Question

A transparent solid cylindrical rod has a refractive index of ​`2/sqrt3`​. It is surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure. The incident angle θ for which the light ray grazes along the wall of the rod is ______.

Options

• `sin^-1(1/2)`

• `sin^-1(sqrt3/2)`

• `sin^-1(2/sqrt3)`

• `sin^-1(1/sqrt3)`

Answer 1

The incident angle θ for which the light ray grazes along the wall of the rod is `underlinebb(sin^-1(1/sqrt3))`.

Explanation:

`sin θ/sin r = 2/sqrt3`

∴ sin θ = `2/sqrt3 sin θ`

= `2/sqrt3 sin(90° - θ_c)`

= `2/sqrt3 cos θ_c`  ...(∵ sin r = cos θ_c)

But sin θ_c = `sqrt3/2`

∴ cos θ_c = `sqrt(1 - sin^2 θ_c)`

= `sqrt(1 - 3/4)`

= `1/2`

Hence, sin θ = `2/sqrt3 xx 1/2`

= `1/sqrt3`

Or θ = `sin^-1 (1/sqrt3)`