Matrix representations of Maxwell's equations have a striking resemblance to the Dirac equation. We exploit this resemblance to build a beam optics formalism from an exact eight-dimensional matrix representation of the Maxwell equations. The Foldy–Wouthuysen iterative diagonalization technique is employed to obtain a Hamiltonian description for a system with varying refractive index. The beam-optical Hamiltonian is shown to have a wavelength-dependent part, resulting in the wavelength-dependent modifications of light beam optics. The present study is the generalization of the traditional and non-traditional prescription of Helmholtz optics.