Question

In Young’s double slit experiment, the intensity on screen at a point where path difference is λ, is K , What will be intensity at the point where path difference is (λ/4) 

(A) (K/2) (B) 2 K (C) 4 K (D) zero

Answer 1

The correct option is (A) (K/2).

Explanation:

Let  I₁ = I₂ = I, ɸ = phase difference between two light wave, then

 I_R = I₁ + I₂ + 2√(I₁ I₂) cos ɸ .

Phase difference = (2π / λ) × path difference.

∴ At path difference λ & (λ/4), phase difference are 2π, (π/2) rad.

respectively,

I_R = I + I + 2√(I ∙ I) cos 2π = 4I.

I_R' = I + I + 2√(I ∙ I) cos (π/2) = 2I.

given I_R = K hence 4I = K

I_R' = 2I = (4I / 2) = (K/2)

Hence intensity at a point where path difference is (λ/4) is (K/2).