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

Options

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

Answer

D

Explanation

`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R ) rArr(3)/(2v)-(1)/(oo)=(3//2-1)/(R ) rArr (3)/(2v)=(1)/(2R)`
`v=3R rArr (d)/(3R)=(d')/(2R)rArr=(2)/(3)d`