A ring angled isosceles prism KLM of refractive index `n_(1)` is placed inside a rectangular block PQRS of refractive index `n_(2)` as shown in the adjoining Fig. The rectangular box is surrounded by a medium of refractive index `n_(3)`. A ray of light AB enters the rectangular block normally. Depending upon the relationships between `n_(1), n_(2) and n_(3)`. it takes one of the four possible paths.

Under what condition the ray follows the path no. 2 (i.e., path ABCIJ)?

Explanation

The ray no. 2 bends away from normal while undergoing refraction at C and bends further away from the normal while undergoing refraction at I. It means that `n_(3) lt n_(2) lt n_(1)`. However, the light ray does not suffer total internal reflaction at C, hence it is clear that `n_(2) gt (n_(1))/(sqrt2).` Hence we conclude that `n_(1) gt n_(2) gt (n)/(sqrt2) and n_(3) lt n_(2)`.