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A parallel beam of light is incident from air at an angle `alpha` on the side PQ of a right angled triangular prism of refractive index `n=sqrt2. Light undergoes total internal reflection in the prism at the face PR when `alpha` has a minimum value of `45degree`.
The angle `theta` of the prism is `

A

`15degree`

B

`22.5degree`

C

`30degree`

D

`45degree`

Text Solution

Verified by Experts

The correct Answer is:
A

Applying Snell's law at A
`1xxsin45degree=sqrt2xxsinr_(1)`
1`:'` `r_(1)=30degree` ...(i)
Applying Snell's law at B
`sqrt2sinC=1xxsin90degree`
`:'` `C=45degree` ….(ii) In `triangle`AMB,`90degree+theta+(90degree-C)=180degree` (From fig.)
`:'` `theta``=15degree`
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