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A triangular medium has varying refracti...

A triangular medium has varying refracting index `mu = mu_(0) + ax` where x is the distance (in cm) along x-axis from origin and `m_(0) = 4//3`. A ray is incident normally on face OA at the mid-point of OA. Find the range of value of a so that light does not escape through face AB when it falls first time on the face AB.

A

`a gt (1)/(9)`

B

`a gt (2)/(9)`

C

`a gt (1)/(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B

Clearly `PM = (3)/(2) cm`
`37^(@) gt "sin"^(-1) (1)/(n_(0)+a(3//2))`
`(3)/(5) gt(1)/(n_(1)+(3a)/(2))rArr 3n_(0)+(9a)/(2) gt 5`
`(9a)/(2) gt 1 rArr a gt (2)/(9)`.
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