Rock that transfers image
I used F'x answer as a starting point, and I found the mineral. It's called Ulexite.


  The fibers of ulexite act as optical fibers, transmitting light along their lengths by internal reflection. When a piece of ulexite is cut with flat polished faces perpendicular to the orientation of the fibers, a good-quality specimen will display an image of whatever surface is adjacent to its other side (as shown in the photograph).