Maximizing light absorption at the bottom of a film

Assuming only the conditions for the Lambert Law, and from considerations of inner filter effects, we derive an expression which yields the net fraction of light absorbed by the bottom layer of a film having any optical density and divided into any number of hypothetical layers. We show that there is an optimum total optical density at which absorption by the bottom layer is maximized. The optimum optical density is a function of the thickness of the bottom layer probed. For an infinitesimally thin bottom layer, the optimum total optical density is 0·4343.