Abstract

It is shown that the radiant flux within Stokes’s pile of plates obeys a simple difference equation. By solving this equation it is possible to obtain, for the first time to my knowledge, the flux distribution within finite and infinite piles consisting of either absorbing or nonabsorbing plates. Given these flux equations, which are mainly of theoretical interest and are needed in continuing work, one can immediately obtain the practically useful reflectances, some that were not previously given by Stokes, and the transmittance. The physical significance of an important parameter (Stokes’s b; bs in this paper) was left obscure in Stokes’s treatment but becomes fully transparent in this treatment. In addition, the method described here is capable of solving problems more difficult than those considered by Stokes. For example, the radiant power absorbed per unit area of plate surface can be obtained for any plate in finite or infinite piles. Finally, a new invariant of the pile of plates is found, in addition to that discovered by Stokes. The treatment presented is much simpler and more straightforward than that of Stokes and is offered as a new approach to the pile of plates.

© 1988 Optical Society of America

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