Microwaves, incident on the metal walls of the
oven, behave similarly to visible light hitting a
silver mirror (e.g. [4]). The microwaves are
absorbed very effectively, since the electric fields
of the waves interact very strongly with the nearly
free electrons of the metal. In a simple model, the
electron behaviour is described as a damped forced
oscillation. These accelerated electrons re-radiate
electromagnetic waves at the same frequency and in phase, hence the microwaves are perfectly
reflected. Macroscopically, this behaviour is
described by the complex dielectric constant ε(ω),
which is the square of the complex refractive index
(ε1 + iε2 = (n1 + in2)2).
The refractive index of many metals gives
reflectivities close to 100% at low frequencies.
The penetration depth of electromagnetic waves
of wavelength λ is given by
δ = λ/4πn2. (1)
For example, for microwaves with λ = 12.2 cm
incident on aluminium, δ ≈ 1.2 μm.
These are similar to skin depths, i.e. the
attenuation depths of alternating currents of
frequency ω in metals. (The relation between skin
depth and refractive index for small frequencies is
discussed, e.g., by Feynman [5].)