A light beam is traveling from Region I to region IV (refer figure). The refractive indices in Region I, II, III, and IV are `n_(0), n_(0)//2,n_(0)//6 and n_(0)//8` , respectively. The angle of incidence `theta` for which the beam just misses entering Region IV is

Options

A. `sin^(1) (3//4)`
B. `sin^(1) (1//8)`
C. `sin^(1) (1//4)`
D. `sin^(1) (1//3)`

Answer

B

Explanation

First of all observe that refractive index is depressing towards region IV and hence light ray is bending away from normal.
Light ray just misses to enter region IV, means that angle of refraction in region IV becomes `90^@` . We can write Snell.s law as follows :
`musin theta ` = constant
`implies n_0sin theta = n_0/theta sin 90^@`
`implies sin theta = 1/ 8`
`implies theta = sin ^(-1) (1/8)`