In Young’s double-slit experiment using wavelength λ, the intensity at a point where path difference is λ is K units. What is the intensity where the path difference is λ/3? Assume equal-intensity coherent slits.
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Question

In Young’s double-slit experiment using wavelength λ, the intensity at a point where path difference is λ is K units. What is the intensity where the path difference is λ/3? Assume equal-intensity coherent slits.

Options

G1 Physics · Accepted Answer

Step 1: For two equal coherent sources, intensity varies as I = I(max) cos²(Δφ/2). Step 2: A path difference of λ gives Δφ = 2π, hence I(λ) = I(max) cos²π = I(max) = K. Step 3: At path difference λ/3, phase difference Δφ = (2π/λ)(λ/3) = 2π/3. Step 4: I(λ/3) = K cos²(π/3) = K × (1/2)² = K/4. Final answer: K/4 (Option D).