Consider a light ray travelling in air is incident into a medium of refractive index $$\sqrt{2n}$$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be

Given: Refractive index $$\mu = \sqrt{2n}$$, and the angle of incidence $$i = 2r$$ where $$r$$ is the angle of refraction.

Using Snell's law:

$$\sin i = \mu \sin r$$

$$\sin 2r = \sqrt{2n} \sin r$$

Using the identity $$\sin 2r = 2\sin r \cos r$$:

$$2\sin r \cos r = \sqrt{2n} \sin r$$

Since $$\sin r \neq 0$$, dividing both sides by $$\sin r$$:

$$2\cos r = \sqrt{2n}$$

$$\cos r = \frac{\sqrt{2n}}{2} = \sqrt{\frac{2n}{4}} = \sqrt{\frac{n}{2}}$$

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

Since $$i = 2r$$:

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

The correct answer is Option D.