Question

An equilateral prism has angle of minimum deviation ${30}^{\circ }$ when the angle of incidence is ${60}^{\circ }$. The angle of deviation of emergent ray is $10n$ degrees if the ray is incident normally on a surface. n is (Write upto two digits after the decimal point.)

Answer 1

$\mu =\frac{\sin \frac{A+{\delta }_m}{2}}{\sin \frac{A}{2}}=\frac{\sin 45}{\sin 30}=\sqrt{2}$
and critical angle $i_c={\sin }^{-}\left(\frac{1}{\mu }\right)={45}^{\circ }$

At face AB, angle of incidence is ${60}^{\circ }$ which is greater than $i_c$, so light undergoes TIR. From the diagram the angle of deviation can be observed to be $2\alpha ={60}^{\circ }$