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Question

What is the path difference for the second dark fringe in a double-slit experiment?

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Explanation

**Double-slit vs single-slit** double-slit interference pattern has equally spaced bright fringes with envelope due to single-slit diffraction, single-slit central maximum width 2λ D/a, intensity of secondary maxima decreases with order, condition for coherence constant frequency and phase, path difference for bright n λ, dark (n+½)λ. Destructive interference occurs at Δ = (n + (1/2))λ . For the second dark fringe, n = 1 , Δ = (1 + (1/2))λ = (3λ/2) . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2),

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