The "mirror" is just a paper with a shiny side on it. Takes up very little space. I have found lids, or other normal mirrors without a hole in the middle being much less accurate.
In the pic it looks like the old disk drive platter from a 2.5" laptop drive or similar... I've found it to be a VERY good mirror and dirt cheap as those drives go bad quite often and you can probably get a throwaway at the local repair shop or buy a low capacity one for pennies on eBay. If that's paper with a shiny side, can you tell us how you cut it so cleanly and where you got it?
P.S. maybe you updated the picture, but not the comments here?