snell's law, we have
$n=\frac{\sin i}{\sin r}$
Given, $n=\sqrt{2},r=30^{\circ }$
$\therefore \sin i=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$
$\Rightarrow i=45^{\circ }$