Mirrors don't flip L/R, they flip Z - optics lesson.

Why does a mirror flip left/right but not up/down. What if the mirror is turned sideways? How does it know? These are some of the discussion questions you could start with. The solution to the puzzle is that the mirror isn't flipping the x-axis, it flips the z-axis.

This model provides a visual aid to help explain this phenomenon. The model is printed as dozens of single-layer thick individual objects that stack together to make a hand. When assembled in the standard order (call it 1,2,3,4) it makes a right hand with a raised R on the back and small embossed R's on the sides. When the same layers are assembled in reverse order (4,3,2,1) it makes a left hand and all the "R's" are backwards.