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 $60^{\circ }.$