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## Lambert's cosine law*See also: Lambertian reflectance*
## Additional recommended knowledgeAn important consequence of Lambert's cosine law is that when a surface is viewed from any angle, it has the same apparent radiance. This means, for example, that to the human eye it has the same apparent brightness (or luminance). It has the same radiance because, although the emitted power from a given area element is reduced by the cosine of the emission angle, the size of the observed area is increased by a corresponding amount, so that while the area element appears the same in reality it has increased by the cosine of the angle and therefore its radiance is the same. For example, in the visible spectrum, the Sun is almost a perfect Lambertian radiator, and as a result the brightness of the Sun is almost the same everywhere on an image of the solar disk even though we see it full-on only in the center of the disk. Also, a black body is a perfect Lambertian radiator. ## Lambertian scatterersWhen an area element is radiating as a result of being illuminated by an external source, the irradiance (energy or photons/time/area) landing on that area element will be proportional to the cosine of the angle between the illuminating source and the normal. A Lambertian scatterer will then scatter this light according to the same cosine law as a Lambertian emitter. This means that although the radiance of the surface depends on the angle from the normal to the illuminating source, it will not depend on the angle from the normal to the observer. For example, if the moon were a Lambertian scatterer, one would expect to see its scattered brightness appreciably diminish towards the terminator due to the increased angle at which sunlight hit the surface. The fact that it does not diminish illustrates that the moon is not a Lambertian scatterer, and in fact tends to scatter more light into the oblique angles than would a Lambertian scatterer. ## Details of equal brightness effectThe situation for a Lambertian surface (emitting or scattering) is illustrated in Figures 1 and 2. For conceptual clarity we will think in terms of photons rather than energy or luminous energy. The wedges in the circle each represent an equal angle It can be seen that the length of each wedge is the product of the diameter of the circle and cos( Figure 2 represents what an observer sees. The observer directly above the area element will be seeing the scene through an aperture of area - photons/(s·cm
^{2}·sr).
The observer at angle - photons/(s·cm
^{2}·sr),
which is the same as the normal observer. |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Lambert's_cosine_law". A list of authors is available in Wikipedia. |