Mie Scattering

Physics: Mie theory (1908): exact solution to Maxwell's equations for a sphere. Size parameter x = 2πr/λ. Rayleigh limit (x << 1): Q_sca ∝ x⁴ ∝ λ⁻⁴ — why the sky is blue (shorter λ scatters more). Geometric optics limit (x >> 1): Q_ext → 2 (extinction paradox — twice the geometric cross-section due to diffraction). Mie resonances: oscillations in Q(x) as sphere size matches resonant modes. Rainbow: primary at 137.5° from angular geometry + Mie interference. Cloud droplets (r ≈ 5 μm) scatter white light equally → grey clouds. Gold nanoparticle Mie peak ≈ 520 nm (red wine color). Glory: backward scattering enhancement at 180°.