Question

Obtain the relation A + δ = i + e for a prism where A is the angle of the prism, δ is the angle of deviation, i is the angle of incidence and e is the angle of emergence. Write this relation for the minimum deviation?

Answer 1

In quadrilateral APOQ,

A + O = 180°  ...(1)

In triangle OPQ,

r₁ + r₂ + O = 180°  ...(2)

In triangle DPQ

δ = (i − r₁) + (e − r₂)

δ = (i + e) – (r₁ + r₂)  ...(3)

From (1) and (2),

A = r₁ + r₂

From (3),

δ = (i + e) – (A)

i + e = A + δ

The sum of the angle of incidence and the angle of emergence is equal to the sum of the angle of the prism and the angle of deviation.