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A point source of light is kept at a dep...

A point source of light is kept at a depth of h in water of refractive index 4/3. The radius of the circle at the surface of water through which light emits is

A

`(3)/(sqrt(7))`h

B

`(sqrt(7))/(3)`h

C

`(sqrt(3))/(7)`h

D

`(7)/(sqrt(3))`h

Text Solution

Verified by Experts

The correct Answer is:
A
`n_(2) sin i_(c ) = n_(1) sin 90^(@)`
`rArr " " i_(c ) = sin^(-1) ((1)/(n_(21)))`
`rArr " " sin i_(c ) = (1)/(n_(21)) = (R )/(sqrt( R^(2) + h^(2)) )`
`rArr " " sin i_(c ) = (3)/(4) = (R )/(sqrt( R^(2) + h^(2) ) )`
`rArr " " 16R^(2) = 9R^(2) + 9h^(2)`
`rArr 7R^(2) = 9h^(2) rArr R = (3)/(sqrt(7)) `h.
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