A light ray falls on a rectangular glass slab as shown. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is

Options

A. `sqrt(3//2)`
B. `((sqrt(3)+1))/(2)`
C. `((sqrt(2)+1))/(2)`
D. `sqrt(5)//2`

Answer

A

Explanation

For point `A, a mu_(g) = (sin 45^(@))/(sin t)`
` rArr sin r = (1)(sqrt(2)mu_(g))`
for point `(90-r) = ""_(g)mu_(g)`
`(90 -r)` is critcal angle .

`therefore cos r = ""_(g)mu_(g) = (1)/(""_(a)mu_(g))`
`rArr ""_(a)mu_(g) = (1)/(cos r)`
`rArr (1)/(sqrt(1-sin^(2)r)) = (1)/(sqrt(1-(1)/(2""_(a)mu_(g)^(2))))`
` rArr ""_(a)mu_(g)^(2) = (1)/(1-(1)/(2""_(a)mu_(g)^(2))) = (2""_(a)mu_(g)^(2))/(2amu_(g)^(2) -1)`
`rArr 2""_(a) mu_(g)^(2) -1 =2 rArr ""_(a)mu_(g)^(2) = sqrt((3)/(2))`