The existence of two populations of BL Lac sources, characterized by different spectral properties and number densities, has been confirmed by the recently obtained complete samples of radio- and X-ray-selected sources. In the framework of relativistic jet models, the different properties of the two populations can be accounted for if the X-ray radiation is less beamed than the radio one. We propose that this can be due to a larger opening angle of the flow velocity in the inner, X-ray-emitting part of a jet of constant bulk Lorentz factor. With these assumptions we compute the expected luminosity functions (LFs) in the radio and X-ray bands for beamed objects deriving from the same parent population but observed at different angles. We apply this formalism to X-ray-selected and radio-selected BL Lac objects, assuming FR I radio galaxies as the parent population. From the available data we derive here the radio LFs of X-ray-selected BL Lac objects and the X-ray LFs of radio-selected BL Lac objects in order to allow a statistically meaningful comparison of the two samples in the same band. We find the average bulk Lorentz factor and the opening angles of the X-ray- and radio-emitting parts of the jet. We conclude that FR I radio galaxies and X-ray- and radio-selected BL Lac objects can be the same phenomenon observed at decreasing angle to the jet axis.
