We use the surface forces apparatus to investigate the transmission of a Fabry-Perot interferometer consisting of a thin dye layer (a few nanometers Rhodamine B) adsorbed from solution and sandwiched between two mica sheets of equal thickness. After adding the dye, we consider not only the shift of the resonance wavelength but also the height and width of the transmission peak; thus, we can deduce the cavity parameters. Knowing the cavity parameters at a resonance wavelength, we can calculate the complex dielectric constant of the dye layer with simple approximate formulas, as we demonstrate by comparison to calculations based on the more complete matrix formulation. The absorption spectrum of a few molecular layers was measured, and based on the integrated absorption, the dye concentration in this thin layer was determined. The spectrum shows a pronounced shift compared to monomers in solution, suggesting that many dye molecules at the interface are arranged as dimers. We are now in the, position to investigate the interaction of dye molecules within the surface forces apparatus.