Question

A ray of light incident at an angle of incidence i₁ passes through an equilateral glass prism such that the refracted ray inside the prism is parallel to its base and emerges at an angle of emergence i₂.

1. How is the angle of emergence ‘i₂’ related to the angle of incidence ‘i₁’.
2. What can you say about the angle of deviation in such a situation?

Answer 1

1. ∠i₁ = ∠i₂
   and refracted ray is parallel to base.
   ∠5 = ∠6 = 90°
   ∵ PQ || BC, ∠APQ = ∠AQP = 60°
   ∵ ΔABC is equilateral and ∠APQ and ∠AQP are corr. ∠K to ∠B and ∠C
   ∴ ∠2 = ∠4    ...[∵ 60° + ∠2 = 60° + ∠4]
   Similarly, ∠1 = ∠3
   
   ∴ ∠1 + ∠2 = ∠3 + ∠4
   ∴ ∠i₁ = ∠i₂
   ∵ ∠i₁ = ∠1 + ∠2; ∠i₂ = ∠3 + ∠4
   ∴ Angle of incidence = Angle of emergence is the relation when PQ || Base BC

2. The angle of deviation is at its smallest when i₁ = i₂ and the refracted beam inside the prism is parallel to the base.
   δ = i + e - A = i₁ + i₂- A
   ∵ i₁ = i₂ = i
   δ = δ_min = 2 i - A
   For a given prism and given colour of light δ_min is unique.