Question

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

• A. ${270}^{\circ }$
• B. ${240}^{\circ }$
• C. ${120}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is A ${270}^{\circ }$

From Snell's law,
$M_1\sin {\theta }_1=M_2\sin {\theta }_2$
$1.\sin {45}^{\circ }=\sqrt{2}\sin r_1$
$r_1={30}^{\circ }$
Here $r_1=r_2=r_3=r_4=r_5=r_6={30}^{\circ }$
$1.\sin =\sqrt{2}\sin r_6$
$\sin e=\frac{1}{\sqrt{2}}$
$e={45}^{\circ }$
Deviation at $1_{st}$ $=i-r_1={45}^{\circ }-{30}^{\circ }={15}^{\circ }$

Deviation at $2_{nd}$ =$180-60={120}^{\circ }$

Deviation at $3_{rd}$=$180-60={120}^{\circ }$
Deviation at $4_{th}$ $=e-r_6={45}^{\circ }-{30}^{\circ }={15}^{\circ }$
Total deviation $=102+102+15+15={270}^{\circ }$.