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 mid point 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 ______.

विकल्प

• `sin^-1(1/2)`

• `sin^-1(sqrt3/2)`

• `sin^-1(2/sqrt3)`

• `sin^-1(1/sqrt3)`

Answer 1

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

Explanation:

sinC = `sqrt3/2`         ...(1)

sin r = sin(90 - C) = cos C = `1/2`

`sintheta/sin"r"=mu_2/mu_1`

sinθ = `2/sqrt3xx1/2`

θ = sin^-1 `(1/sqrt3)`