In a single-slit Fraunhofer diffraction pattern, a direction satisfies a sinθ = 3λ ÷ 2. If I₀ is the central maximum intensity, what is I ÷ I₀ at this direction?
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Question

In a single-slit Fraunhofer diffraction pattern, a direction satisfies a sinθ = 3λ ÷ 2. If I₀ is the central maximum intensity, what is I ÷ I₀ at this direction?

G1 Physics · Accepted Answer

For single-slit diffraction, I ÷ I₀ = [sin u ÷ u]², with u = πa sinθ ÷ λ. Given, a sinθ = 3λ ÷ 2. Thus, u = 3π ÷ 2. Now, sin(3π ÷ 2) = −1. Therefore, I ÷ I₀ = [−1 ÷ (3π ÷ 2)]² = [2 ÷ (3π)]² = 4 ÷ (9π²). Correct option: A.