The structure of a dipolar fluid in contact with a solid is investigated using the optimized cluster theory. The solid-liquid interaction is described by an effective one-dimensional potential. The model of a perfect impenetrable wall is dropped. An adsorption potential similar to the non-electrostatic potential appearing in the classical models of the double layer is introduced. We show that the effect of a reasonable adsorption potential is localized in the first monolayer in contact with the solid although the total effect of the solid is non localized in this monolayer. No states of orientation predominate in such a way that we can justify a two- or three-state model. The potential drop gs(dip) across the interface and the change in the surface Gibbs energy due to the adsorption potential are calculated. An adsorption potential of magnitude 1kT gives gs(dip) - −0.6 V. In order to obtain the values of gs(dip) generally accepted in the literature, no dielectric constant or clusters should be introduced. Because of the competition between the dipolar interaction and the adsorption potential, an increase of the dipole moment does not necessarily increase gs(dip).