Light Flux Distribution in a Rectangular Parallelepiped and its Simplifying Scale

Interior-lighting is an important branch of illuminating engineering, a branch in which the space under consideration is usually enclosed in a rectangular parallelepiped. A rigorous treatment of the rectangular parallelepiped, however, would involve extremely complicated calculations, and the problem has therefore remained unsolved to this day.

During the past ten years, lighting research has advanced in a striking manner so that today we can calculate light distribution from large sources and can deal theoretically with daylight illumination. Methods have been obtained for the calculation of illumination from large surface sources and of total flux from one surface to another. Furthermore, the basic theory of interreflections has been developed and the interreflection theory for the circular cylinder has been completed. The distribution of flex in a rectangular parallelepiped, however, still remains an unsolved problem.

Observing that the luminous flux distribution in a rectangular parallelepiped is of great practical importance, the author investigated the possibility of expressing the result in simple form. He obtained the simplifying scale described in this paper. Calculations and experiments prove that the use of this simplifying scale allows every rectangular parallelepiped to be replaced by a rectangular parallelepiped with square base (equivalent square room). Thus experiments or calculations need to be made only on square rooms.