First, know that backing a natural stone with a reflective foil is
considered cheating these days.
That said, you’ll find the formulae and techniques for making and
setting foils for colored stones in Cellini’s writings on
The Treatises of Benvenuto Cellini on Goldsmithing and Sculpture.
Published by Dover Publications, 1966
While currently out of print there are still used copies floating
around. Try searching Abebooks.com