Convex and Concave Lenses Ground as a Pair

Rub one glass disc over another with wet grit and both change shape: the one on top goes hollow, the one beneath goes domed, and they stay a perfect fit. Grind both faces of a pair this way and the bottom disc becomes a double-convex lens, the top one a double-concave lens of the same curve. Longer work gives deeper curves and shorter focal lengths. The picture: a double-convex lens held at arm's length shows the scene small and upside down.