Summary:
Maxwell's equations in vacuum
EM-waves travel at speed c = 1/ (εοµο)1/2
E and B self-sustain each other:
produces
B
B
=0
EM-waves travelling inside a material:
The index of refraction
εο ,µο
In vacuum
Inside a material
ε, µ
(gas, liquid, solid)
ε ,µ
Notice
Since
ε > εo , µ>µ
Since
ε = ε(ω ) , µ=µ(ω )
Definition of the
index of refraction
then
v< c
then
v = v(ω)
Electromagnetic waves appear to propagate in
matter with speed v that is smaller than c
while inside the material
waves no necessarily in
phase
This phase difference affects the resultant
wave in such a way that the latter appears to
be travelling at velocity v (v<c)
Incident
wave
Transmitted
wave
The incident wave and the transmitted wave:
- travel at the same speed
- have a phase difference
The phase difference can be calculated by
assuming that light slowed down while
travelling inside the glass plate
EM radiation propagating through
different mediums
The index of refraction changes with
frequency
nA = nA (ω)
ng = ng (ω)
Light dispersion at a air-glass interface