Particles In The Troposphere

À 750 nm, the first case corresponds to particles with D 0.03 /jum and the third to particles with D 10 /jum. Particles with sizes between these two extremes fall in the second category where D ~ A; as we have seen, this is the most important size regime for atmospheric particles.

A common convention used when discussing light scattering as a function of particle size is to define a dimensionless size parameter a, which is the ratio of the circumference of the particle to the wavelength of the incident light:

tt D

Scattering plane

Incident light, l0

Scattering plane

Incident light, l0

FIGURE 9.18 Diagram showing scattering angle, scattering plane, and the polarized components of scattered light. (From Hinds, W. C. Aerosol Technology. Copyright © 1982 John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons, Inc.)

FIGURE 9.18 Diagram showing scattering angle, scattering plane, and the polarized components of scattered light. (From Hinds, W. C. Aerosol Technology. Copyright © 1982 John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons, Inc.)

Very small particles (a 3) behave like gaseous molecules in scattering light and hence produce Rayleigh scattering, described in Chapter 3. Because the particles or molecules undergoing this type of scattering are small relative to the incident wavelength, the entire species is subjected at any instant of time to what appears to be a uniform electromagnetic field; this creates a dipole that oscillates with the changing electromagnetic field of the light wave and reradiates the energy in all directions. Thus Rayleigh scattering is symmetric in the forward and backward directions relative to the incident light beam and, as we saw in Chapter 3, varies as A 4.

Very large particles, on the other hand, that is, those with D » A (a > 3), undergo geometric scattering, where the light beam refracted through the particle can be treated using classical optics. Between these two regimes where D ~ A (a ~ 3), much more complex light scattering occurs, known as Mie scattering.

Because particles undergoing Mie scattering have dimensions of the same order as the wavelength of the incident light, the electromagnetic field of the light wave is not uniform over the entire particle at one instant of time, and a three-dimensional charge distribution is set up in the scattering particle. In 1908 Mie developed the solutions for scattering of light of wavelength A by a homogeneous sphere of diameter D. As shown in Fig. 9.18, light is considered to be incident on the sphere and to be scattered at various angles 0 to the direction of the unscattered beam. The incident and scattered beams are shown as the combination of two independent polarized beams: one (/,) has its electric vector perpendicular to the scattering plane defined by the incident and the scattered beams, and the other (7n) is parallel to it. The intensity of light at a distance R and a scattering angle 6 from the particle is given by

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