DEVIATION FROM THE LAMBERT LAW IN ULTRATHIN FILMS SUCH AS BLACK SOAP FILMS

A theoretical investigation has been made of the difference in absorba nce between that calculated from the Lambert law and that from thin-la yer optics which fully takes into account the effect of multiple refle ctions on a symmetrical five-layer film such as black soap film, The a bsorbance of a black soap film can be very different from that of a th ick 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 absor bance by a stratified medium due to the presence of an absorbing layer , These equations are appropriate for film thickness on the order of 5 0 nm for incident radiation at 3400 cm(-1) and are accurate to less th an 2.5% error.