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Scattering

Waves, sound and light · level 6, lesson 4 of 6

A question to start

Air is colourless. So why is Earth's daytime sky blue, and why do sunsets glow orange and red?

The idea

When sunlight passes through air, a little of it is knocked off in all directions by the gas molecules. This is scattering. Molecules are far smaller than a wavelength of light, and for such tiny particles the scattering is much stronger for short wavelengths:

\[\text{scattering} \propto \frac{1}{\lambda^4}.\]

This is Rayleigh scattering. Blue light is scattered several times more than red.

  • Daytime: scattered blue light comes at you from every part of the sky, so the sky looks blue.
  • Sunset: the sunlight crosses far more air to reach you. Most of the blue is scattered out on the way, and the light that is left is orange and red.
blue scattered all over the skyred and orangeget through

Worked examples

1. Blue against red. For 450 nm blue and 700 nm red: \((700/450)^4 = 5.9\). Blue is scattered about 6 times as much.

2. Violet. Violet is scattered even more, but sunlight has less violet in it, and our eyes are less sensitive to it, so the sky looks blue rather than violet.

3. A long path. At sunset, sunlight crosses many times more air than at noon, so even most of the green is scattered away.

Try it

  1. What is scattering?
  2. How many times more is 400 nm light scattered than 600 nm light?
  3. Why is the sky blue in the daytime?
  4. Why are sunsets red and orange?
Answers
  1. Light being knocked off in different directions by particles.
  2. \((600/400)^4 = 5.1\) times.
  3. Air molecules scatter blue light much more than red, and the scattered blue reaches you from all over the sky.
  4. The light crosses so much air that most of the blue is scattered out, leaving red and orange.

Common mistake

"The sky is blue because it reflects the sea." The sky is blue over deserts too. It comes from light scattered by the air itself.

Where it leads