Question

Q.4. Monochromatic ray of light in air passes through a prism and emerges into air.
iii) Show that a) r1 + 12 = A
b) i+e= A +S.
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Answer 1

Given info : A monochromatic ray of light in air passes through a prism and emerges into air.

To show : (a) r₁ + r₂ = A

(b) i + e = A + δ

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)

hence proved

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

δ = i + e - A

⇒i + e = A + δ

hence proved