In a single-slit Fraunhofer diffraction pattern, the condition a sinθ = λ ÷ 2 is satisfied at a certain point. If I₀ is the intensity at the centre of the pattern, what is the intensity at this point?
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Question

In a single-slit Fraunhofer diffraction pattern, the condition a sinθ = λ ÷ 2 is satisfied at a certain point. If I₀ is the intensity at the centre of the pattern, what is the intensity at this point?

Options

G1 Physics · Accepted Answer

For a single slit, I = I₀[sin u ÷ u]², where u = πa sinθ ÷ λ. Given, a sinθ = λ ÷ 2. Therefore, u = π(λ ÷ 2) ÷ λ = π ÷ 2. Hence, I = I₀[sin(π ÷ 2) ÷ (π ÷ 2)]² = I₀[1 ÷ (π ÷ 2)]² = 4I₀ ÷ π². Correct option: B.