The first equality in Eq.(C.56) implies that the angle of incidence equals angle of reflection:
We now wish to find the wavenumber in medium 2. Let denote the phase velocity in wave impedance :
In impedance , we have in particular
Solving for gives
Since from above,
We have thus derived
We earlier established (for agreement along the boundary, by pressure continuity). This describes the refraction of the plane wave as it passes through the impedance-change boundary. The refraction angle depends on ratio of phase velocities . This ratio is often called the index of refraction:
and the relation is called Snell's Law (of refraction).