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)(Sqrt(3)//2)`
B. `sin^(-1)(2sqrt(3))`
C. `sin^(-1)((1//sqrt(3))`
D. `sin^(-1)(1//2)`

Explanation

As is clear from Fig. 10(CF).3, `phi+C=90^(@)`
`phi=(90^(@)-C)`

Using Snell's law, `mu=(sin i)/(sin r)=(sin phi)/(sin phi)`
or `sin theta=mu sin phi=mu sin (90^(@)-C)=mu cos C`
`=musqrt(1-sin^(2)C)=musqrt(1-(1)/(mu^(2))`
`=sqrt(mu^(2)-1)=sqrt((4)/(2)-1)=(1)/sqrt(3)`
`theta=sin^(-1)(1//sqrt(3))`