Everyday Physics · Day 02
Sunlight is white — every colour mixed together. Yet look up and it's unmistakably blue. The answer is a single equation involving the fourth power of wavelength.
[ 01 — The Setup ]
The Sun emits a continuous spectrum of visible light — from deep violet (~380 nm) to far red (~700 nm). When all wavelengths arrive together in roughly equal intensity, we perceive the mix as white. A prism splits this mix back into its components; a rainbow does the same using water droplets.
So the question isn't "where does the blue come from?" — all the colours are already there. The real question is: why does the atmosphere preferentially send blue light to your eyes, while letting red and orange pass straight through?
Key Observation
A prism doesn't add colour to white light — it separates colours that were already there. The sky does the opposite: it filters the white light that passes through it, redirecting blue preferentially toward your eyes.
[ 02 — The Mechanism ]
The atmosphere is full of nitrogen (N₂) and oxygen (O₂) molecules — roughly 10²⁵ molecules per cubic metre. When a photon of light strikes one of these tiny particles, it is absorbed and immediately re-emitted in a random direction. This is Rayleigh scattering.
Crucially, the efficiency of this scattering is not the same for all colours. It depends very strongly on the wavelength of the light — and blue light, with its shorter wavelength, is scattered far more strongly than red.
Why scattering happens
When an electromagnetic wave passes an electrically neutral molecule, the oscillating field momentarily distorts the electron cloud — creating a tiny oscillating dipole. This dipole radiates energy in all directions.
The smaller the particle compared to the wavelength of light, the more this Rayleigh regime applies.
Mie vs Rayleigh
When particles are larger — like water droplets or dust — Mie scattering takes over. Mie scattering is wavelength-independent, which is why clouds appear white: all colours are scattered equally.
Rayleigh applies only when particle size ≪ wavelength.
[ 03 — The Math ]
Lord Rayleigh derived the scattering intensity in 1871. The result is deceptively simple: scattering intensity is inversely proportional to the fourth power of wavelength.
The exponent of 4 is brutal. Blue light (~450 nm) has a wavelength about 1.6× shorter than red (~700 nm). That ratio to the 4th power: 1.6⁴ ≈ 6.5. Blue light is scattered roughly 6–9 times more than red.
The Number
Blue (450 nm) scatters ~9× more than red (700 nm). This is why the overhead sky is decisively blue — your eyes are being flooded with redirected blue photons from every part of the sky dome above you.
[ 04 — The Twist ]
At noon the Sun is overhead. Its light travels through roughly 100 km of atmosphere to reach you — a relatively short path. Blue is scattered toward you from all directions: sky is blue.
At sunset, the Sun is near the horizon. Its light now travels through ~1,800–3,000 km of atmosphere — up to 30× more air. By the time it reaches you, almost all the blue has already been scattered away in other directions. What remains is the long-wavelength tail: orange, red, and deep crimson.
Noon sky
Sun overhead → short path (~100 km of dense atmosphere). Blue scatters from every angle. The overhead sky appears deep blue and the Sun itself looks white-yellow.
Sunset sky
Sun near horizon → path up to 30× longer. Blue and violet have been scattered out long before the light reaches you. Only orange and red wavelengths survive the journey.
[ 05 — Explore ]
The chart below plots scattering intensity (I ∝ λ⁻⁴) across the full visible spectrum. Hover or tap any point to see exact values. The drop from violet to red is steep — nearly two orders of magnitude.
Notice that violet (380 nm) actually scatters more than blue (450 nm). So why isn't the sky violet? Two reasons: the Sun emits less violet light than blue, and the human eye is roughly 3× less sensitive to violet than to blue. The combination means blue wins perceptually.
Why not violet?
Three factors conspire to make the sky look blue and not violet:
1. The Sun's spectrum peaks in green — violet output is already lower.
2. Some violet is absorbed in the upper atmosphere (ozone).
3. Your eye has ~3× fewer violet-sensitive cones than blue-sensitive ones.
The sky IS scattered violet light — your visual system just doesn't register it as such.
[ 06 — The Paradox ]
Violet light (~400 nm) has a shorter wavelength than blue (~450 nm). By the λ⁻⁴ law, violet scatters roughly 14× red — compared to blue's 9×. Physics predicts a violet sky. We see a blue one. Three separate factors cancel violet's advantage.
Factor 1 — Solar spectrum
The Sun's output peaks around 500 nm (green-yellow) and falls steeply toward violet. Far fewer violet photons arrive at the top of the atmosphere than blue photons — even before any scattering happens. Less input means less output, no matter how efficiently it scatters.
Factor 2 — Ozone absorption
The ozone layer in the stratosphere absorbs near-UV and violet wavelengths preferentially. By the time sunlight reaches the lower atmosphere where most scattering occurs, much of the violet supply has already been stripped out by ozone.
Factor 3 — Eye sensitivity
The human eye's S-cones peak around 440 nm and fall sharply below 420 nm. Your visual system is roughly 3–5× less sensitive to 400 nm violet than to 450 nm blue. Even when violet photons reach your eye, they produce a weaker neural signal.
The combined result
Multiply scattering × solar output × ozone transmission × eye sensitivity. The product peaks near 470–490 nm — which is precisely the blue your brain registers when you look at the sky. Violet's raw scattering advantage is overwhelmed on three fronts simultaneously.
[ 07 — Aurora ]
If the eye is less sensitive to violet, why do we see violet in the northern lights? Because aurora light is not scattered sunlight. It is direct atomic emission — a fundamentally different mechanism that bypasses the three factors that suppress violet in the sky.
In the aurora, charged particles from the solar wind slam into oxygen and nitrogen atoms at 100–300 km altitude. The collisions knock electrons into higher energy states. When those electrons fall back down, they release photons at exact, fixed wavelengths determined by atomic structure — not by the Sun's spectrum or the ozone layer.
Why we CAN see aurora violet
Three things change in the aurora vs. the sky:
1. No solar spectrum dependency. The N₂⁺ emission at 391 nm and 428 nm is generated independently — the Sun's low violet output is irrelevant.
2. No ozone absorption issue. Aurora glows below the ozone layer (100–300 km), so emitted photons travel straight down to your eye without re-crossing the ozone.
3. Intensity overcomes sensitivity. "Nearly blind" is not "completely blind." The S-cones can respond to violet — they just need a brighter signal. An aurora intense enough to be visible already exceeds that threshold. Sensitivity matters at low flux; at aurora brightness, violet is visible.
Aurora colour by source
Violet / Purple — N₂⁺ ions at 391 nm and 428 nm
Blue — N₂⁺ at 470 nm range
Green — Oxygen atoms at 557.7 nm (100–150 km)
Red — Oxygen atoms at 630 nm (200+ km altitude)
Pink / Magenta — Red oxygen + blue-violet nitrogen mixed
Scattering vs. Emission
Rayleigh scattering: existing photons from the Sun are redirected. The output spectrum is shaped by solar input, ozone, and wavelength-dependent efficiency. No new photons are created.
Atomic emission: new photons are created when electrons transition between energy levels. The wavelengths are fixed by quantum mechanics — completely independent of any incoming light source.
[ 08 — The Full Picture ]
Nitrogen and oxygen molecules scatter sunlight. Scattering efficiency ∝ λ⁻⁴. Blue is 6–9× more scattered than red. Scattered blue floods your visual field from every direction in the sky dome.
A longer atmospheric path removes blue via scattering before it reaches you. Only long-wavelength red and orange photons survive the journey to your eye.
Water droplets are much larger than atmospheric molecules — Mie scattering applies. Mie scattering is wavelength-independent: all colours scatter equally, producing white.
No atmosphere → no molecules → no scattering. Without scattering, light only travels in straight lines from its source. The rest of space stays black.
Mars's thin atmosphere is full of fine iron-oxide dust. Dust particles are large enough to trigger Mie scattering with a slight red bias — producing the characteristic pinkish hue.
The sky's colour is not a property of the atmosphere — it's a property of light interacting with small particles. The same physics governs why sunsets are red, why deep water looks blue, and why X-ray telescopes must be in space.