A light beam is incident on a denser medium whose refractive index is 1.414 at an angle of incidence $$45^\circ$$. Find the ratio of width of refracted beam in a medium to the width of the incident beam in air.

A

$$\sqrt{3} : \sqrt{2}$$

B

$$1 : \sqrt{2}$$

C

$$\sqrt{2} : 1$$

D

$$\sqrt{2} : \sqrt{3}$$