In Young's double slit experiment, one of the slit is wider than another, so that amplitude of the light from one slit is double of that from other slit. If I m be the maximum intensity, the resu

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In Young's double slit experiment, one of the slit is wider than another, so that amplitude of the light from one slit is double of that from other slit. If I m be the maximum intensity, the resultant intensity I when they interfere at phase difference ϕ is given by

TestHub · Accepted Answer

Given, a 1 = 2 a 2 I 1 = 4 I ′ , I 2 = I ′ We know that, I m = I 1 + I 2 2 = 4 I ′ + I ′ 2 = 9 I ′ ∴ I = I 1 + I 2 + 2 I 1 I 2 cos ⁡ ϕ = 4 I ′ + I ′ + 2 4 I ′ ⋅ I ′ cos ⁡ ϕ = 4 I ′ + I ′ + 4 I ′ cos ⁡ ϕ = 5 I ′ + 4 I ′ cos ⁡ ϕ = I ′ 5 + 4 cos ⁡ ϕ = I m 9 5 + 4 2 cos 2 ⁡ ϕ 2 - 1 = I m 9 5 + 8 cos 2 ⁡ ϕ 2 - 4 = I m 9 1 + 8 cos 2 ⁡ ϕ 2

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