The light Bloch oscillations in the array of optical waveguides are investigated based on the electrodynamics of continual approach. The array possesses a step-like refractive index profile. Usually, these oscillations are described in a phenomenological manner. However, the parameters entering the phenomenological equations are obtained either from additional numerical simulations or from experiments. The approach proposed here is based on multiple-scattering formalism. This approach allows us to justify the phenomenological description. The phenomenological approach is valid only if the interaction between the waveguides is weak and the nearest neighbor approximation is applicable. To describe the path of light, we calculate the local isofrequency curve. It is shown that the path represents Bloch oscillations. The results obtained are found to correlate with the experiments available.