Question

A ray of light passes through an equilateral prism $(\mu =1.5)$ such that the angle of incidence is equal to the angle of emergence & the either is equal to $\frac{3}{4}th$ of the angle of prism. Calculate angle of deviation.

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${20}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

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

Given:
$i=e=\frac{3}{4}A$

As the prism is equilateral prism
$A={60}^{\circ }$

$\therefore i=e=\frac{3}{4}\times A=\frac{3}{4}\times {60}^{\circ }={45}^{\circ }$

Angle of deviation in prism is given by

$\delta =(i+e)-A$

$\Rightarrow \delta =({45}^{\circ }+{45}^{\circ })-{60}^{\circ }={30}^{\circ }$

Hence, option $\left(a\right)$ is correct.