A parallel beam of light is incident from air at an angle a on the side PQ of a right angled triangular prism of refractive index $$n = \sqrt{2}$$. Light undergoes total internal reflection in the prism at the face PR when a has a minimum value of $$45^\circ$$. The angle $$\theta$$ of the prism is

A

$$15^\circ$$

B

$$22.5^\circ$$

C

$$30^\circ$$

D

$$45^\circ$$