Question

A ray PQ incident on the refracting face BA is refracted in the prism BA C as shown in the figure and emerges from the other refracting face AC as RS, such that AQ = AR. If the angle of prism $A = 60^\circ$ and the refractive index of the material of prism is $\sqrt 3,$ then the angle of deviation of the ray is

• A. $ 60^\circ $
• B. $ 45^\circ $
• C. $ 30^\circ $
• D. None of these

Answer 1

Answer: (A)

For a given prism, the angle of deviation depends upon the angle of incidence of the light rays falling on the prism.
Taking triangle FQR, we have
$ S = \angle FQR + \angle FRQ $

Since, $\Delta AQR$ is an equilateral triangle, therefore,
$ S = \angle FQR = \frac{60^\circ}{2}=30^\circ = \angle FRQ $
$\therefore \delta = 30^\circ + 30^\circ = 60^\circ $
Hence, angle of deviation of the ray is $ 60^\circ. $