A light beam of diameter `sqrt(3R)` is incident symmetrically on a glass hemispher of radius R and of refractive index `n=sqrt(3)` . Find radius of the beam at the base of hemispher.

Explanation

`mu_(1)sini=mu_(2)sinr`
`1xxsin60^@=sqrt(3)xxsinr,r=30^@`
`DeltaMNPtan30^@=x//(R//2)`
`x=(R)/(2sqrt(3))`
`r=(sqrt(3))/(2)R-x=(sqrt(3))/(2)R-(R)/(2sqrt(3))`
`=((3-1)/(2sqrt(3)))R=(R)/(sqrt(3))`