Two coherent waves have amplitudes 2a and 3a. At a certain point, their phase difference is 90°. If the intensity corresponding to amplitude a is I₀, the resultant intensity is NI₀. Find N.
Physics · Wave Optics · interferece of light and huygen principle
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Question

Two coherent waves have amplitudes 2a and 3a. At a certain point, their phase difference is 90°. If the intensity corresponding to amplitude a is I₀, the resultant intensity is NI₀. Find N.

G1 Physics · Accepted Answer

Resultant amplitude squared is A² = A₁²+A₂²+2A₁A₂ cosφ. With A₁ = 2a, A₂ = 3a, φ = 90°, the interference term is zero. Therefore, A² = 4a²+9a² = 13a². Hence the intensity is 13I₀. Thus N = 13.