Question

A transparent sphere of radius $R=2.0m$ has a mirror on the surface on its right half as shown in figure. A light ray travelling in air is incident on the left side of the sphere. The incident light ray (1) & exiting light ray (2) are parallel & separated by distance $d=2.0m$. Then find the refractive index of the material. (take: $\sin {15}^o=0.25$)

Answer 1

snell's law : $\sin {\theta }_{INC}=n\sin {\theta }_2\to n=\frac{\sin {\theta }^{}}{\sin {\theta }_z}$

Find ${\theta }_{INC},{\theta }_2$

${\theta }_2:$ From THE DRAWING:

(Refer image .2) $2{\theta }_2+{150}^0={180}^0$

$\Rightarrow {\theta }_2={15}^0$

${\theta }_{INC}:$ EVEN SIMPLER !

(Refer image .3) ${\theta }_{INC}={30}^0$

$n=\frac{\sin {\theta }_{INC}}{\sin {\theta }_2}=\frac{\sin {30}^0}{\sin {15}^0}=1.93$