Question

At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.

Answer 1

The incident, refracted and emergent rays associated with a glass prism ABC are shown in the given figure.

Angle of prism, ∠A = 60°

Refractive index of the prism, µ = 1.524

i₁ = Incident angle

r₁ = Refracted angle

r₂ = Angle of incidence at the face AC

e = Emergent angle = 90°

According to Snell’s law, for face AC, we can have:

`(sin "e")/(sin "r"_2) = µ`

`sin "r"_2 = 1/µ xx sin 90°`

= `1/1.524`

= 0.6562

∴ r₂ = sin⁻¹ 0.6562 ≈ 41°

It is clear from the figure that angle A = r₁ + r₂

∴ r₁ = A − r₂ = 60 − 41 = 19°

According to Snell’s law, we have the relation:

µ = `(sin "i"_1)/(sin "r"_1)`

`sin "i"_1 = µ  sin "r"_1`

= 1.524 × sin 19°

= 1.524 × 0.3256

= 0.496

∴ i₁ = 29.75°

Hence, the angle of incidence is 29.75°.