Question

why for making good quality mirror only a thin coating of silver outs the back of a plane of glass is needed ?

Answer 1

To reflect the light? You make curved mirrors the same way, for large telescopes for example. There is a thicker shaped glass in front of the silver plated background. The glass bends the light while the silver coat in the back reflects it. In the case of mirror the glass plane in front of the coating is flat.

The coating is thin because of economic reasons. Coating a 1.5m mirror with high quality finish can cost about 1000 Euros. Often aluminum is also used instead of silver for the coating.