Fundamental Concept
Light and other Electromagnetic Waves have dual character, i.e. they show properties of both matter and waves. Young's Double Slit Experiment is a proof of the Wave Nature of Light while The Photoelectric Effect proves the partical Nature of Light.
The basic logic as I understand it is that, when particles meet at a point, they collide. When two waves meet at a point they interfere. It is like drawing two graphs on the same graph paper and then getting the resultant.
If two waves interfere at a point, then there Amplitudes are related as :
Anet = A1 + A2