JEE Main 2021 · 27 August · evening · Single correct · +4 / −1

The light waves from two coherent sources have same intensity I₁ = I₂ = I₀. In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima?

  1. (a) I₀
  2. (b) 2 I₀
  3. (c) 5 I₀
  4. (d) 4 I₀
Answer and solution

Answer (d) 4 I₀

Solution

Physics sir · 4 steps

Add amplitudes, not intensities: equal waves in phase give double the amplitude, so four times the intensity.

  1. Intensity formula. When two coherent waves meet with phase difference φ, the resultant intensity is not just I₁ + I₂. An interference term appears.

    I = I₁ + I₂ + 2√(I₁ I₂)cos φ

  2. Check the minima. At a minimum, cos φ = -1, so Iₘᵢₙ = (√I₁ - √I₂)². With I₁ = I₂ = I₀ this is 0, which matches the question.
  3. Find the maxima. At a maximum, cos φ = +1, so Iₘₐₓ = (√I₁ + √I₂)² = (2√I₀)² = 4I₀.
  4. So. The intensity at the maxima is 4I₀, option (d). Energy is not created: the bright fringes get 4I₀ and the dark fringes get 0, so the average is still 2I₀.

The idea to keep. In interference, add square roots of intensities (that is, amplitudes) and then square: Iₘₐₓ = (√I₁+√I₂)², Iₘᵢₙ = (√I₁-√I₂)².

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.