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Planck's law of blackbody radiation

Planck's law states that B ν (T) = 2 h ν 3 c 2 1 e h ν / k T − 1, {\displaystyle B_{\nu }(T)={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{h\nu /kT}-1}},} where

For a black body surface, the spectral radiance density (defined per unit of area normal to the propagation) is independent of the angle θ {\displaystyle \theta } of emission with respect to the normal. However, this means that, following Lambert's cosine law, B ν (T) cos θ {\displaystyle B_{\nu }(T)\cos \theta } is the radiance density per unit area of emitting surface as the surface area involved in generating the radiance is increased by a factor 1 / cos θ {\displaystyle 1/\cos \theta } with respect to an area normal to the propagation direction. At oblique angles, the solid angle spans involved do get smaller, resulting in lower aggregate intensities.

The emitted energy flux density or irradiance B ν (T, E) {\displaystyle B_{\nu }(T,E)}, is related to the photon flux density b ν (T, E) {\displaystyle b_{\nu }(T,E)} through B ν (T, E) = E b ν (T, E) {\displaystyle B_{\nu }(T,E)=Eb_{\nu }(T,E)}