A beam of diameter 'd' is incident on a glass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to d, then the diameter of the beam at the base of the hemisphere will be

Options

A. `(3)/(4)d`
B. d
C. `(d)/(3)`
D. `(2)/(3)d`

Answer

D

Explanation

`mu_(1) =1 , mu_(2) = 3//2`
(mu_(2))/(v)- (mu_(1))/(mu) = (mu_(2)-mu_(1))/(R)`
`(3)/(2v)- (1)/(-oo)= (3//2-1)/(R) = (1)/(2R)`
`v=3R`
`triangleABE` & `triangleCDE` are similar `(d)/(3R) = ("x")/(2R)`
`x = (2)/(3)d`