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. 1 (i.e., path ABCI)?

Explanation

Since the ray shown as 1 suffers total internal reflection at C as well as D, where angle of incidence is `45^(@)`. It means that value of critical angle `i_(c) le 45^(@)` and it is possible of
`n_(12)(=(n_(1))/(n_(2)))ge(1)/(sin 45^(@)) rArr n_(1) ge sqrt2n_(2)`