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.

Given:

Angle of prism, A = 60°
Refractive index of the prism, μ = 1.524

Emergent angle, e = 90°

i₁ = Incident angle
r₁ = Refracted angle
r₂ = Angle of incidence at the face AC
According to Snell’s law, for face AC, we can have:

…(1)

From equation(1) we have,

⇒ sin r₂ =

Putting the values in the above equation we find that,

r₂ = sin

r₂ = 41°

We know that, refracted angle r₁ is given by,

r₁ = A- r₂

r₁ = 60-41 = 19°

Therefore r₁ = A−r₂ = 60−41 = 19°
According to Snell’s law, we have the relation:

μ =

Sin i₁ = 1.524 × sin19° = 0.496

⇒ i₁ = 29.75°

Therefore, the angle of incidence is 29.75°