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A parallel beam of light is incident fro...

A parallel beam of light is incident from air at an angle `alpha` on the side of right angled triangular prism of refractive index `mu = sqrt(2)`. Light undergoes total internal reflection in the prism at the face `PR` when `alpha` has a minimum value of `45^@`. The angle `theta` of the prism is.
.

A

`15^(@)`

B

`22.5^(@)`

C

`30^(@)`

D

`45^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
Snell. law
` sin 45^(@) = sqrt(2) sin beta `
`rArr beta = 30^(@)`
`i_(c) = beta + theta = sin ^(-1) ((1)/(n))`
`rArr beta + theta = sin ^(-1) ((1)/( sqrt(2))) = 45^(@)`
`theta = 45^(@) - beta = 45^(@) - 30^(@) = 15^(@)`
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