Part 1: Imagine that you have an opaque screen with three horizont...

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Part 1: Imagine that you have an opaque screen with three horizontal 1 very narrow parallel slits in it. The second slit is a center-to-center distance a beneath the first, and the third is a distance 5a/2 beneath the first, (a) Write a complex exponential expression in terms of o for the amplitude of the electric field at some point P at an elevation 0 on a distant screen where 5 - ka sin 0. Prove that - I(0) + 21(0) (cos 8 + cos 38/2 + cos 58/2) 3 9 Verify that at e =0,1(8) = ((0). Part 2: This is an extension of the above problem. Assume that, rather than point sources (oscillators) you have slits with a finite width: the top slit has width b, the one below that has width 2b, and the third one has width b (i.e. the middle slit is twice the width of the other two slits). Integrate over the source plane to find the irradiance pattern for this more realistic case.

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