A new representation is developed for the fields excited on a planar dielectric interface by an arbitrarily incident electromagnetic field. The new formulation is obtained by analytically inverting the spatial-domain boundary integral equation (BIE) formulation of the half-space scattering problem. Unlike spectral solution methods, the spatial-domain solution leads to stable BIE formulations of electromagnetic scattering from non-planar dielectric configurations. The resulting equations reduce to stable formulations in the perfectly conducting limit. The forcing terms in the new equations are the tangent plane solutions in the high frequency limit. For these reasons. the new integral formulations are referred to as Fresnel integral equations.