Question

Prove the relations, " i+e= A+ δ" When white light is disperse through the prism​

Answer 1

We have to prove that the relation, “ i + e = A + δ ” when white light is disperse through the prism.

solution : let a beam of light incident the the surface of prism and makes an angle i with normal after refraction, it deviates and makes r₁ angle with normal then moves to 2nd surface which makes r₂ with normal and finally refractes with an angle e through the prism. see diagram to understand more better.

let θ₁ is deviation angle of 1st refraction and θ₂ is deviation angle of 2nd refraction.

here, θ₁ = i - r₁

θ₂ = e - r₂

so, total deviation, δ = θ₁ + θ₂

= i + e - (r₁ + r₂) ...(1)

now let A is the angle of prism.

we know, sum of all angles of triangle is 180°

so, A + (90° - r₁) + (90° - r₂) = 180°

⇒A = r₁ + r₂ ...(2)

from equations (1) and (2) we get,

δ = i + e - A

⇒i + e = A + δ

hence proved