Rayleigh & Mie Scattering Mechanics
Air molecules (N₂, O₂) scatter light inversely proportional to the fourth power of wavelength:
I_Rayleigh(λ) ∝ 1 / λ⁴ (Blue scatters ~9.4× more than Red)
At noon, short blue wavelengths scatter in all directions, illuminating the sky. At sunset, the optical path length (Air Mass) increases over 38-fold, extinguishing blue and green photons and allowing only long red-orange wavelengths to reach the observer.
The Chappuis Ozone Band & Twilight
During the "Blue Hour" (-4° to -8° solar depression), sunlight passes through the high stratosphere where the Chappuis absorption band of Ozone (O₃) attenuates yellow and orange light (550–610 nm), preserving deep royal blue and violet twilight skies.
Air Mass (Kasten-Young): AM ≈ 1 / [sin(θ) + 0.50572·(θ + 6.07995)^-1.6364]