It is shown that the Dirac equation may describe a coupled system of electromagnetic (in the terms of field strengths) and scalar fields. The unitary relationship between the slightly generalized Maxwell equations with gradient-type 4-current and the Dirac equation is found. It is demonstrated that together with spinor symmetry the massless Dirac equation has also Poincare tensor-scalar and vector symmetries. In the considered Maxwell equations an interaction with external potential field, modeling some medium, is introduced. It is shown that the solutions of the Maxwell equations in such medium reconstruct the discrete states and the relativistic spectra of the hydrogen-like atoms. These facts are interpreted as the consequences of the unitary relationship between the Dirac and slightly generalized Maxwell equations. Thus, the electrodynamical aspect of the Dirac equation is demonstrated.