A light ray is incident normal to one face of a right-angled isosceles prism and is totally internally reflected at the glass air interface. If the angle of reflection is $π/4$, what can be concluded about the refractive index?

$μ>\sqrt{2}$

The correct answer is Option (3) → $μ>\sqrt{2}$

For total internal reflection at the glass-air interface, the critical angle $\theta_c$ satisfies:

$\sin \theta_c = \frac{n_2}{n_1}$

Here, $n_1$ is the refractive index of the prism (glass), $n_2$ is that of air ($\approx 1$).

Given: The angle of incidence at the interface is $\theta_i = \pi/4$ and total internal reflection occurs:

$\theta_i \ge \theta_c \Rightarrow \sin \theta_c \le \sin (\pi/4) = \frac{\sqrt{2}}{2}$

Thus:

$\frac{1}{n_1} \le \frac{\sqrt{2}}{2} \Rightarrow n_1 \ge \sqrt{2}$

The refractive index of the prism must be at least $\sqrt{2}$