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Question

What is the intensity at a point in a double-slit experiment where the phase difference is \( 3\pi \),
if the maximum intensity is \( 4I_0 \)?

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Explanation

**Frequency of light** remains unchanged when refracts from air into water because frequency determined by source, energy E= h f conserved, speed decreases v= c/n, wavelength decreases λ'=v/f= λ/n, energy of wave proportional to amplitude² not speed, intensity I =½ c ε₀ E₀², energy not depend on speed directly, when speed decreases amplitude may change but energy conserved, interference redistributes energy, total energy same, bright regions gain from dark. Intensity I = 4I₀ cos²(Φ/2) . For Φ = 3π , I = 4I₀ cos²((3π/2)) = 4I₀ × 0 = 0 . Using Δ = d sinθ, y = n λ D/d, a sinθ = n

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