Editing Black body (section)

=== Cavity with a hole ===
A widely used model of a black surface is a small hole in a cavity with walls that are opaque to radiation.<ref name=Siegel/>  Radiation incident on the hole will pass into the cavity, and is very unlikely to be re-emitted if the cavity is large. Lack of any re-emission, means that the hole is behaving like a perfect black surface. The hole is not quite a perfect black surface—in particular, if the wavelength of the incident radiation is greater than the diameter of the hole, part will be reflected.  Similarly, even in perfect thermal equilibrium, the radiation inside a finite-sized cavity will not have an ideal Planck spectrum for wavelengths comparable to or larger than the size of the cavity.<ref name=Zee/>

Suppose the cavity is held at a fixed temperature ''T'' and the radiation trapped inside the enclosure is at [[thermal equilibrium]] with the enclosure. The hole in the enclosure will allow some radiation to escape. If the hole is small, radiation passing in and out of the hole has negligible effect upon the equilibrium of the radiation inside the cavity. This escaping radiation will approximate [[black-body radiation]] that exhibits a distribution in energy characteristic of the temperature ''T'' and does not depend upon the properties of the cavity or the hole, at least for wavelengths smaller than the size of the hole.<ref name=Zee/> See the figure in the Introduction for the [[Frequency spectrum#Light|spectrum]] as a function of the [[Frequency spectrum|frequency]] of the radiation, which is related to the energy of the radiation by the equation ''E'' = ''hf'', with ''E'' = energy, ''h'' = [[Planck constant]], ''f'' = frequency.

At any given time the radiation in the cavity may not be in thermal equilibrium, but [[laws of thermodynamics|the second law of thermodynamics]] states that if left undisturbed it will eventually reach equilibrium,<ref name="Adkins"/> although the time it takes to do so may be very long.<ref name=Batrouni/> Typically, equilibrium is reached by continual absorption and emission of radiation by material in the cavity or its walls.<ref name=Landsberg/><ref name="Planck 1914 44">{{harvnb|Planck|1914|page=44, §52}}</ref><ref>{{harvnb|Loudon|2000}}, Chapter 1</ref><ref>{{harvnb|Mandel|Wolf|1995}}, Chapter 13</ref> Radiation entering the cavity will be "[[H-theorem|thermalized]]" by this mechanism: the energy will be redistributed until the ensemble of photons achieves a [[Planck's law|Planck distribution]]. The time taken for thermalization is much faster with condensed matter present than with rarefied matter such as a dilute gas.  At temperatures below billions of Kelvin, direct [[Euler–Heisenberg Lagrangian|photon–photon interactions]]<ref name=Karplus>Robert Karplus* and Maurice Neuman, "The Scattering of Light by Light", Phys. Rev. 83, 776–784 (1951)</ref> are usually negligible compared to interactions with matter.<ref name=Bergmann/> Photons are an example of an interacting [[boson]] gas,<ref name=boson/> and as described by the [[H-theorem]],<ref name=Tolman/> under very general conditions any interacting boson gas will approach thermal equilibrium.