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Hi Silv
I'm no optics expert and and am far from a genius just to put my credentials out there. My assumption would be, referring to your ping pong ball that unless the mirror was the exact inverse curvature as the object being observed complete flattening would not occur given he angle of incidence of the incoming rays from the varied surfaces of the object. Furthermore I would then expect the flat mirror to give the opposite angles of reflection.
I could be completely wrong but that's just my 2 cents
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