What you are seeing is a moiré pattern, which you get when two shiny surfaces come into contact. You get it with plastics and glass, and it's a real problem in reprographics, particularly scanning photographic prints, where it shows as grey patches on the final scan. Transparencies are usually mounted in clear oil, to stop it happening, which is a real PITA to get right, believe me! You can also get a spray that puts microscopic 'beads' on the surface to roughen it, allowing a slight air gap, stopping the moiré rings from happening, which is effectively what crankboy is describing with the baby talc trick.
Every day's a school day, eh?