4.2
which was already known. He brilliantly concluded that light is an electromagnetic wave.
In the 1880s the German physicist Heinrich Hertz experimentally confirmed that
electromagnetic waves can be generated and have the same speed as light. His work laid
the foundation for radio communication that has shaped the modern world.
The electromagnetic theory can perfectly describe how light propagates. However, it
fails to explain how light is emitted and absorbed by matter. For this purpose, quantum
mechanics is required.
Electromagnetic waves
As shown in Appendix A.2, electromagnetic waves are described by
for the electric field ξ(r, t), where c 0 denotes the speed of light in vacuo and n is the
refractive index of the material. In a similar manner we can derive the wave equation for
the magnetic field ζ,
The simplest solution to the wave equations (4.1) is the plane harmonic wave, where
light of constant wavelength λ propagates in one direction. Without loss of generality, we
assume that the wave travels along the z direction. The electric and magnetic fields in this
case are
where ξ 0 and ζ 0 are constant vectors (the amplitudes), k z is the wave number and ω is
the angular frequency. By substituting Eq. (4.2a) into Eq. (4.1a) we find that k z and ω are
connected to each other via
Thus,
The angular frequency, measured in radians per second is related to the frequency of the
wave ν, measured in hertz, via