At sufficiently high electrolyte concentrations (at suppressed electrostatic repulsion), the free foam films thin gradually, until reaching a certain critical thickness, and then they break. The value of this critical thickness is sensitive to the magnitude of the attractive surface forces acting in the film. We experimentally investigated the rupture of the films formed from aqueous solutions of sodium dodecyl sulfate (SDS) in the presence of 0.3 M NaCl added. The theoretical fits of the data indicate that the van der Waals interaction, alone, is insufficient to explain the measured critical thickness, especially for the lower SDS concentrations. If the difference is attributed to the hydrophobic attraction, then a very good agreement between the theory and experiment is achieved. From the best fit, we determine that the decay length of the hydrophobic force is about 15.8 nm, which coincides with the value obtained by other authors for hydrophobized mica surfaces. The strength of the hydrophobic interaction increases with the decrease of the SDS concentration, which can be explained with the fact that between the adsorbed surfactant molecules greater areas of bare hydrophobic air-water interface are uncovered. In the investigated concentration range, the strength of the hydrophobic force is found to be inversely proportional to the surface density of the adsorbed ions.