Monochromatic light of wavelength 600 nm falls normally on a single slit of width 0.20 mm. The diffraction pattern is observed on a screen 2 m away. Find the width of the central maximum in millimetres.
Physics · Wave Optics · diffraction of light
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Question

Monochromatic light of wavelength 600 nm falls normally on a single slit of width 0.20 mm. The diffraction pattern is observed on a screen 2 m away. Find the width of the central maximum in millimetres.

Physics · Wave Optics · diffraction of light

G1 Physics · Accepted Answer

For single-slit Fraunhofer diffraction, the first minima occur at a sinθ = ±λ. For small angles, θ ≈ λ ÷ a. The angular width of the central maximum is therefore 2λ ÷ a. Hence the linear width on a screen at distance D is W = 2Dλ ÷ a. Substitute: D = 2 m, λ = 600×10⁻⁹ m, a = 0.20×10⁻³ m. Thus, W = 2×2×600×10⁻⁹ ÷ (0.20×10⁻³) = 12×10⁻³ m = 12 mm. Therefore the answer is 12.