Interference with light is understandable because light act as a wave and wave is disturbance or oscillation of medium propagating in space. As they can be represented by vector having phase, they add constructively and destructively. Their dark and bright fringes are result of probability of many particles moving together (disturbing nearby), that is why two wave superimpose at same space because they behave as effect.
This can may be happen to very small particles. The appearnce of quality of fringes depends upon more number of particles at a time. We know that probability gives better result on number of trials or participants. This is evident in interference of electrons, as intensity was low so a bad interference pattern appear. As time pass, number of electrons increases and fringes seen distinctlively.
One thing more, as interference depends upon slit equivalent to wavelength in perpendicular direction, it means that they are not just oscillating in that direction. But their motion, whether photon or electron moves in helical path and their wavelength is size of circle they form. And electric and magnetic field are perpendicular at a point and also perpendicular to motion. But overall magnetic field is in direction of direction of propagation, like tangent, normal and torsional vector behave.