Consider an equilateral prism (refractive index $$\sqrt{2}$$). A ray of light is incident on its one surface at a certain angle $$i$$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ______.

We have an equilateral prism, so the prism angle $$A = 60^{\circ}$$, and the refractive index $$\mu = \sqrt{2}$$.

The emergent ray grazes along the second surface, which means the angle of emergence is $$e = 90^{\circ}$$. This means the angle of refraction at the second surface equals the critical angle $$C$$.

At the critical angle, $$\sin C = \frac{1}{\mu} = \frac{1}{\sqrt{2}}$$

So, $$C = 45^{\circ}$$

This means the angle of refraction at the second surface is $$r_2 = C = 45^{\circ}$$.

For a prism, the relation between the prism angle and the angles of refraction at the two surfaces is:

$$r_1 + r_2 = A$$

where $$r_1$$ is the angle of refraction at the incident surface and $$r_2$$ is the angle of refraction at the emergent surface.

So, $$r_1 = A - r_2 = 60^{\circ} - 45^{\circ} = 15^{\circ}$$

Hence, the angle of refraction at the incident surface is $$15^{\circ}$$, which corresponds to Option D.