Intensity and the Double Slit Experiment.

[Sefrez]

In viewing a derivation of the formula describing the intensity of the interfering waves, I noticed how the electric field components were combined - one from slit a, the other from slit b. The intensity is then proportional to the square of this value. But this would mean that two in phase waves of equal magnitude would result in 4 times the intensity of one alone. However, if you had two light sources of intensity I separate from one another and measured the energy per unit of time transferred to A area, shouldn't you only get twice the energy flow when then combining the two sources? Otherwise it seems energy is not conserved. In another way put: E^2 + E^2 ≠(E + E)^2 at which the first case in the derivation uses the latter.

 

[haruspex]

You're overlooking that elsewhere the waves are canceling. When you calculate the total energy it comes out right.

 

[Sefrez]

Yes, I believe I understand this. I guess what confuses me is the "union" of fields. It does't seem as if this thinking could be used under any situation. For example when all waves from two sources are in phase (not speaking as in a double split experiment.) Then all waves would be constructive.