Two beams of light of intensities I₁ and I₂ interfere to give an interference pattern. If the ratio of the maximum intensity to the minimum intensity is (16)/4, then I₁ : I₂ = .

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(1) 9 : 1. Given: (Iₘₐₓ)/(Iₘᵢₙ) = (16)/4 = 4 for two interfering beams. Idea: maxima and minima are formed by adding and subtracting amplitudes, so the algebra has to be done in √I, not in I. (Iₘₐₓ)/(Iₘᵢₙ) = ((√I₁+√I₂)/(√I₁-√I₂))² = 4, so (√I₁+√I₂)/(√I₁-√I₂) = 2. Cross-multiplying, √I₁+√I₂ = 2√I₁-2√I₂, which gives √I₁ = 3√I₂. Squaring, (I₁)/(I₂) = 9. So I₁ : I₂ = 9 : 1.

Two beams of light of intensities I₁ and I₂ interfere to give an interference pattern. If the ratio of the maximum intensity to the minimum intensity is (16)/4, then I₁ : I₂ = ________.

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