Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

Solution

Physics sir · 3 steps

Intensities never add directly; take square roots to get amplitudes, add them, then square back.

1. Go to amplitudes. Intensity is proportional to amplitude squared, so I₁ : I₂ = 1 : 9 gives a₁ : a₂ = √1 : √9 = 1 : 3.
2. Bright and dark. At a maximum the waves meet in phase, so the amplitudes add. At a minimum they meet out of phase, so the amplitudes subtract. Square each result to get the intensity.

   Iₘₐₓ/Iₘᵢₙ = ((a₁ + a₂)/(a₂ - a₁))² = ((1 + 3)/(3 - 1))² = (4/2)² = 4

3. So. Iₘₐₓ : Iₘᵢₙ = 16 : 4 = 4 : 1, which is option (b).

The idea to keep. In interference, amplitudes add and subtract, not intensities. Use Iₘₐₓ/Iₘᵢₙ = ((√I₁+√I₂)/(√I₁-√I₂))², and remember the square at the end.

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