The infrared analysis of thin films on a thick substrate is discussed using the example of plasma-deposited, amorphous, hydrogenated carbon layers (a-C:H) on silicon substrates. The framework for the optical analysis of thin films is presented. The main characteristic of thin film optics is the occurrence of interference effects due to the coherent superposition of light multiply reflected at the various internal and external interfaces of the optical system. These interference effects lead to a sinusoidal variation of the transmitted and reflected intensity. As a consequence, the Lambert-Beer law is not applicable for the determination of the absorption coefficient of thin films. Furthermore, observable changes of the transmission and reflection spectra occur in the vicinity of strong absorption bands due to the Kramers-Kronig relation. For a sound data evaluation these effects have to be included in the analysis. To be able to extract the full information contained in a measured optical thin film spectrum, an experimentally measured spectrum has to be simulated using the full formalism including the Kramers-Kronig relation. Infrared absorption spectra and the resulting k spectra in the range of the CH vibrational bands around 3000 cm-1 are presented for a variety of a-C:H layers. The shape and the total intensity of the peak are quite sensitive to the film structure. Soft, polymerlike hydrocarbon layers are characterized by a well structured, intense IR absorption band, while hard, amorphous, hydrogenated carbon layers exhibit a structureless, broad IR absorption band with relative low intensity. The k spectra of the CH vibrational bands can be considered as fingerprint for the type of a-C:H film.