Background Spinors are more special objects than tensor. Therefore possess more properties than the more generic objects such as tensors. Group of Lorentz two-spinors is the covering group of the Lorentz group. Purpose Since the Lorentz group is a symmetry group of Maxwell’s equations, it is assumed to reasonable to use when writing the Maxwell equations Lorentz two-spinors and not tensors. Method We write the Maxwell equations using Lorentz two-spinors. Also used a convenient representation of Lorentz two-spinors in terms of the Riemann- Silberstein’s complex vectors. Results In the spinor formalism (in the representation of the Lorentz spinors and Riemann-Silberstein’s vectors) we have constructed the Hamiltonian of Maxwellian optics. With the use of spinors Maxwell’s equations take the form similar to the Dirac equation. Conclusions For Maxwell’s equations in the Dirac-like form we can expand re- search methods at the expense of the methods of quantum field theory. In this form, clearly visible the connection between the Hamiltonians of geometric, beam and Maxwellian optics.