Question

An isosceles prism of angle ${120}^{\circ }$ has a refractive index $\sqrt{2}$. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. in figure. Find the angle between the emerging rays

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$


$\frac{sinr}{sin{30}^{\circ }}=\sqrt{2}sin{30}^{\circ }sinr=\frac{1}{\sqrt{2}}\Rightarrow r={45}^{\circ }$
Angle $\angle ={45}^{\circ }-{30}^{\circ }={15}^{\circ }$
Required angle =$2d={30}^{\circ }$