JEE Main 2021 · 25 February · morning · Single correct · +4 / −1

Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio (Iₘₐₓ - Iₘᵢₙ)/(Iₘₐₓ + Iₘᵢₙ) will be :

  1. (a) 2√2x/(2x + 1)
  2. (b) 2√2x/(x + 1)
  3. (c) √2x/(x + 1)
  4. (d) √2x/(2x + 1)
Answer and solution

Answer (a) 2√2x/(2x + 1)

Solution

Physics sir · 4 steps

Write both intensities with amplitudes, subtract and add, and the ratio reduces to one tidy formula.

  1. Maxima and minima. For coherent sources, Iₘₐₓ = (√I₁+√I₂)² and Iₘᵢₙ = (√I₁-√I₂)².
  2. Difference and sum. Expanding the squares, Iₘₐₓ - Iₘᵢₙ = 4√(I₁ I₂) and Iₘₐₓ + Iₘᵢₙ = 2(I₁ + I₂).

    (Iₘₐₓ-Iₘᵢₙ)/(Iₘₐₓ+Iₘᵢₙ) = 2√(I₁ I₂)/(I₁+I₂)

  3. Put in the ratio. Take I₁ = 2x I₂. The numerator becomes 2√2x I₂ and the denominator becomes (2x+1) I₂, so I₂ cancels.
  4. So. The ratio is 2√2x/(2x+1), which is option (a).

The idea to keep. Remember (Iₘₐₓ-Iₘᵢₙ)/(Iₘₐₓ+Iₘᵢₙ) = 2√(I₁ I₂)/(I₁+I₂). This is the fringe visibility, and you only need the intensity ratio to find it.

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 2021.