Question

Two identical coherent waves, each of intensity I, are producing an interference pattern. Find the value of the resultant intensity at a point

(i) constructive interference and

(ii) destructive interference.

Answer 1

The resultant intensity at any point due to interference is given by

I' = I₁ + I₂ + 2\(\sqrt{I_1I_2}\) cos Φ

Where Φ is the phase difference 

Given I₁ = I₂ = I

So I' = I + I + 2\(\sqrt{I.I}\) cos Φ

= 2I (1 + cos Φ)

(i) At a point of constructive interference

Φ = 2nπ (n = 0, 1, 2, ..........)

So cos Φ = 1

∴ I'_max = 2I (1 + 1) = 4I

(ii) At a point of destructive interference

Φ = (2n - 1) π (n = 0, 1, 2, ..........)

So cos Φ = 0

∴ I'_min = 2I (1 - 1) = 0.