For one tiny slit of amplitude A, the intensity is taken to be constant far away, so averaging
over space gives an average intensity of A^2. [This omits any time averaging.]
For two tiny slits far away, each of amplitude A, the combined amplitude is 2 A cos (phi/2)
where phi is the phase difference between the two waves. This varies between 0 and 2A.
When we square this and take the average over space, we find the average to be 1/2
(2A)^2 = 2A. This is the same as the space average of both slits taken separately.
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Mike
Mike Moloney, Dept of Physics & Applied Optics, Rose-Hulman Institute of Technology