There are still some open questions about how the thickness of a liquid or solid quantum film, such as liquid helium or solid hydrogen, develops in certain limits. One of these is the thick-film limit, i.e., the crossover from the thick film to the bulk. We have performed measurements in this range using the surface plasmon resonance technique and an evaporated Ag film deposited on a glass substrate. The thickness of the adsorbed helium film is varied by changing the distance h of the bulk reservoir to the surface of the substrate. In the limiting case when h→0 the film thickness approaches about 100 nm, following the van der Waals law in the retarded regime. The film thickness and its dependence on h is determined precisely and modeled theoretically. The behavior of the equilibrium film thickness is discussed in detail. The agreement between theory and experiment is very good.