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My hypothesis: Reflection of the image isn't the issue ...
plain old distance is what matters.
The deflection of the drumhead isn't very large, so
it is like a telescope mirror with a rather long
focal length. If you look at it up close, you
are so far inside the focal length that the
surface might as well be flat, and small changes
don't matter. But if you observe from a distance
on the order of a focal length, it might well
gather a whole bunch of light and focus it
onto where you are sitting.