The skylight that we observe on a clear day is the result of the scattering of sunlight by the gas of the atmosphere. In the literature, two approaches have been used to account for this scattering. The first approach involves the direct summation of the sunlight scattered by the individual molecules of the gas and is the method originally used by Rayleigh. The second approach involves the scattering of sunlight by fluctuations in the relative permittivity of the gas and is the method developed by Smoluchowski and Einstein. In discussions of the origin of skylight, only one of these two approaches is generally followed, and it is sometimes stated or implied that the other approach is inaccurate or not applicable to the scattering of light by the atmosphere. In this paper, a simple model is adopted for the gas in the atmosphere. Then this model is used to obtain the irradiance for the sunlight scattered by the molecules contained in a coherence volume. The irradiance involves the statistical evaluation of a sum, and this sum is taken as the common starting point for investigating the two approaches mentioned before. Simple numerical calculations, based on a random number generator, are used to perform the statistical calculations, and in the end, the observed irradiances are shown to be the same for both approaches.

Topics
Ideal gas, Electromagnetism, Electric dipole moments, Data science, Polarizability, Probability theory, Atmospheric and ocean optics, Optical properties, Scattering, Scholarly publishing
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2008
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