Lambert's Cosine Law for Lambertian Reflectors states that the radiant intensity $I$ (watts per square meter per steradian) of reflected light as a function of the angle $\theta$ from the normal to the surface of the reflector is $I(\theta)=I\cos\theta$. Because of this law, uniformly-lit diffusely-reflecting planar surfaces (which approximate perfect Lambertian Reflectors) also appear uniformly-lit to an observer, which is to say that the radiant intensity of light reaching the observer from such a planar surface is constant no matter where on the surface the observer looks.
So far so good. There is, however, a deep mystery lurking beneath this simple principle, because it would seem that it would be far more parsimonious for the radiant intensity of light reflected by a Lambertian Reflector to be constant for all $\theta$ (i.e. have no angular dependence) at the "cost" of having the observer perceive an angular dependence to the radiant intensity of light reflected by a uniformly-lit planar Lambertian Reflector. Why is the observer "privileged" in such a manner by Lambert's Cosine Law?
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