Wave impedance ($Z=\sqrt{\mu /ϵ}$)

For a plane electromagnetic wave in a homogeneous, linear, lossless, isotropic medium with permittivity $ϵ$ and magnetic permeability $\mu$, the wave impedance relates the field amplitudes by $Z=E/H=\sqrt{\mu /ϵ}$. Its units are ohms. Impedance differences determine the normal-incidence amplitude Fresnel equations, $r=(Z_2-Z_1)/(Z_2+Z_1)$ and $t=2Z_2/(Z_2+Z_1)$, with a common tangential electric-field axis.

The ratio of transmitted to incident normal time-averaged power for a specified wave and interface. Converting a field-amplitude transmission coefficient into power requires the appropriate impedances or flux normalization. For a displacement wave on a string with impedance $Z$, $\mathcal{T}=(Z_2/Z_1)|t{|}^2$; using an electric-field amplitude in electromagnetic waves instead gives the corresponding electromagnetic flux ratio. Amplitude squared alone is sufficient only when the relevant incident and transmitted normalizations agree.

The energy flux carried into a transmitted wave, integrated over the relevant cross section. The power transmission coefficient compares this with incident power. A displacement or field-amplitude transmission coefficient must be converted with the appropriate wave impedances; its squared modulus alone need not be the power fraction. This distinction applies both to electromagnetic waves and transverse string waves.