Prism, Dispersion & Scattering question from NEET 2024

Answer: (b)

1. Ray inside is parallel to $BC$, so $r_1 = 90^\circ - B = C$ at face $AB$ and the angle of incidence on $AC$ is $r_2 = 90^\circ - C = B$.
2. It emerges along $AC$ (grazing), so $r_2$ is the critical angle: $\mu \sin B = 1$.
3. At $P$: $\sin 30^\circ = \mu \sin C = \mu \cos B \Rightarrow \mu \cos B = \frac{1}{2}$.
4. Square and add: $\mu^2 = 1 + \frac{1}{4} = \frac{5}{4}$
5. So the answer is (b) $\mu = \frac{\sqrt{5}}{2}$.