Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index `mu`. A student finds that, irrespective of what the incident angle I (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of `mu` is :

Options

A. `(5)/( sqrt(3))`
B. ` (4)/(3)`
C. ` (3)/( sqrt( 5))`
D. ` sqrt(( 5)/( 3))`

Answer

C

Explanation

` 1. sin 90^(@) = mu sin theta rArr sin theta = (1)/(mu)`
`mu sin theta = 1.5 sin r `
` mu tan theta = 1.5 rArr tan theta = (1.5)/(mu)`
`sin theta = (3)/( sqrt(9 + 4 mu^(2))) = (1)/(mu)`
`9 mu^(2) = 9 + 4 mu ^(2) rArr mu = (3)/( sqrt(5))`