Corpuscular description of the speed of light in a homogeneous medium

We are used to describe the detection of light in terms of particles and its propagation from the source to the detection, by waves. For instance, the slowing down of light in a transparent medium is always explained within the electromagnetic wave framework. We propose to approach that phenomenon through a purely corpuscular description. We find expression for the refractive indices which differ slightly from the usual Maxwell wave approach. We thus compare these expressions against experimental refractive indices and we show that both reproduce well the data. We show also how this corpuscular framework gives a very natural interpretation to the self focusing Kerr effect. Finally an experimental expectation of fluctuation of the speed of light is presented.