Given data

• Light goes from air to a medium of refractive index $\mu = \sqrt{2n}$
• Angle of incidence $i$ is twice the angle of refraction $r$: $i = 2r$

Apply Snell's law For air to medium, $\sin i = \mu \sin r$ $\sin i = \sqrt{2n}\,\sin r$

Use the condition $i=2r$ $\sin 2r = \sqrt{2n}\,\sin r$

Using $\sin 2r = 2\sin r \cos r$ we get $2\sin r \cos r = \sqrt{2n}\,\sin r$

Cancel $\sin r$ For non-zero refraction angle, $2\cos r = \sqrt{2n}$ $\cos r = \sqrt{\frac{n}{2}}$

Hence, $r = \cos^{-1}\left(\sqrt{\frac{n}{2}}\right)$

Find the angle of incidence Since $i=2r$, $i = 2\cos^{-1}\left(\sqrt{\frac{n}{2}}\right)$

Match with options This corresponds to: $\boxed{2\cos^{-1}\left(\sqrt{\frac{n}{2}}\right)}$ which is Option D.

Comparison with stored answer Stored correct answer: D

Our derived answer also gives D, so they agree.