The Fresnel equations give the ratio of the reflected and transmitted electric field amplitude to initial electric field for electromagnetic radiation incident on a dielectric. In general, when a wave reaches a boundary between two different dielectric constants, part of the wave is reflected and part is transmitted, with the sum of the energies in these two waves equal to that of the original wave. Since electromagnetic waves are transverse, there are separate coefficients in the directions perpendicular to and parallel to the surface of the dielectric. The coefficients for reflection and transmission of the "transverse electric field" (abbreviated "TE") are denoted and , respectively, while the coefficients for reflection and transmission of the "transverse magnetic field" (abbreviated "TM") are denoted and , respectively. In this formulation, a negative sign for an amplitude coefficient denotes a ray in the opposite direction as the incident ray. In addition to the amplitude coefficients, power (or intensity) coefficients are often defined as the square of the corresponding amplitude coefficients, i.e.,





For TE radiation,


where is the dielectric constant in the original medium, is the dielectric constant in the second medium, is the angle to the normal in the initial medium, is the angle in the second medium (which is different from due to refraction), is the magnetic permeability in the original medium, and is the permittivity in the second medium. For most substances , so we can take , giving the simplified equations


From the Fresnel equation (7), it follows that is negative only when . For this condition is then equivalent to

Using Snell's law

then gives

so

Therefore, is negative for and positive for all This is equivalent to stating that the TE component of the electric field suffers a phase shift upon reflection of


For TM radiation,


For , these simplify to


The angle at which , resulting in completely polarized reflected light, is called Brewster's angle.
At normal incidence (i.e., ) with , the reflection and transmission amplitude coefficients coincide for each of TE and TM radiation, giving


The squares of these quantities


are known as the reflectance and transmittance, respectively.