Question

A ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and each of these equal to $3/4$ of the angle of the prism. The angle of deviation is

• A. ${45}^{\circ }$
• B. ${39}^{\circ }$
• C. ${20}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

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

Let the angle of incidence of light at prism. $i=x$

So, Angle of emergence , $e=x$

Angle of prism , $A=\frac{4}{3}x$

Since prism is equilateral $⟹3A={180}^o⟹x={45}^o$

From prism formula:

Angle of deviation , $\delta =i+e-A=45+45-60={30}^o$