Question

At what angle, a ray of light should be incident on the first face AB of a regular glass prism ABC, so that the emergent ray grazes the adjacent face AC? (Refractive index of glass = 1.6)

Answer 1

For the emergent ray to graze the face AC, r₂ must be equal to the critical angle.

∴ sin r₂ = `1/n`

sin r₂ = `1/1.6`

sin r₂ = 0.625

r₂ = sin⁻¹ (0.625)

r₂ = 38.68°

Also, r₁ + r₂ = 60° ....(In a prism A = r₁ + r₂)

∴ r₁ = 60° − r₂

r₁ = 60° − 38.68°

r₁ = 21.32°

If i is the angle of incidence, then

`(sin i)/(sin r_1)` = 1.6

`sin i/(sin 21.32°)` = 1.6

`sin i/0.3636` = 1.6

sin i = 1.6 × 0.3636

sin i = 0.5817

i = sin⁻¹ (0.5817)

∴ i = 35.57°