Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be :

Solution

Physics sir · 3 steps

Intensities never add directly: take square roots to get amplitudes, add and subtract, then square back.

1. Intensity to amplitude. Intensity goes as amplitude squared, I ∝ a². So a₁/a₂ = √(9/4) = 3/2. Take a₁ = 3 and a₂ = 2.
2. Maxima and minima. At a maximum the waves meet in phase, so the amplitudes add: 3 + 2 = 5. At a minimum they meet out of phase, so the amplitudes subtract: 3 - 2 = 1.

   Iₘₐₓ/Iₘᵢₙ = (a₁ + a₂)²/(a₁ - a₂)² = (3+2)²/(3-2)² = 25/1

3. So. The ratio of maximum to minimum intensity is 25 : 1, option (d).

The idea to keep. In interference, amplitudes add, not intensities. Use Iₘₐₓ/Iₘᵢₙ = ((√I₁+√I₂)/(√I₁-√I₂))², and remember the maximum is always the bigger number.

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