The term “extinction” means the loss of light in the atmosphere from a directly transmitted beam. Two different mechanisms contribute to extinction: absorption and scattering. Normally, most of the extinction in the Earth's atmosphere is due to scattering; absorption becomes important when the air is full of smoke — a situation that occurs frequently in brush-fire season here in Southern California.
Extinction is responsible for the dimness of the setting Sun. At the sea horizon, it's not dazzling or hazardous to the eye — unlike its dangerous brightness higher in the sky.
Because the extinction is generally larger at short (blue) wavelengths, the setting Sun is usually so dim at short wavelengths as to be lost in the scattered light of the foreground sky, and the remaining transmitted light appears red. That is, the extinction is much stronger in blue light than in red light. This effect is usually called “reddening” — a term that refers to the difference in extinction at different wavelengths. When the atmospheric reddening is large, green flashes cannot be seen. because only red and orange light are transmitted near the horizon.
Two kinds of scattering are important: scattering by molecules of air, and scattering by solid particles or liquid droplets suspended in the air. Molecular scattering is usually called Rayleigh scattering, as it was first studied and explained by Lord Rayleigh. The suspended particles, on the other hand, are collectively known as aerosols, and their contribution is called aerosol scattering.
Rayleigh's original paper [Phil. Mag. 41, 107–120, 274–279 (1871)] was intended to show that the blue sky could be explained as scattering by small particles; but he later realized that the “particles” could well be the molecules of air itself. Assuming that the scatterers are small compared to the wavelength of light, Rayleigh showed that the scattered intensity should be inversely proportional to the fourth power of the wavelength of light, and that this was in good agreement with the spectral distribution of the light in the blue sky. Furthermore, the theory described the polarization, and the variation in intensity with direction, of the scattered light.
A remarkable aspect of Rayleigh's 1871 paper is that the development was done entirely on the basis of the “elastic-solid” theory of the luminiferous ether. In a later paper [Phil. Mag. 12, 81–101 (1881)], Rayleigh re-derived the same results from the electromagnetic theory, which had recently been introduced by James Clerk Maxwell. Still later [Phil. Mag. 47, 375–394 (1899)], he concluded that the scattering by molecules alone would suffice to account for the blue sky, as well as for the refractivity of air (see below).
A feature of Rayleigh's theory that is often forgotten today is that the intensity of the scattering depends on the refractive index of the scattering medium. Because the refractivity of air is dispersive, the actual intensity of Rayleigh scattering in air is somewhat steeper than an inverse-fourth-power law, and amounts to about an inverse 4.08-power law across the visible spectrum. This wavelength dependence is responsible for the reddening of clear air.
The connection between Rayleigh scattering and refraction is very fundamental. Both are due (from the point of view of electromagnetic theory) to the electrical polarization of the scatterers by the incident electromagnetic wave. The waves re-radiated by the dipoles induced in the scatterers by the incident field are incoherent, as seen by an observer located to the side of the incident beam of light. But, in the forward direction, the re-radiated waves are completely coherent with the incident waves, but retarded in phase. These retarded waves make the incident wave train propagate more slowly in the scattering medium than in a vacuum; the ratio of the speed of propagation in vacuo to the speed in the medium is just the refractive index of the medium. Thus refraction and Rayleigh scattering are two aspects of a single phenomenon.
In a 1918 paper, Rayleigh also showed that there is more scattering from anisotropic molecules than from spherical ones. Part of this “anisotropy scattering” is displaced in frequency, owing to the internal motions of the molecules; these displaced components are usually called “Raman scattering”. They amount to several per cent of the total scattering. [For more information on Rayleigh scattering, see my review of the subject in Physics Today 35, 42–48 (1982).]
Atmospheric aerosols are very diverse. They include tiny grains of mineral dust stirred up from the ground; particles of salt left when droplets of sea spray evaporate; bacteria, pollen grains, mold spores, and other “biosol” particles; photochemically produced droplets of sulfuric acid and other pollutants; soot particles produced in fires, and in vehicle exhaust; and many other materials. As most of these are produced at or near ground level, and are washed out of the atmosphere by condensation of cloud droplets on them, followed by precipitation, the aerosols all tend to be concentrated in the lowest part of the atmosphere; an exponential distribution with a scale height of about 1.5 km is a rough approximation to their vertical distribution.
Because of their diversity, aerosol particles have a wide range of sizes. However, the ones most important for optical scattering turn out to be comparable to the wavelength being scattered, for typical size distributions. Therefore, as the wavelength decreases, we “see” the smaller particles better; the wavelength dependence of aerosol scattering is almost inversely proportional to the wavelength. (A λ−1.2 power law is often used.) This produces considerable reddening in addition to that due to molecular scattering.
Most of the aerosol particles are so weakly absorbing that their extinction is almost entirely due to scattering, rather than absorption. However, soot (carbon) particles are quite strong absorbers, and a considerable part of their reddening is due to the increase of their absorption at short wavelengths.
Absorption by molecules is sometimes called “true absorption,” to emphasize its difference from extinction due to scattering; or “selective absorption,” to emphasize its concentration in narrow spectral bands. The main absorbers in the visible spectrum are ozone (which absorbs in the Chappuis bands, in the orange part of the spectrum), water vapor (several bands in the longer-wavelength regions, noticed mainly under very humid conditions — hence the name “rain bands”), and oxygen (which produces Fraunhofer's A and B bands).
Of these, the Chappuis bands of ozone are probably most important in green flashes, as they absorb strongly just in the wavelengths between red and green, and probably contribute to the abruptness of the color change seen in green flashes. The water-vapor bands are usually much less important.
A remarkable conection between extinction and refraction was noticed by Laplace two centuries ago. It requires a more mathematical treatment, which is given on a separate page.
Copyright © 2003 – 2008 Andrew T. Young
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