Download 158 The components of light

158 The components of light
Subject
One often says that white light consists of components with different
wavelengths or frequencies:
„White light consists of a mixture of all wavelengths of light.“
„Why does white light consist of many different wavelengths?“
„Dispersion is the separation of white light into its constituent colors.“
„Light consists of photons; a photon has a well-defined wavelength; light consists of contributions of different wavelengths.“
Deficiencies
We prescind form solecisms like „white light consists of different
wavelengths“ or „white light consists of different colors“, i.e. formulations that must hurt everybody who is accustomed to conceptual
clearness. The subject had been discussed in our article Nr. 144.
Light can be described in various ways. In other words, there exist
various theories of the light: geometrical optics, who deals with optical imaging, nonimaging optics who is mainly about energy flow
distributions in light fields, wave optics, which is essentially an electromagnetic description, the thermodynamical description of light,
which is important for instance for determining the efficiency of solar cells, and finally quantum optics. Non of these theories is incorrect – of course not. Nor can it be said that one of them is better
than the other. Which theory one chooses only depends on the kind
of problem one wants to solve. In the following we limit ourselves on that descriptions which are
important in school: wave optics and the thermodynamics of light. Let us come back to our quotes, which can be considered as typical statements about the light: According to them light consists of
components of various wavelengths. However, light does not consist of sine components, if the wording
„consist of“ is understood in the meaning of the colloquial language. „Consist of“ means: the components of an object are contained within the object and can be recognized in it. Instead of
„consist of“ one should better say: „can be decomposed in“ (contributions of different wavelengths). Actually, the light can be decomposed not only in sine contributions. There are many other possible decompositions. Would we say, that the waves at the surface of the sea consist of
waves of different wavelengths? If somebody would say so, probably we would spontaneously object: But you see that these are not
sine waves – until we remember that the chaotic movement of the
water of the sea can be Fourier decomposed just as the light of the
sun. There is reason to fear that in the mind of our pupils we create an
idea about the light that corresponds to Fig. 1, where the wave
trains may possibly be identified with the photons. (Perhaps one
says that a photon has a well-defined wavelength, see our forth
quote. In this case the photon should be of infinite length. At the
same time one suggests that the photon is not very long, but rather
point-like, and one says nothing about its width.) Fig. 1. Constituents of the light? Photons?
It would be more appropriate to begin the description of the state of
the electromagnetic field that we call sunlight without reference to
the Fourier decomposition: the field is in a state of maximum disorder, or maximum entropy. One can also say, in a state of maximum
washing out in phase space with maximum incoherence. The time
dependence of the amount of the field strength looks roughly like
Fig. 2. Fig. 2. White light: Field strength at a given point as a function of time
As a physicist one tends to consider this field as ugly. In communications engineering one would call such a time function noise, and
noise is a phenomenon that is preferably to be avoided or eliminated. Isn’t it true that a monochromatic plane wave is best for experimenting? Also the mathematical description of the monochromatic
wave is much simpler than that of the chaotic white light, isn’t it? Not
necessarily. The chaotic or „thermal“ light is the most simple according to another criterion. It can be described by means of only two
variables: its temperature and its chemical potential. And in most of
the situations one is interested in the chemical potential is zero.
Thus, what from one point of view appears as a maximum of complexity, is from another one particularly simple. Philosophers of science describe this simplicity that grows out of complexity as emergence.
Origin
In the first place the prism: If behind it light of the various colors
come out, the conclusion appears obvious, that these contributions
had been the constituents of the light that entered the prism. A similar flippancy in the use of the „consists of“ can be observed in other
contexts, for example in atomic physics: It is sometimes said that the
electronic shell of an atom consists of certain, well-defined orbitals.
However, the shell can also be decomposed is a different way, and
this is indeed done, when it is convenient. These parts or contributions is then given the somewhat daunting name hybrid orbitals. To
the student it appears as something that is fundamentally new, and
that is hard to understand, maybe even as a sleight of hand. Actually, the entire atomic-shell-cake has simply been divided in pieces of
another shape.
It may be that yet another factor contributes to the idea, that white
light consists of sine waves. The statement „Light is an electromagnetic wave“ is not incorrect in the sense of physics. However, in our
colloquial language by a wave we understand a periodic phenomenon. A function like that of Fig. 2 would not be called a wave.
Disposal
Carefulness with our wording. Make clear that the spectral decomposition is only one among many others.
Do not introduce the sine waves as the real nature of light. Do also
show images of non-sine light distributions.
And finally: A little thermodynamics is not harmful.
[1] F. Herrmann: Historical burdens on physics, 43, The field of permanent magnets
[2] F. Herrmann: Historical burdens on physics, 60. Inductivity
[3] A. Sommerfeld: Elektrodynamik, 4. Auflage, Akademische Verlagsgesellschaft Geest & Portig, Leipzig, 1964, Vorwort, S. VI