The radiation patterns of electric and magnetic line sources placed near the truncation of a semi-infinite grounded dielectric layer structure have been investigated. Two polarizations (parallel and normal to the edge) have been considered for both sources. In order to perform the analysis a new formulation is proposed for the aperture integral equations derived from the principle of equivalence. The novelty of this formulation is that it involves only the fringe components of the magnetic current. The total magnetic current flowing on the aperture is expressed in terms of the physical optics (PO) current and the fringe current. Although the PO current is not known analytically, we can calculate the field excited by this current using the relationship between the surface magnetic PO current on the aperture and the electric polarization PO current in the grounded dielectric slab. The latter PO current is approximated analytically by the expansion wave concept. This step opens a simple and effective way to calculate the right part of the integral equations and as a consequence the radiation pattern of the line sources. For comparison reasons the problem is solved also by using the method of Physical Optics and the Uniform Theory of Diffraction.