On analysing transparent thin films by angularly scanning light passing through a prism, one finds two characteristic angles theta _A and theta _B where the reflectance is equal for layers of uniform thickness. The first angle is found for a particular sequence of thicknesses and valid for both p- and s-polarization. The second is the well known pseudo-Brewster angle, corresponding to a null Fresnel reflection coefficient at the film-air interface and is valid for p-polarization only. These two angles allow the determination of the dielectric constant and the thickness of the layer. The use of these angles is also discussed in the case of weakly absorbing films and for metals when covered by dielectric overlayers.