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

Angle of Prism, A = 60°, n = 1.524

As the ray suffer TIR at the face AC

∴ r₂ = c(critical angle)

 As sin c = 1/n = 1/1.524 = 0.6561

∴ c = 41°

Also, r₂ = 41°. As, r₁ + r₂ = A 

∴ r₁ = A – r₂ = 60° – 41° = 19° 

According to Snell’s law.

n = sin i/sin r₁

∴ sin i = n. sin r₁ = 1.524 × sin 19° = 1.524 × 0. 325 = 0.4962

∴ i ≈ 30°.