Question

A ray LM of monochromatic light incident normally on one refracting surface AB of a regular glass prism ABC emerges in air from the adjacent surface AC as shown in the figure. Calculate the refractive index of the material of the prism.

Answer 1

Given:

Prism angle A = 60°

Incident ray is normal to face AB ⇒ i = 0° ⇒ no deviation

Grazing emergence ⇒ emergent angle (e) = 90°

To Find:

Refractive index of glass (n)

Step 1: Use the prism angle relationship:

r₁ + r₂ = A

0° + r₂ = 60°

r₂ = 60°

Step 2: Apply Snell’s law at surface AC:

n × sin r = 1 × sin e

n × sin (60°) = sin (90°)

`n xx sqrt3/2 = 1`

n = `2/sqrt3`

n ≈ 1.15