Question

The refractive index of the material of a

prism is $\mu = \sqrt{2}$ and the angle of the prism is $A = 30^\circ$.

One of the two refracting surfaces of the

prism is made a mirror inwards, by silver

coating. A beam of monochromatic light

entering the prism from the other face will

retrace its path (after reflection from the

silvered surface) if its angle of incidence on

the prism is $i$.

Accepted Answer

$$\frac{\sin i}{\sin 30^\circ} = \frac{\sqrt{2}}{1}$$

$$\Rightarrow \sin i = \sqrt{2} 	imes \frac{1}{2}$$

$$\sin i = \frac{1}{\sqrt{2}} 	ext{ i.e. } i = 45^\circ$$