Question

The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is $30^{\circ }$ . One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface, if its angle of incidence on the prism is:

• A. ${45}^o$
• B. ${60}^o$
• C. $0^o$
• D. ${30}^o$

Answer 1

Answer: (A)

According to the given condition, the beam light will retrace its path after reflection from $BC$
$\angle CPQ={90}^{\circ }$ Thus, angle of refraction at surface $AC$
$\angle PQN=\angle r={90}^{\circ }-{60}^{\circ }={30}^{\circ }$
By Snells law $\mu =\frac{\sin i}{\sin r}$
$\Rightarrow$ $\sqrt{2}=\frac{\sin i}{\sin {30}^{\circ }}$
$\therefore$ $\sqrt{2}\times \sin {30}^{\circ }=\sin i$
$\Rightarrow$ $\sqrt{2}\times \frac{1}{2}=\sin i$
$\Rightarrow$ $i={45}^{\circ }$