A1 Derivations

A.1.1. The Planck function

A blackbody is a theoretical construct that absorbs 100% of the radiation that hits it. Therefore it reflects no radiation and appears perfectly black. It is also a perfect emitter of radiation. Planck showed that the power per unit area, per unit solid angle, per unit wavelength, emitted by a black body is given by:


A5 exp hc

where h is Planck's constant, c is the speed of light, k is Boltzmann's constant and A is the wavelength of the radiation. Figures 2.2 and 2.3 are plots of Ba(T) against wavelength for various T's.

If Ba is integrated over all wavelengths, one obtains the blackbody radiance:

where a = 2n5ki/15h3c2 is the Stefan-Boltzmann constant. The above can be written as an integral over ln A thus:

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