I'm having trouble understanding the reflectivity and transmissivity (the ratios of energy reflected and transmitted through a boundary separating different media). Since energy is proportional to the square of the field, if you have a superposition of two fields at a point, to obtain the energy density at that place you cannot just sum the energies of the separate fields. You have to sum the fields and then square the total field. So my problem is that to calculate the total energy that enters a patch of boundary, on the media of the incident wave, there are two fields, the incident and the reflected. Yet somehow everywhere I look they separate the energies, as the incident energy and the reflected energies, and then assume that the total energy entering the patch is the sum (incident energy - reflected energy) (with a minus sign because the reflected energy goes away from the patch). I don't understand this. Can someone help me here?