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A light ray falls on a rectangular glass...

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

A

`sqrt(3//2)`

B

`((sqrt(3)+1))/(2)`

C

`((sqrt(2)+1))/(2)`

D

`sqrt(5)//2`

Text Solution

Verified by Experts

The correct Answer is:
A
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))`
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