Question

A ray of light is incident at an angle of ${60}^{\circ }$ on one face of a prism which has refracting angle of ${30}^{\circ }$. The ray emerging out of the prism makes an angle of ${30}^{\circ }$ with the incident ray. If the refractive index of the material of the prism is $\mu =\sqrt{a}$, find the value of $a$.

Answer 1

For a prism with refracting angle A, and angle of deviation of light $\delta$, We have

$i+e=\delta +A$

${60}^{\circ }+e={30}^{\circ }+{30}^{\circ }$

Hence $e=0^{\circ }$

Applying Snell's law at the point of emergence,

$\mu \sin r_2=\sin e=0$

$r_2=0$

Also we know that for a prism, $r_1+r_2=A$

Then $r_1=A={30}^{\circ }$

Applying Snell's Law at the point of incidence,

$\sin i=\mu \sin r_1$

Hence, $\mu =\sqrt{3}=\sqrt{a}$

Hence $a=3$