Rayleigh Scattering

A light wave is made up of an alternating electric field with an associated (but perpendicular) alternating magnetic field.  This is why light is called an ‘electromagnetic’ wave.  For now though, we will neglect the magnetic part and focus entirely on the electric.

When a metal is subject to an electric field, charged particles called electrons move in response to the electric field, producing an electric current. These electrons are also found in atoms (along with the oppositely charged ‘protons’ which together ensure the electrical neutrality of the atom), but in atoms they are not free to move as they do in metals and are instead ‘stuck’ to the atom.

When light, with its alternating electric field, falls onto an atom, the electrons in the atom oscillate with the electric field and then re-radiate it out of the atom.  This re-radiated electric field is what is known as the scattered light.  Just as the discomfort to a bus passenger is dependent on the frequency of the bus engine and peaks as the engine frequency approaches the resonance of the bus seat, so the amount of scattered light depends on the resonance of the atom.  Consequently the power of the scattered light depends on the frequency of the incident light and the proximity of this frequency to the resonance frequency of the atom.

For the air molecules, the resonance frequency is far away from the frequency of visible light and so the light scattered is simply proportional to the frequency of light raised to the fourth power. (Equally we could say that it is inversely proportional to the wavelength raised to the fourth power). This type of scattering is known as Rayleigh scattering. If the frequency of light nearly doubles (red to blue), the scattered intensity increases by a factor of almost 16; blue light is scattered much more than red.

If, rather than a single atom or molecule, the atoms or molecules form clusters, then the scattering amplitude increases with the number of atoms in the cluster (provided that the cluster size is less than the wavelength of the incident light).  Therefore, as long as the particle is smaller than the wavelength of the light, the intensity of the scattered light increases with the particle size.  To a first approximation therefore, milk-y water will scatter far more blue light than individual air molecules do and so we can play with sunsets in a milk glass while we would not see the effect in an empty glass.  Although the air molecules in the empty glass are scattering the light, they do so far more weakly than the milk particles in suspension. Similarly, as a cloud starts to form, it will scatter blue light more strongly than the air around it as the water particles come together into droplets.  However, as the water in the cloud condenses still further, the droplet size will quickly become larger than the wavelength of visible light.  When the particles get to this size, there is less of a wavelength dependence to the scattered light, it is no longer Rayleigh scattering, and the clouds appear white.