Rayleigh Scattering and Mie Scattering

In the Earth's atmosphere, particles responsible for scattering light range from atoms (about 10^-10 m) to raindrops (about 10^-2 m). The physics of the interaction between light and particles -- that is, how the light behaves when it encounters a particle -- is greatly affected by the size of the particle relative to the wavelength of the light. A convenient way to express the relationship between these two lengths is the size parameter x, defined as:

x = 2r/

where r is the radius of the particle and is the wavelength of light (both expressed in the same units). Some typical values for important atmospheric constituents are given in Table 3.

Table 3. Size Parameters for Typical Atmospheric Particles

Particle Type	Smallest-Largest Radii (m)	Size Parameter Range in Visible Region	Dominant type of scattering
Atoms	10-10 - 10-9	10-3 - 10-2	Rayleigh
Haze particles	10-8 - 10-6	10 -1 - 101	Mie
Cloud/rain droplets	10-4 - 10-2	103 - 105	Mie

The scattering of light from particles smaller than the wavelength of light (i.e., whose size parameter x is less than 1) is called Rayleigh scattering, after Lord Rayleigh who was among the first to study this phenomena. Rayleigh scattering has a very strong wavelength dependence: The shorter the wavelength, stronger the scattering. It also has a marked dependence on the polarization of the light: Scattering is stronger in the plane perpendicular to the plane of polarization and the direction of polarization is unchanged by the scattering event. The nitrogen and oxygen molecules in the atmosphere, whose sizes are on the order of 10^-10 m, scatter visible light, with wavelengths on the order of 10^-6 m through Rayleigh scattering. The shorter wavelength, blue light is scattered about nine times more strongly than the longer wavelength, red light, which is why the sky overhead looks blue. Conversely, when the sun is near the horizon, it passes through a lot of atmospheric gas on its way to us. By the time it reaches us, much of the blue light has been scattered out of the beam, leaving the unscattered red light to provide us with spectacular sunrises and sunsets.

Particles that are larger than the wavelength of light, often called aerosols, scatter light in a different fashion. This is called Mie scattering after Gustav Mie who studied light scattering by transparent spheres. Mie scattering does exhibit some wavelength dependence, particularly for very small "haze" aerosols. However, the wavelength dependence in Mie scattering is much weaker than that seen in Rayleigh scattering. Cloud droplets, whose typical sizes are on the order of 100-1000 times as large as wavelengths of visible light, give rise to Mie scattering. The relatively small wavelength dependence of Mie scattering, in contrast to Rayleigh scattering, causes clouds to look white. Further, Mie scattering tends to depolarize polarized light.

The tendency of a particle to scatter light (by either Rayleigh or Mie scattering) can be expressed as a scattering cross section. For the moment, think of a photon as a point moving in a straight line through space, approaching a single particle, which has a some definite size. The target particle, viewed from the approaching photon, presents a certain area, which, like any other area, we can express in units like square meters (m²). We call this area the scattering cross section, often denoted as . The smaller the particle's cross section, the less likely the photon will be to hit it, and so, in a collection (gas, aerosol, cloud) of such particles the light will be less strongly scattered. That is, more of the photons will make it through undeflected.

To make this idea concrete, let's think of a beam of light coming down a tube, and put a particle in the tube. Let's keep this simple, and think of the particle as being perfectly spherical, with radius r. From the oncoming photons, this particle looks like a circle whose area is given by A = r². If we put a flat wall behind the particle, the particle will cast a circular shadow whose area is just A.. That is what we mean by the cross section. The light that hits the particle is deflected into some new direction.

Now, that is a useful model, and it gives us a very definite quantity, . In reality, the model we used is not quite right. Photons do not really behave like perfectly pointlike particles. Their electric fields influence charged particles at some distance from the photon's "position." Also, those charged particles, the electrons, are more or less susceptible to the photon's influence, depending on how they are bound to the particle. For these reasons, the physical size of a particle -- for example, as given in the table above -- is not directly related to the scattering cross section.

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