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Question

What is the angular position of the first minimum in a single-slit diffraction pattern if the slit
width is \( 10.0 \, \mu\text{m} \) and the wavelength is \( 500 \, \text{nm} \)?

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Explanation

**Huygens principle** predicts shape of wavefront after propagation, for point source close spherical, far plane, after reflection from plane mirror spherical wave becomes spherical with centre mirrored, plane wave remains plane but direction changes angle of incidence equals reflection, after passing through thin prism plane wavefront tilts due to different path. First minimum occurs at sin θ = (λ/a) . λ = 5.0 × 10⁻⁷ m , a = 1.0 × 10⁻⁵ m . sin θ = (5.0 × 10⁻⁷/1.0 × 10⁻⁵) = 0.05 , θ = sin⁻¹(0.05) ≈ 2.9° . Using Δ = d sinθ, y = n λ D/d, a sinθ = n

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