The finite electromagnetic vector is achieved by factorizing into a mapping matrix and a Jones vector. The vectorial property can be described by a degree of freedom of the mapping matrix that can be determined by the azimuthal angle of a fixed unit vector with respect to the wave vector. The representation formalism of the reflected and transmitted vector light beams is theoretically developed between the interfaces. The transverse shift, which is correlative with the spin Hall effect, is discussed. The transverse shift of the linearly polarized light beam (σ=0) is zero. The transverse shift of the circularly polarized light beam (σ=±1) is maximum and the left and right circularly polarized light beam is the same.The dependence of transverse shift of the left circularly polarized light beam on the incidence angle is algo analyzed.