Deviation from the Lambert Law in Ultrathin Films Such as Black Soap Films

Abstract

A theoretical investigation has been made of the difference in absorbance between that calculated from the Lambert law and that from thin-layer optics which fully takes into account the effect of multiple reflections on a symmetrical five-layer film such as black soap film. The absorbance of a black soap film can be very different from that of a thick film because of interference effects. The error involved may be as large as 25%. In addition, for both three-layer and symmetrical five-layer films, general approximate equations are presented for the absorbance by a stratified medium due to the presence of an absorbing layer. These equations are appropriate for film thickness on the order of 50 nm for incident radiation at 3400 cm⁻¹ and are accurate to less than 2.5% error.