Question

The face BC of a prism of refractive index $\mu =\sqrt{2}$ is silvered. Angle $\angle BCA={30}^{\circ }$. A light ray incident on the face AC retraces the path. The value of incident angle $\theta$ is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

The light ray retraces the path if it falls along the normal on the force BC. Angle of refraction in the prism = r
$\angle D={90}^{\circ }\therefore r={90}^{\circ }-\angle CED=90-60={30}^{\circ }$
Applying shell's law,
$\left(1\right)sin\theta =\sqrt{2}sin{30}^{\circ }$
$=\sqrt{2}\times \frac{1}{2}$
$\theta ={45}^{\circ }$