Question

A ray of light passing through a prism having $\mu =\sqrt{2}$ suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. What is the angle of prism?

• A. ${90}^0$
• B. ${60}^0$
• C. ${30}^0$
• D. ${45}^0$

Answer 1

The correct option is A ${90}^0$

Let

Angle of incidence = $\angle i$

Angle of refraction = $\angle r$

According to the given data, $\angle i=2\angle r$

$\mu =\sqrt{2}$

From Snell’s law

$\mu =\frac{\sin i}{\sin r}$

$\mu =\frac{\sin 2r}{\sin r}=\frac{2\sin r\cos r}{\sin r}=2\cos r$

$\mu =2\cos r$

$2\cos r=\sqrt{2}$

$\cos r=\frac{1}{\sqrt{2}}$

$r={45}^{\circ }$

For the lay of light to suffer minimum deviation, the condition will be

$r=r_1=r_2$

The angle of prism is given by the formula

$a=2r$

$a=2\times {45}^{\circ }$

$a={90}^{\circ }$

The angle of the prism is ${90}^{\circ }$.