If one face of a prism of prism angle 30° and $μ = \sqrt{2}$ is silvered, the incident ray retraces its initial path. What is the angle of incident?

45°

As in ΔAED

$30° + 90° + ∠D = 180°$

$∠D = 60°$

Now as by construction

$∠D + ∠r = 90°$

$∠r = 90° – 60° = 30°$

Applying Snell’s law at surface AC

$\sin i = (\sqrt{2})\sin 30° = \sqrt{2} × \frac{1}{2}= \frac{1}{\sqrt{2}}$

$i = \sin^{–1} (\frac{1}{\sqrt{2}}) = 45°$