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A transparent solid cylindrical rod has ...

A transparent solid cylindrical rod has a refractive index of `(2)/(sqrt3)` .It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle `theta` for which the light ray grazes along the wall of the rod is:
`

A

`sin ^(-1) (1//2)`

B

` sin^(-1) ( sqrt(3) //2)`

C

` sin^(-1) (2// sqrt(3))`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
At (1)
` sin theta = n sin r `

At (2)
`n sin (90^(@) - r) = sin 90^(@)`
`rArr n cos r = 1 rArr cos r = (1)/( 2// sqrt(3)) = (sqrt(3))/( 2) rArr r = 30^(@)`
`:. sin theta = (2)/( sqrt( 3)) sin 30^(@) = (1)/( sqrt(3))`
`:. theta = sin ^(-1) ((1)/( sqrt(3)))`
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