JEE Main 2022 · 25 June · evening · Single correct · +4 / −1

The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio (Iₘₐₓ + Iₘᵢₙ)/(Iₘₐₓ - Iₘᵢₙ) is 5/x. Then, the value of x will be equal to :

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

Answer (b) 4

Solution

Physics sir · 3 steps

Take square roots first: intensities 4 : 1 mean amplitudes 2 : 1, and amplitudes are what add.

  1. Amplitudes, not intensities. Intensity goes as amplitude squared, so I₁ : I₂ = 4 : 1 gives a₁ : a₂ = 2 : 1. Take a₁ = 2a and a₂ = a.
  2. Bright and dark fringes. At a maximum the amplitudes add, so Iₘₐₓ ∝ (2a + a)² = 9a². At a minimum they subtract, so Iₘᵢₙ ∝ (2a - a)² = a².

    (Iₘₐₓ + Iₘᵢₙ)/(Iₘₐₓ - Iₘᵢₙ) = (9 + 1)/(9 - 1) = 10/8 = 5/4

  3. So. Comparing with 5/x gives x = 4, which is option (b).

The idea to keep. In interference, add or subtract amplitudes √I, then square. A shortcut: (Iₘₐₓ+Iₘᵢₙ)/(Iₘₐₓ-Iₘᵢₙ) = (I₁+I₂)/2√(I₁ I₂).

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

Study Wave Optics

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