JEE Main 2022 · 27 July · evening · Single correct · +4 / −1

Two coherent sources of light interfere. The intensity ratio of two sources is 1: 4. For this interference pattern if the value of (Iₘₐₓ+Iₘᵢₙ)/(Iₘₐₓ-Iₘᵢₙ) is equal to (2 α+1)/(β+3), then α/β will be :

  1. (a) 1.5
  2. (b) 2
  3. (c) 0.5
  4. (d) 1
Answer and solution

Answer (b) 2

Solution

Physics sir · 4 steps

Take square roots of the intensities first; the amplitudes 1 and 2 give Iₘₐₓ and Iₘᵢₙ.

  1. Amplitudes first. Intensity goes as amplitude squared, so I₁ : I₂ = 1 : 4 means a₁ : a₂ = 1 : 2. Take I₁ = I and I₂ = 4I.
  2. Maximum and minimum. Iₘₐₓ = (√I₁ + √I₂)² = (1+2)² I = 9I and Iₘᵢₙ = (√I₂ - √I₁)² = (2-1)² I = I.

    (Iₘₐₓ+Iₘᵢₙ)/(Iₘₐₓ-Iₘᵢₙ) = (9I + I)/(9I - I) = 10/8 = 5/4

  3. Match the form. Set (2α+1)/(β+3) = 5/4 and compare top with top and bottom with bottom. Then 2α + 1 = 5 gives α = 2, and β + 3 = 4 gives β = 1.
  4. So. α/β = 2/1 = 2, which is option (b).

The idea to keep. In interference, intensities never add directly. Convert to amplitudes with square roots, then Iₘₐₓ = (√I₁+√I₂)² and Iₘᵢₙ = (√I₁-√I₂)².

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 140 times in JEE Main since 2020. This question is from 2022.