It is shown, in a simple manner, that the illumination
E, at a point
P on a plane
C, due to an extended light source
S, of uniform brightness
b, is given by
E=b/2∫cosδdθ, where the integration is to be performed along the entire boundary of
S, δ being the angle, on the side opposite with
S, between the plane
C and the plane determined by the point
P and the line element
ds of the boundary curve of
S, and
dθ being the elementary angle subtended by
ds at
P.
The above relation was rigorously proved by
Z. Yamauti, by means of Stokes' theorem, whereas the present author gives an easy derivation of the same result, without recource to higher mathematics.
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