Temat 15: What is light?

The nature of light has fascinated explorers of nature since at least the time of he ancient Greeks. The answer appeared in 1848, when Gustav Kirchhoff noted hat the experimental values on both sides of the equation

agreed within measurement errors. This suggested the answer to the question asked two thousand years earlier:
⊳ Light is an electromagnetic wave.
Ten years later, in 1858, Bernhard Riemann* proved mathematically that any electromagnetic wave must propagate with a speed c given by the above equation. Note that the right-hand side contains electric and magnetic quantities, and the left-hand side is an optical quantity.The expression of Kirchhoff and Riemann thus unifies electromagnetism and optics. The modern value for the speed of electromagnetic waves, usually called c from Latin celeritas, is
c = 299 792 458 m/s .
The value for c is an integer number, because the meter is nowadays defined in such a way as to exactly achieve this number.
In 1865, Maxwell summarized all data on electricity and magnetism collected in the 2500 years in his equations. Almost nobody read his papers, because he wrote them using quaternions. The equations were then simplified independently by Heinrich Hertz and Oliver Heaviside.They deduced the original result of Riemann: in the case of empty space, the equations of the electromagnetic potentials can be written as

Experiments in empty space confirm that the phase velocity c is independent of the frequency of the wave.This phase velocity thus characterizes electromagnetic waves, and distinguishes them from all other types of waves in everyday life.


What are electromagnetic waves? To get a clearer idea of electromagnetic waves, we explore their properties. The wave equation for the electromagnetic field is linear in the field; this means that the sum of two allowed situations is itself an allowed situation. Mathematically speaking, any superposition of two solutions is also a solution. We therefore know that electromagnetic waves must show interference, as all linear waves do.

FIGURE 50 The general structure of a plane, monochromatic and linearly polarized electromagnetic wave at a specific instant of time.

Linearity also implies that two waves can cross each other without disturbing each other, and that electromagnetic waves can travel undisturbed across static electromagnetic fields.
Linearity also means that every electromagnetic wave can be described as a superposition of harmonic, or pure sine waves, each of which is described by expression. The simplest possible electromagnetic wave, the harmonic plane wave with linear polarization, is illustrated in Figure 50. Note that for this simplest type of waves, the electric and the magnetic field are in phase. (Can you prove this experimentally and by calculation?) The surfaces formed by all points of maximal field intensity are parallel planes, spaced by (half the) wavelength; these planes move along the direction of the propagation with the phase velocity.
After Riemann and Maxwell predicted the existence of electromagnetic waves, in the years between 1885 and 1889, Heinrich Hertz* discovered and studied them. He fabricated a very simple transmitter and receiver for 2GHz waves, shown in Figure 53. Such waves are still used today: cordless telephones and the last generation of mobile phones work at this frequency – though the transmitters and the receivers look somewhat differently nowadays. Such waves are now also called radio waves, since physicists tend to call all moving force fields radiation, recycling somewhat incorrectly a Greek term that originally meant ‘light emission.’

Today Hertz’s experiment can be repeated in a much simpler way. As shown in Figure 54, a budget of a few euro is sufficient to remotely switch on a light emitting diode with a gas lighter. (After each activation, the coherer has to be gently tapped, in order to get ready for the next activation.) Attaching longer wires as antennas and ground allows this set-up to achieve transmission distances up to 30 m.
Hertz also measured the speed of the waves he produced. In fact, you can also measure the speed at home, with a chocolate bar and a (older) kitchen microwave oven. A microwave oven emits radio waves at 2.5GHz – not far from Hertz’s value. Inside the oven, these waves form standing waves. Just put the chocolate bar (or a piece of cheese) in the oven and switch the power off as soon as melting begins. You will notice that the bar melts at regularly spaced spots. These spots are half a wavelength apart. From the measured wavelength value and the frequency, the speed of light and radio waves simply follows as the product of the two.
If you are not convinced, you can measure the speed directly, by telephoning a friend on another continent, if you can make sure of using a satellite line (choose a low cost provider). There is about half a second additional delay between the end of a sentence and the answer of the friend, compared with normal conversation. In this half second, the signal goes up to the geostationary satellite, down again and returns the same way.
This half second gives a speed of c ≈ 4 ⋅ 36 000 km/0.5 s ≈ 3 ⋅ 105 km/s, which is close to the precise value. Radio amateurs who reflect their signals from the Moon can perform a similar experiment and achieve higher precision.
In summary, electromagnetic waves exist and move with the speed of light.