A light ray enters through a right angled prism at point $P$ with the angle of incidence $30^{\circ}$ as shown in figure. It travels through the prism parallel to its base $B C$ and emerges along the face $A C$. The refractive index of the prism is:

Question

Aicharya · Accepted Answer

In prism, $r_1+c=A$ $\begin{gathered} r_1=90^{\circ}-c \ldots(1)\\ \sin c=\frac{1}{\mu} \Rightarrow \cos c=\frac{\sqrt{\mu^2-1}}{\mu} \end{gathered}$ $\Rightarrow$ Apply Snell's law, on incidence surface $\begin{aligned} 1 \cdot \sin 30^{\circ}=\mu \sin \left(r_1\right) \Rightarrow 1 \times \frac{1}{2} & =\mu \times \sin \left(90^{\circ}-c\right) \\ \frac{1}{2} & =\mu \times \frac{\sqrt{\mu^2-1}}{\mu} \end{aligned}$ On squaring $\frac{1}{4}=\mu^2-1$ $\Rightarrow \mu^2=\frac{5}{4} \Rightarrow \mu=\frac{\sqrt{5}}{2}$

A light ray enters through a right angled prism at point $P$ with the angle of incidence $30^{\circ}$ as…

Solution