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Reflection and Refraction
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).
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