Practice question

**Single-slit pattern** intensity I = I₀ (sinα/α)², α=π a sinθ/λ, central maximum at α=0, minima at α=nπ, so a sinθ=nλ, width increases with λ and D decreases with a, for a=15 μm λ=750 nm first minimum sinθ=750/15000=0.05 θ≈2.87°, angular width of central maximum 2θ≈5.74°. Secondary maxima occur at θ ≈ ((n + (1/2))λ/a) . For the first secondary maximum, n = 1 . λ = 4.5 × 10⁻⁷ m , a = 9.0 × 10⁻⁶ m . sin θ = ((1 + (1/2)) × 4.5 × 10⁻⁷/9.0 × 10⁻⁶) = (1.5 × 4.5 × 10⁻⁷/9.0 × 10⁻⁶) = 0.075 , θ = sin⁻¹(0.075) ≈ 4.3°