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I know this question has been discussed on web forums before, as one can
find by googling. But I'm not very satisfied with the complexity of some of
those discussions.
Assuming you buy my explanation (do you?) here are two follow-on issues:
How does the diameter of the sun affect things?> Well, the angular diameter
of the sun is about 1/2 degree. That will mean each fringe is actually a
set of fringes spread over an angle of about 1/2 degree.
So to avoid
blurring out the fringes, they need to be farther apart than that. That is
why I chose the value of d above that I did: it means fringes spaced by
about (500 nm)/d in rad or about 3 degrees.
Okay, so the sun works. How about using an old-fashioned light bulb? Put it
say r = 1 m away. Then for the same slits we have d^2/r = 1e-10 m, still
plenty good enough. (Use a bulb with a clear envelope and a reasonably
small filament to keep its angular size small.)