The results of spectral and angle-dependent ellipsometric measurements of r.f. magnetron-sputtered very thin tungsten films (2/8 nm) deposited onto [100] oriented silicon substrates have been reported. Ellipsometric data were taken over the spectral range from 406 to 806 nm. The parameters of the films, namely, film thicknesses and volume fractions for the constituents have been calculated from the ellipsometric data by the best fitting procedure using some three layer and four layer optical models. We have estimated the roughness on the film surfaces and contamination of the films by Si and SiO2 using Maxwell-Garnett and Bruggeman effective medium approximations. The roughness of the films and substrate surfaces have also been measured independently on profilometer. The ellipsometric measurements along with computer data processing will be useful for quality control during the manufacturing of the films, which have applications in soft X-ray optical systems.