A set of equations is presented for the reflection and transmission of normally incident radiation by absorbing (metal) films on nonabsorbing backings.
Using these equations, the results of two different methods of calculation of the reflection and transmission coefficients of a thick nonabsorbing plate are shown to be practically identical, both with and without an absorbing (metal) film on one surface of the plate. One of these methods involves the addition of intensities of the multiple reflections from the two surfaces of the plate. The other method is a rigorous calculation involving solution of the boundary condition equations (amplitude addition) for small areas followed by intensity averaging over the whole plate.
In order to calculate optical constants of a metal film on a thick nonabsorbing backing, the much simpler method of intensity addition of internal reflections in the backing may usually be applied.
LOUIS HARRIS, JOHN K. BEASLEY, and ARTHUR L. LOEB, "Reflection and Transmission of Radiation by Metal Films and the Influence of Nonabsorbing Backings," J. Opt. Soc. Am. 41, 604-610 (1951)