Question

A ray of light is incident at an angle of ${60}^{\circ }$ on one face of a prism of angle ${30}^{\circ }$. The ray emerging out of the prism makes an angle of ${30}^{\circ }$ with the incident ray. The emergent ray is

• A. Normal to the face through which it emerges.
• B. Inclined at ${30}^{\circ }$ to the face through which it emerges.
• C. Inclined at ${60}^{\circ }$ to the face through which it emerges.
• D. None of the above

Answer 1

The correct option is A Normal to the face through which it emerges.

Deviation of ray in a prism is given by
$\delta =i+e-A$
So, $e=\delta +A-i$
$={30}^{\circ }+{30}^{\circ }-{60}^{\circ }$
$=0^{\circ }$
So, emergent ray will be perpendicular to the face.
i.e emergent ray will make an angle of ${90}^{\circ }$ with the face through which it emerges.

Why this question? Tip: The angle of deviation is equal to the sum of deviation due to refraction at the first face and the second face of the prism. So, $\delta =(i-r_1)+(e-r_2)=i+e-(r_1+r_2)=i+e-A$