A medium is material through which waves propagate; electromagnetic waves in optics. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. The medium has an intrinsic impedance, given by

$\backslash eta\; =\; \backslash sqrt\{\backslash mu\; \backslash over\; \backslash varepsilon\}$

where $\backslash mu$ is the permeability of the medium and $\backslash varepsilon$ is the permittivity of the medium.

Waves propagate through a medium with velocity $c\_w\; =\; \backslash nu\; \backslash lambda$, where $\backslash nu$ is the frequency and $\backslash lambda$ is the wavelength of the electromagnetic waves. This can also be put in the form

$c\_w\; =\; \{\backslash omega\; \backslash over\; k\}\backslash \; ,$

where $\backslash omega$ is the angular frequency of the wave and $k$ is the wavenumber of the wave. In electrical engineering, the symbol $\backslash beta$, called the phase constant, is often used instead of $k$.

The propagation velocity of electromagnetic waves in free space, i.e. the absence of a medium, is

$c\_w\; =\; \{1\; \backslash over\; \backslash sqrt\{\backslash varepsilon\_0\; \backslash mu\_0\}\}\backslash \; ,$

where $\backslash varepsilon\_0$ is the permittivity of free space

$~\; \backslash mu\_0\; ~$ is the permeability of free space.

See also

---

• Electromagnetic spectrum
• Electromagnetic radiation
• Optics

References

---

Optics | Electric and magnetic fields in matter