A comparison of two approaches for determining the molecular contributions to skylight

The properties of skylight, particularly its blue color and state of polarization, are popular topics for discussion in classes on electromagnetism and optics, and both can be readily explained by considering the scattering of sunlight by a single molecule [1], [2]. However, it is the scattering by a large number of molecules that we actually see, and the two different approaches used to sum these contributions are the topic of this presentation. The first approach involves the direct summation of the sunlight scattered by the individual molecules and is the method originally used by Lord Rayleigh [3]. The second approach involves the scattering of sunlight by fluctuations in the relative permittivity of the gas, or equivalently in the number density for the molecules, and is the method developed by Smoluchowski and later by Einstein [4], [5]. The relationship between these two approaches is often not clearly stated, and this can lead to some confusion on the part of students.