Path Length Distribution

The probability distribution for the path length x a photon travels before it is scattered or absorbed is given in Section 5.1, rewritten here as where x is the physical path length and t the total mean free path. It is more convenient here to express this distribution in terms of the optical path length r x t the integral of which from 0 to to is 1, as it must be if this is a proper probability distribution. As we did previously for the probability distribution 2x, we find r as a function of ,...

Pdysaid d dy

Figure 6.4 The continuous probability distribution p exp(-t) for the variable t can be approximated by dividing the t-axis into equal intervals (bins) 1000 bins were used here. Values are assigned to each bin with a random number generator. The number of values in each bin divided by the total number times the bin width is the probability density for the bin. The discrete probability densities (solid circles) more closely approximate the continuous distribution (solid line) the greater the...

Absorption Cross Section

Determining the absorption coefficient of liquids and solids from the absorption properties of their individual molecules is not an easy task because they are sufficiently close together that they interact strongly. This is evident from Figs. 1.11 and 1.12, which show that the spectral emissivity of liquid water bears little resemblance to that of water vapor. Beginning with the latter it is not an easy step to the former. Interactions between water molecules in the liquid phase all but destroy...

The General Radiation Field

Light is a superposition of electromagnetic waves, intertwined electric fields E and magnetic fields H. Because these fields are vectors, so are electromagnetic waves. They satisfy vector wave equations similar to the scalar wave equation derived in Section 3.3 for the vibrating string. We usually are most interested in the rate at which radiant energy is transported by electromagnetic waves. The electric and magnetic fields determine this transport rate by way of the Poynting vector where E...

Classical versus Quantum Mechanical Interpretation of Absorption

What once was, and perhaps still is, the standard treatise on atomic spectra, by Condon and Shortley, fills 432 pages of text. Herzberg's treatises fill 581 pages for diatomic molecules, 538 pages for polyatomic molecules, and 670 pages for the electronic spectra of polyatomic molecules. Townes and Schawlow devote 648 pages to microwave spectroscopy. And the physical strain of just lifting these nearly 3000 pages is as nothing compared to the mental strain of absorbing them. Add to these tomes...

Scattering by an Isotropic Homogeneous Sphere

Atmospheric Isotropic Interruption

An isotropic, homogeneous sphere is the simplest finite scatterer, the theory of scattering by which is attached to the name of Gustav Mie. So firm is this attachment that in defiance of logic and history every particle under the sun has been dubbed a Mie scatterer, and Mie scattering has been promoted from a particular theory of limited applicability to the unearned rank of general scattering process. Mie was not the first to solve the problem of scattering by an arbitrary sphere. It would be...