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Monochromatic light is incident on a gla...

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is `mu`, a ray, incident at an angle `theta`, on the face AB would get transmitted through the face AC of the prism provided:

A

`theta gt sin ^(-1) [ mu sin ( A - sin^(-1) ((1)/(mu)))]`

B

`theta lt sin ^(-1) [ mu sin ( A - sin^(-1) ((1)/(mu)))]`

C

`theta gt cos ^(-1) [ mu sin ( A + sin^(-1) ((1)/(mu)))]`

D

`theta lt cos ^(-1) [ mu sin ( A + sin^(-1) ((1)/(mu)))]`

Text Solution

Verified by Experts

The correct Answer is:
A
At interface P
`1 sin theta = mu sin r_(1)`
and at point R
`mu sin theta _(c) = sin 90^(@)`
` rArr sin theta _(c) = (1)/(mu)`

Now,` r_(2) lt theta `
`rArr sin r_(2) lt sin theta _(C) `
` r_(1) + r_(2) = A rArr r_(1) = A - r_(2)`
`rArr r_(1) = A - theta _(C)`
` sin r_(1) gt sin (A - theta _(C))`
`rArr mu sin r_(1) gt mu sin (A - theta _(C)) rArr sin theta gt mu sin (A - theta _(C))`
`rArr theta gt sin ^(-1) [ mu sin (A - sin ^(-1) "" (1)/(mu)) ]`
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