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

Answer

D

Explanation

Refraction at ①-①
`1xxsintheta=musinr=2/sqrt3sinr`
`sinr=sqrt3/2sintheta`
`sinC=1/mu=(1)/(2//sqrt3)=sqrt3/2impliesC=60^@`
Refraction at ②-②
`r^'=90^@` i.e. `i=90^@-r=C`
`90^@-r=60^@impliesr=30^@`
`sinr=sqrt3/2sinthetaimpliessin30^@=sqrt3/2sintheta`
`sintheta=1/sqrt3impliestheta=sin^-1(1//sqrt3)`