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:
`

Options

A. `sin^(-1)((sqrt3)/(2))`
B. `sin^(-1)((2)/(sqrt3))`
C. `sin^(-1)((1)/(sqrt3))`
D. `sin^(-1)((1)/(2))`

Answer

C

Explanation

Applying Snell's law at Q
`n=(sin90^circ)/(sinC)=(1)/(sinC)`
`:'``sinC=(1)/(n)=(sqrt3)/(2)`
`:'``C=60^circ`
Applying Snell's law at P
`n=(sintheta)/(sin(90-C))impliessintheta=nxxsin(90-C)`, from (1)
`impliessintheta=ncos`
`theta=sin^(-1)[(2)/(sqrt3)xxcos60^circ]`
or `theta=sin^(-1)((1)/(sqrt3))`