Two sources of intensity I and 4I are used in an interference experiment. Find the intensity at a point where the waves from the two sources superimpose with a phase difference of (i) zero (ii) $π / 2$ (iii) $π$ .

Solution

Given, two sources with interference I and 4I respectively.

In case of interference,

I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} cosϕ

(i) When phase difference,

ϕ = 0 then, \cos ϕ = 1

∴

I = 4 I + I + 2 \sqrt{4 I \times I} \times 1 = 9 I

(ii) When phase difference,

ϕ = π / 2, \cos ϕ = 0

∴

I = 4 I + I + 2 \sqrt{4 I \times I} \times 0 = 5 I

(iii) when phase difference,

ϕ = π, \cos ϕ = - 1

∴

I = 4 I + I + 2 \sqrt{4 I \times I} \times (- 1) = I .

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