Q:

Reflected and refracted wave sphased

When we derive refraction and reflection laws for a generical plane wave on a surface, we say that reflected and refracted must be in phase with the incident wave. Why a medium cannot do a sphased reaction beside incident wave? Sorry for my trivial question.

A:

It is possible. Take a look at phase conjugated mirror on Wikipedia.
Also, phase shifts do happen on reflection from flat surfaces -- all the time. It's called the Goos-Hänchen effect. It's just very very small, so that's probably why you ignore it in your derivation.

