Question

A light ray passes from a vacuum into a medium of refractive index n. The angle of refraction is found to be half the angle of incidence. The angle of incidence is ______.

Options

• `cos^-1 (n/2)`

• `2cos^-1 (n/2)`

• 2 sin⁻¹ (n)

• `2sin^-1 (n/2)`

Answer 1

A light ray passes from a vacuum into a medium of refractive index n. The angle of refraction is found to be half the angle of incidence. The angle of incidence is `bbunderline(2cos^-1 (n/2))`.

Explanation:

Given: Light is passing from a vacuum to a medium of refractive index n.

Angle of refraction, r = `i/2`

Apply Snell’s law:

sin i = `n sin(i/2)`

Use identity:

sin i = `2 sin(i/2) cos(i/2)`

Substitute:

`2 sin(i/2) cos(i/2) = n sin(i/2)`

Cancel `sin⁡(i/2)` from both sides:

⇒ `2 cos(i/2) = n`

⇒ `cos(i/2) = n/2`

⇒ `cos^-1(n/2)`

⇒ i = `2 cos^-1(n/2)`