Question

A light ray is incident on a transparent sphere of index $=\sqrt{2}$ at an angle of incidence $={45}^o$. What is the deviation of a tiny fraction of the ray, which enters the sphere, undergoes two internal reflection and then refracts out into air?

Answer 1

From Snell's law,

$M_1\sin {\theta }_1=M_2\sin {\theta }_2$

$1.\sin 45°=\sqrt{2}\sin r_1$

$r_1=30°$

Here $r_1=r_2=r_3=r_4=r_5=r_6=30°$

$1.\sin =\sqrt{2}\sin r_6$

$\sin e=\frac{1}{\sqrt{2}}$

$e=45°$

Deviation at $I^{st}$ surface $=i-r_1=45°-30°=15°$

Deviation at $I{I}^{nd}$ surface $=e-r_6=45°-30°=15°$

Total deviation $=15+15={30}^{\circ }$