When light strikes small particles, it bounces or scatters, changing direction. Rayleigh scattering is the scattering that occurs when the particles are smaller than the wavelength of the light. For Rayleigh scattering of visible light the particles must be smaller than 400 to 700 nanometres – the range of wavelengths of visible light. Scattering can occur off larger particles, but it will follow a different scattering law.
The Rayleigh scattering law, derived by Lord Rayleigh in 1871, applies to particles smaller than the wavelength of the light being scattered. It states that the percentage of light is proportional to
Small particles will scatter a much higher percentage of short wavelength light than long wavelength light. Because the mathematical relationship involves the fourth power of the wavelength even a small wavelength difference can mean a large difference in scattering efficiencies. For example, applying the Rayleigh law to the wavelengths of red and blue light given above shows that small particles will scatter blue light roughly 10 times more efficiently than red light, since the ratio of the wavelengths is
or
so light will be scattered in the ratio
The earth's atmosphere contains lots of particles. The nitrogen and oxygen molecules in the earth's atmosphere are particles small enough that Rayleigh scattering applies with blue light being scattered about 10 times as much as red light. When the Sun is high overhead on a clear day, some of the blue light is scattered. Much of it is scattered more than once before eventually hitting our eyes, so we see blue light coming not directly from the sun but from all over the sky. The sky is then a pretty shade of blue. In the evening, when there is less blue light coming directly from the Sun it will appear redder than it really is. When the sun is low in the sky, the light must travel through much more atmosphere to reach our eyes. Even more of the blue light is scattered, and the Sun appears redder than when it is overhead, so sunsets and sunrises are red.
