Part of JOP-02 — Wave Optics: YDSE, Diffraction & Polarization

Single Slit Diffraction

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Single slit diffraction occurs when light passes through a slit of width a comparable to wavelength. Minima at a sinθ = nλ (n = ±1, ±2, ...) — note this is the same form as the interference maxima condition, a common source of errors. Central maximum angular width = 2λ/a, linear width = 2λD/a. Secondary maxima approximately at a sinθ ≈ (2n+1)λ/2, with rapidly decreasing intensity: 4.5% of central for the first, 1.6% for the second. The central maximum contains ~84% of total energy. As slit width increases, the pattern narrows (less diffraction); as a → λ, the central maximum fills the entire forward hemisphere. In reality, YDSE patterns are modulated by the single-slit diffraction envelope. Missing orders occur when d/a is an integer — the mth interference maximum is suppressed when m = da\frac{d}{a}, 2d/a, etc. The Fresnel distance ZFZ_F = a2a^{2}/λ separates the near-field (ray optics) from far-field (diffraction) regimes.

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