Question

A ray $PQ$ incident on the refracting face $BA$ is refracted in the prism $BAC$ 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. $35^{\circ }$
• C. $30^{\circ }$
• D. None of these

Answer 1

Answer: (A)

Given $AQ=AR$ and $\angle A=60^{\circ }$
$\therefore \angle AQR=\angle ARQ=60^{\circ }$
$\therefore r_1=r_2=30^{\circ }$
Applying Snell's law on face $AB$.
$\sin i_1=\mu \sin r_1$
$\Rightarrow \sin i_1=\sqrt{3}\sin 30^{\circ }$
$=\sqrt{3}\times \frac{1}{2}=\frac{\sqrt{3}}{2}$
$\therefore i_1=60^{\circ }$
Similarly, $i_2=60^{\circ }$
In a prism, deviation
$\delta =i_1+i_2-A$
$=60^{\circ }+60^{\circ }-60^{\circ }=60^{\circ }$