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Question:

The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio (Imax - Imin) / (Imax + Imin) will be

2√n/(n+1)

√n(n+1)/2

2√n(n+1)/2

√n/(n+1)

Solution:

Given : I₂ = nI₁
Maximum intensity of interference
Imax = (√I₁ + √I₂)²
∴Imax = (√I₁ + √nI₁)² = (1 + √n)²I₁ = (1 + n + 2√n)I₁
Minimum intensity of interference
Imin = (√I₁ - √I₂)²
∴Imin = (√I₁ - √nI₁)² = (1 - √n)²I₁ = (1 + n - 2√n)I₁
∴(Imax - Imin) / (Imax + Imin) = 2√n / (1 + n)