Atmospheric optics · one causal model

The Sun Never Turned Red

Move the Sun toward the horizon.

Sun elevation 45°

Current observation

At 45°, the route through the air is getting longer. More blue light is redirected sideways, so the direct beam reaching you starts to look warmer.

What reached the aperture

blue · redirectedred · transmitted

Resulting direct lightspectrum-derived colour

What to notice as you drag

Read the sunset without the maths

Lower Sun, longer trip through air. Overhead, the light takes a short route down. Near the horizon, it cuts sideways through much more atmosphere.
Blue light is scattered sideways, not destroyed. Those short blue wavelengths are redirected into other directions. Some of that scattered light is what makes the rest of the sky look blue.
The direct sunlight loses more blue, so it looks warmer. The beam reaching the aperture contains a larger share of orange and red light, even though the Sun itself did not change.
Blue sky and warm sunset are the same event seen two ways. Look away from the Sun and you notice the blue light that got scattered around the sky. Look straight at the Sun and you notice the warmer light that stayed in the direct beam.
Real sunsets have extra ingredients. Dust, smoke, water droplets and clouds can strengthen or flatten the colours. This small model only shows clean-air scattering.

Why the colour changes

01 · PATH Relative air mass ×1.4
This number simply means “how much air is in the way”. It is close to 1× overhead, then rises sharply near the horizon.
m(h) = [sin h + 0.50572(h + 6.07995)^−1.6364]⁻¹ h is apparent elevation. Near the horizon, light crosses much more atmosphere.
02 · SCATTER Fourth power: why blue leaves first
Shorter wavelengths are easier for air molecules to redirect. A small change in wavelength produces a much bigger change in scattering.
τ_R(λ) ∝ λ⁻⁴ λ is wavelength. Rayleigh scattering redirects 450 nm blue light about 4.4x more strongly than 650 nm red light.
03 · TRANSMIT What survives to your eye
After that longer trip, the straight beam has lost more blue than red. What reaches you is both dimmer and warmer.
T(λ,h) = e^{−m(h)τ_R(λ)} The transmitted direct light is the direct beam that survives. A longer path removes more blue, so it arrives dimmer and warmer.

Qualitative atmospheric model. The equations are physical approximations; colour is illustrative, not calibrated.