Editing Fresnel equations (section)

=== Material parameters ===
In order to compute meaningful Fresnel coefficients, we must assume that the medium is (approximately) [[linearity|linear]] and [[homogeneity (physics)|homogeneous]]. If the medium is also [[isotropy|isotropic]], the four field vectors {{math|'''E''',{{nnbsp}}'''B''',{{nnbsp}}'''D''',{{nnbsp}}'''H'''}}{{tsp}} are [[Constitutive equation#Electromagnetism|related]] by
<math display=block>\begin{align}
\mathbf{D} &= \epsilon \mathbf{E} \\
\mathbf{B} &= \mu \mathbf{H}\,,
\end{align}
</math>
where {{math|''ϵ''}} and {{math|''μ''}} are scalars, known respectively as the (electric) ''[[permittivity]]'' and the (magnetic) ''[[permeability (electromagnetism)|permeability]]'' of the medium. For vacuum, these have the values {{math|''ϵ''<sub>0</sub>}} and {{math|''μ''<sub>0</sub>}}, respectively. Hence we define the ''relative'' permittivity (or [[dielectric constant]]) {{math|''ϵ''<sub>rel</sub> {{=}} ''ϵ''/''ϵ''<sub>0</sub>}}, and the ''relative'' permeability {{math|''μ''<sub>rel</sub> {{=}} ''μ''/''μ''<sub>0</sub>}}.

In optics it is common to assume that the medium is non-magnetic, so that {{math|1=''μ''<sub>rel</sub> = 1}}. For [[ferromagnetic]] materials at radio/microwave frequencies, larger values of {{math|''μ''<sub>rel</sub>}} must be taken into account. But, for optically transparent media, and for all other materials at optical frequencies (except possible [[metamaterial]]s), {{math|''μ''<sub>rel</sub>}} is indeed very close to 1; that is, {{math|''μ'' ≈ ''μ''<sub>0</sub>}}.

In optics, one usually knows the [[refractive index]] {{math|''n''}} of the medium, which is the ratio of the speed of light in vacuum ({{mvar|c}}) to the speed of light in the medium. In the analysis of partial reflection and transmission, one is also interested in the electromagnetic [[wave impedance]] {{mvar|Z}}, which is the ratio of the amplitude of {{math|'''E'''}} to the amplitude of {{math|'''H'''}}. It is therefore desirable to express {{math|''n''}} and {{mvar|Z}} in terms of {{math|''ϵ''}} and {{math|''μ''}}, and thence to relate {{mvar|Z}} to {{math|''n''}}. The last-mentioned relation, however, will make it convenient to derive the reflection coefficients in terms of the wave ''admittance'' {{mvar|Y}}, which is the reciprocal of the wave impedance {{mvar|Z}}.

In the case of ''uniform [[plane wave|plane]] [[sine wave|sinusoidal]]'' waves, the wave impedance or admittance is known as the ''intrinsic'' impedance or admittance of the medium. This case is the one for which the Fresnel coefficients are to be derived.