Question 285: Ray Optics

Question

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:

Accepted Answer

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

Answer

$$
\frac{\sqrt{5}}{4}
$$

Answer

$$
\frac{\sqrt{5}}{2}
$$

Answer

$$
\frac{\sqrt{3}}{4}
$$

Answer

$$
\frac{\sqrt{3}}{2}
$$

Ray Optics

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:

Choose the correct answer: