[whatshisface]

Phillips gave you a good answer, but another good answer is that Maxwell's equations are linear; forbidding any interaction between solutions f and g because if L is a linear operator, L[f+g] must = L[f] + L[g].

[jdbburg]

This is what we are taught in high school / college as the super-position principle

[earthscienceman]

Oooo. Wow. This is a great answer, thanks for explaining it that way.

[acchow]

Where do they teach physics like this? Anywhere?

[whatshisface]

I feel like this would be mentioned in a typical undergraduate wave mechanics course taught in a typical American university, but I have not been to enough undergraduate wave mechanics courses in enough American universities to know, really.