Typical problem of photonics and plasmonics is the scattering of a plane wave by objects with different shapes. Particularly, in quantum mechanics, the general method to get an approximate solution of the scattering problem is the Born series. However, it is not directly applicable to electromagnetic problems because the boundary conditions are different. In this paper, we develop an advanced, optics-compliant, Born approximation, which obeys these conditions. A formula for the field scattered on two dielectric cylinders is derived. We test its accuracy by comparison with the numerical calculations.