Lambert’s Cosine Law

The radiation power in the direction of the normal vector to the surface dA in a space angle dio (see Fig. 4.31) is

Dcп> = L dA da, (4.210)

Where dA cos # is the projection surface of the opening in the direction concerned. Thus the radiation power is distributed to different directions at a ratio of cos This is the cosine law of Lambert. It is valid for a blackbody and approximately valid for insulating materials, but it cannot be used for bright metal surfaces. Substituting in Eq. (4.211) gives

Dio = d<p sini> d"d — dip d(cosft) (4.212)

And integrating for the radiation intensity to the semispace by a blackbody gives

D<t> = Mm dA = 7rLw dA, (4.213)

Where Mm = 7rLm = trT4.

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