Diffuse radiators. Lamberts cosine law

No radiator exists that has a spectral intensity Lx independent of the wave length. However, the assumption that Lx does not depend on j3 and ip applies in many cases as a useful approximation. Bodies with spectral intensities independent of direction, Lx = Lx(X,T), are known as diffuse radiators or as bodies with diffuse radiating surfaces. According to (5.9), for their hemispherical spectral emissive power it follows that 

The double integral here has the value n, so that for diffuse radiating surfaces 

For a diffuse radiating surface, it follows from (5.19) that 

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