Extended versus point light source: where does the difference in the illuminance exist?

Abstract

In this paper we derive and analyse the expressions to find the illuminance from luminous ball, disc and line in the case of general position of the light receiver. We show that one can always replace a luminous ball with a point light source located at its center and having the appropriate luminous intensity. Any luminous disc or line can be considered, with reasonable accuracy (the relative error in the determination of the illuminance is less than $5 \%$ ), as the point light source with anisotropic (cosine) luminous intensity and placed at their center, if the distance to the observation point is approximately four times larger than their characteristic sizes. The issues outlined in this article will be useful for undergraduate students, who study the basics of photometry.