If radiation is included through conducting solids, then usually the difference in refractive indices between the fluid and solid determines the amount of reflection and refraction that occurs. The probability of being reflected is given by Fresnels’ equation

(8–18)

The fraction of the electromagnetic wave that is reflected normally depends on the polarization of the photon. CFX does not keep track of photon polarizations. Assuming that the photons are randomly polarized, then it is sufficient to take the average result. The two extreme polarizations are termed transverse electric (TE) and transverse magnetic (TM), and describe the orientations of the electric and magnetic vectors relative to the interface.

For the TE mode, the ratio of reflected to incident wave amplitude (E _E) is given by:

(8–19)

and for the TM mode the ratio of reflected to incident wave amplitude () is given by:

(8–20)

where and are the incident and refracted angles, and and are the refractive indices of the two media.

The probability of being reflected is determined by the energy flow at the interface which is proportional to the square of the wave amplitude. Thus, the average reflection coefficient is given as:

(8–21)

and the probability of being transmitted is:

(8–22)

No absorption takes place at the interface, so the probability of transmission plus reflection is always one. If the photon is transmitted, then the angle of refraction is determined by Snells’ law:

(8–23)

CFX performs these calculations at every radiation element boundary, although, in most cases, there is no change of refractive index.