Up to now radiation has been treated as propagating electromagnetic waves. The electromagnetic theory relates the optical properties such as reflectivity and transmissivity at an interface between two media to the indices of refraction, n, of the media. An imaginary part to the index of refraction accounts for absorption of radiation. However, in a medium that is emitting, scattering, and absorbing radiation, the electromagnetic theory of plane wave propagation does not apply. In this case, sources for emission, scattering, and absorption must be included. Radiation transfer theory accounts for these sources in a macroscopic manner through the introduction of absorption and scattering coefficients. These properties depend upon the atomic structure of the medium. To determine these properties a quantum mechanical model must be employed. However, in the analysis to follow, the absorption coefficient, a, and the scattering coefficient, os, are treated as given properties. As discussed in Section 1.5.2 the absorption coefficient in the electromagnetic theory is related to the imaginary part of the index of refraction, equation (1.41).
In the electromagnetic theory calculation of reflectivity and transmissivity it is assumed that the interface is perfectly flat. Therefore, for uneven surfaces, which are most probable, these results do not necessarily apply. However, an uneven surface can be approximated as a series of flat surfaces. And since reflectivity is nearly constant for most angles of incidence, as already discussed in Section 1.5.5, it is a reasonable approximation to use the zero angle of incidence reflectivity calculated by electromagnetic theory even for rough surfaces. In Chapter 3 the spectral emittance of an emitting medium will be calculated using radiation transfer theory. In that calculation the electromagnetic theory reflectivity, which is defined in terms of the energy flux, I, is used to determine the reflected intensity, i, at an interface. Thus the emittance calculation combines both electromagnetic and radiation transfer theory.