5.4
5.5
As a matter of fact, it had already been discovered in 1879 and 1884 by Jožef Stefan and
Ludwig Boltzmann, respectively, i.e. about twenty years prior to the derivation of Planck’s
law. This law is very important because it tells us that if the temperature of a body (in K)
is doubled, it emits 16 times as much power. Small temperature variations thus have a
large influence on the total emitted power.
Another important property of blackbody radiation is Wien’s displacement law, which
states that the wavelength of maximal radiance is inversely proportional to the
temperature,
Figure 5.4 shows the spectra for three different temperatures. Note the strong increase
in radiance with temperature and also the shift of the maximum to shorter wavelengths.
Wave-particle duality
In Planck’s law, as stated in Eqs. (5.18), the constant h appeared for the first time. Its
product with the frequency, hν = hc/λ has the unit of energy. Planck himself did not see the
implications of h. It was Einstein, who understood in 1905 that Planck’s law actually has
to be interpreted such that light comes in quanta of energy with the size
Nowadays, these quanta are called photons. In terms of classical mechanics we could say
that light shows the behaviour of particles.
On the other hand, we have seen in Chapter 4 that light also shows wave character
which becomes obvious when looking at the propagation of light through space or at
reflection and refraction at a flat interface. It also was discovered that other particles, such
as electrons, show wave-like properties.
This behaviour is called wave-particle duality and is a very intriguing property of
quantum mechanics that was discovered and developed in the first quarter of the twentieth
century. Many discussion were held on how this duality was to be interpreted – but this is
out of the focus of this book. So we will just accept that depending on the situation, light
might behave as a wave or as a particle.
Solar spectra
As we already mentioned in Chapter 3, only photons of appropriate energy can be
5.5
As a matter of fact, it had already been discovered in 1879 and 1884 by Jožef Stefan and
Ludwig Boltzmann, respectively, i.e. about twenty years prior to the derivation of Planck’s
law. This law is very important because it tells us that if the temperature of a body (in K)
is doubled, it emits 16 times as much power. Small temperature variations thus have a
large influence on the total emitted power.
Another important property of blackbody radiation is Wien’s displacement law, which
states that the wavelength of maximal radiance is inversely proportional to the
temperature,
Figure 5.4 shows the spectra for three different temperatures. Note the strong increase
in radiance with temperature and also the shift of the maximum to shorter wavelengths.
Wave-particle duality
In Planck’s law, as stated in Eqs. (5.18), the constant h appeared for the first time. Its
product with the frequency, hν = hc/λ has the unit of energy. Planck himself did not see the
implications of h. It was Einstein, who understood in 1905 that Planck’s law actually has
to be interpreted such that light comes in quanta of energy with the size
Nowadays, these quanta are called photons. In terms of classical mechanics we could say
that light shows the behaviour of particles.
On the other hand, we have seen in Chapter 4 that light also shows wave character
which becomes obvious when looking at the propagation of light through space or at
reflection and refraction at a flat interface. It also was discovered that other particles, such
as electrons, show wave-like properties.
This behaviour is called wave-particle duality and is a very intriguing property of
quantum mechanics that was discovered and developed in the first quarter of the twentieth
century. Many discussion were held on how this duality was to be interpreted – but this is
out of the focus of this book. So we will just accept that depending on the situation, light
might behave as a wave or as a particle.
Solar spectra
As we already mentioned in Chapter 3, only photons of appropriate energy can be