Question

An isosceles prism of angle $120^{\circ}$ has a refractive index of $1.44$. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerging from the opposite faces

• A. Are parallel to each other
• B. Are diverging
• C. Make an angle $2 \sin ^{-1}(0.72)$ with each other
• D. Make an angle $2\left\{\sin ^{-1}(0.72)-30^{\circ}\right\}$ with each other

Answer 1

Answer: (D)

At point $A . \frac{\sin 30^{\circ}}{\sin r}=\frac{1}{1.44}$

$\Rightarrow r=\sin ^{-1}(0.72)$ also $\angle B A D=180^{\circ}-\angle r$
In rectangle $A B C D, \angle A+\angle B+\angle C+\angle D=360^{\circ}$
$\Rightarrow \left(180^{\circ}-r\right)+60^{\circ}+\left(180^{\circ}-r\right)+\theta=360^{\circ}$
$\Rightarrow \theta=2\left[\sin ^{-1}(0.72)-30^{\circ}\right]$