Editing Wave impedance (section)

== Definition ==
[[File:Impedance mismatch due to absorption.gif|300px|thumb|right|alt=Impedance mismatch leads to reflections.|To avoid reflections, the impedance of two media must match. On the other hand, even if the real part of the refractive index is the same, but one has a large absorption coefficient, the impedance mismatch will make the interface highly reflective.]]
The wave impedance is given by
: <math>Z = {E_0^-(x) \over H_0^-(x)}</math>
where <math>E_0^-(x)</math> is the electric field and <math>H_0^-(x)</math> is the magnetic field, in [[phasor]] representation. The impedance is, in general, a [[complex number]].

In terms of the parameters of an electromagnetic wave and the medium it travels through, the wave impedance is given by
: <math>Z = \sqrt {j \omega \mu \over \sigma + j \omega \varepsilon} </math>
where ''μ'' is the [[magnetic permeability]], ''ε'' is the (real) [[permittivity|electric permittivity]] and ''σ'' is the [[electrical conductivity]] of the material the wave is travelling through (corresponding to the imaginary component of the permittivity multiplied by omega). In the equation, ''j'' is the [[imaginary unit]], and ''ω'' is the [[angular frequency]] of the wave. Just as for [[electrical impedance]], the impedance is a function of frequency. In the case of an ideal [[dielectric]] (where the conductivity is zero), the equation reduces to the real number
: <math>Z = \sqrt {\mu \over \varepsilon }.</math>