If I were to take an incoherent light source such as lamp and measured the incom

Question

If I were to take an incoherent light source such as lamp and measured the incoming light at a given point in space some distance from that lamp, surely, the number of light waves at the minimum point on their oscillation and the number of light waves at the maximum point on their oscillation would be equal. And so, would we not expect them to interfere destructively giving a net effect of zero light, or close to zero light? What I am trying to say is if the lamp emits lots of random beams of light won't they all just cancel giving a net effect of zero? Clearly, the lamp still appears bright so where does this logic fall down?

Explanation / Answer

Let's look at that electric field E in the light at some point. It's getting waves from all the different parts of the lamp. So we can treat the total E as the sum of those parts. You're right that there's no particular reason for the E from one part of the lamp to point the same way as that from another part. So sometimes they cancel. If you follow that line of thought carefully, though, you end up with a light intensity that just is the sum of the intensities from all the parts, on average.

How does this work? First, remember that the energy in the beam goes as the square of E. Let's say that E in some spot is the sum of a lot of little parts: E1, E2... where each part is independent of each other. That means they sometimes add up and sometimes cancel. On the average, how big is (E1+ E2)^2 = E1^2+ E2^2+ 2(E1

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