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

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In Young's double slit experiment, one of the slit is wider than other, so that the 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

Let A 1 ​ = A 0 ​ , A 2 ​ = 2 A 0 ​ If amplitude of resultant wave is A then A 2 = A 1 2 ​ + A 2 2 ​ + 2 A 1 ​ A 2 ​ cos ϕ For maximum intensity, A m a x 2 ​ = A 1 2 ​ + A 2 2 ​ + 2 A 1 ​ A 2 ​ ∴ A m a x 2 ​ A 2 ​ = A 1 2 ​ + A 2 2 ​ + 2 A 1 ​ A 2 ​ A 1 2 ​ + A 2 2 ​ + 2 A 1 ​ A 2 ​ c o s ϕ ​ = A 0 2 ​ + 4 A 0 2 ​ + 2 ( A 0 ​ ) ( 2 A 0 ​ ) A 0 2 ​ + 4 A 0 2 ​ + 2 ( A 0 ​ ) ( 2 A 0 ​ ) c o s ϕ ​ I m ​ I ​ = 9 5 + 4 c o s ϕ ​ = 9 1 + 8 c o s 2 ( ϕ /2 ) ​

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