Two equal-intensity coherent waves produce resultant intensity 2I at point P, where each wave alone would produce intensity I. The path difference at P is known to lie between λ and 3λ ÷ 2. What is the path difference?
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Question

Two equal-intensity coherent waves produce resultant intensity 2I at point P, where each wave alone would produce intensity I. The path difference at P is known to lie between λ and 3λ ÷ 2. What is the path difference?

Options

G1 Physics · Accepted Answer

For equal intensities, I(resultant) = 4I cos²(πΔ ÷ λ). Given, I(resultant) = 2I. Thus, cos²(πΔ ÷ λ) = 1 ÷ 2. The possible path differences are one-quarter or three-quarters of a wavelength away from an integral multiple of λ. Between λ and 3λ ÷ 2, the only allowed value is Δ = 5λ ÷ 4. Correct option: A.