Standard electromagnetic theory (ibid.) also implies that the normal component of the electric displacement, as well as the tangential component of the electric field, are continuous at the interface. In other words,

(590)

and

(591)

The former of these conditions again gives Equation(589), whereas the latter yields

(592)

Here,

(593)(594)

It follows that

(595)(596)

The electromagnetic energy flux in the-direction (i.e., normal to the interface) is (see AppendixC),

(597)

[cf. Equation(486)]. Thus, the mean energy fluxes associated with the incident, reflected, and refracted waves are

(598)(599)(600)

respectively. The coefficients of reflection and transmission are defined

(601)(602)

respectively. Hence, it follows that

(603)(604)

These expressions are known asFresnel relations, and are the generalizations of expressions (510) and (511) for the case of oblique incidence (with the polarization in which the magnetic field is parallel to the interface).

Let us now consider the second polarization, in which the electric components of the incident, reflected, and refracted waves are all parallel to the interface. In this case, the governing equations ar