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A ray of light entering from air into a ...

A ray of light entering from air into a denser medium of refractive index `(4)/(3)`, as shown in figure
The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle `theta` should be equal to :

A

`sin^(-1) "" (sqrt(7))/(4)`

B

`sin^(-1) (sqrt(7))/(3)`

C

`sin^(-1)"" (sqrt(5))/(3)`

D

`sin^(-1)"" (sqrt(5))/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B

At maximum angle `theta ` ray at point B goes in gazing emergence, at all less values of `theta `
TIR occurs at point B
`(4)/(3) xx sin theta.. = 1 xx sin 90^(@)`
`theta .. = sin ^(-1) ((3)/(4)) rArr theta. = ((pi)/(2) - theta ..)`
At point A
`1 xx sin theta = (4)/(3) xx sin theta `
`sin theta = (4)/(3) xx sin ((pi)/(2) - theta ..)`
` sin theta = (4)/(3) cos [cos ^(-1) "" (sqrt(7))/(4)]`
` sin theta =(4)/(3) xx (sqrt(7))/(4) rArr theta = sin ^(-1) (( sqrt(7))/(3))`
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