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. The issue is how come one can do two-slit interference
with sunlight (even without passing it through a pinhole first)? See for
example the Veritasium video https://www.youtube.com/watch?v=Iuv6hY6zsd0
although I note that use of a color filter at the slits would presumably
have avoided the color separation.
Here is my back-of-envelope explanation:
Distance to sun = r = 1e11 m (to 1 sigfig), and separation between the two
slits is say d = 1e-5 m. Then the extra distance sunlight *starting from a
single point on the sun* has to travel to get to one slit compared to the
other is approximately d^2/r = 1e-22 m. Assuming a coherence length for
white light of at least a few wavelengths around 500 nm, we thus get an
interference pattern.
(I'm thinking of the coherence length as meaning the point on the sun emits
a "burst" of light that is at least a few optical cycles in duration.)
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.)