Scattering, reflection, and refraction

If a charged particle interacts with an electromagnetic wave, it experiences a force proportional to the strength of the electric field and thus is forced to change its motion in accordance with the frequency of the electric field wave. In doing so, it becomes a source of electromagnetic radiation of the same frequency, as described in the previous section. The energy for the work done in accelerating the charged particle and emitting this secondary radiation comes from and is lost by the primary wave. This process is called scattering.

Since the energy density of the electromagnetic radiation is proportional to the square of the electric field strength and the field strength is caused by acceleration of a charge, the energy radiated by such a charge oscillator increases with the square of the acceleration. On the other hand, the acceleration of an oscillator depends on the frequency of the back-and-forth oscillation. The acceleration increases with the square of the frequency. This leads to the important result that the electromagnetic energy radiated by an oscillator increases very rapidly—namely, with the square of the square or, as one says, with the fourth power of the frequency. Doubling the frequency thus produces an increase in radiated energy by a factor of 16.

This rapid increase in scattering with the frequency of electromagnetic radiation can be seen on any sunny day: it is the reason the sky is blue and the setting Sun is red. The higher-frequency blue light from the Sun is scattered much more by the atoms and molecules of Earth’s atmosphere than is the lower-frequency red light. Hence, the light of the setting Sun, which passes through a thick layer of atmosphere, has much more red than yellow or blue light, while light scattered from the sky contains much more blue than yellow or red light.

The process of scattering, or reradiating part of the electromagnetic wave by a charge oscillator, is fundamental to understanding the interaction of electromagnetic radiation with solids, liquids, or any matter that contains a very large number of charges and thus an enormous number of charge oscillators. This also explains why a substance that has charge oscillators of certain frequencies absorbs and emits radiation of those frequencies.

When electromagnetic radiation falls on a large collection of individual small charge oscillators, as in a piece of glass or metal or a brick wall, all of these oscillators perform oscillations in unison, following the beat of the electric wave. As a result, all the oscillators emit secondary radiation in unison (or coherently), and the total secondary radiation coming from the solid consists of the sum of all these secondary coherent electromagnetic waves. This sum total yields radiation that is reflected from the surface of the solid and radiation that goes into the solid at a certain angle with respect to the normal of (i.e., a line perpendicular to) the surface. The latter is the refracted radiation that may be attenuated (absorbed) on its way through the solid.

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How Is Light Both a Particle and a Wave?

Superposition and interference

When two electromagnetic waves of the same frequency superpose in space, the resultant electric and magnetic field strength of any point of space and time is the sum of the respective fields of the two waves. When one forms the sum, both the magnitude and the direction of the fields need be considered, which means that they sum like vectors. In the special case when two equally strong waves have their fields in the same direction in space and time (i.e., when they are in phase), the resultant field is twice that of each individual wave. The resultant intensity, being proportional to the square of the field strength, is therefore not two but four times the intensity of each of the two superposing waves.

By contrast, the superposition of a wave that has an electric field in one direction (positive) in space and time with a wave of the same frequency having an electric field in the opposite direction (negative) in space and time leads to cancellation and no resultant wave at all (zero intensity). Two waves of this sort are termed out of phase. The first example, that of in-phase superposition yielding four times the individual intensity, constitutes what is called constructive interference. The second example, that of out-of-phase superposition yielding zero intensity, is destructive interference. Since the resultant field at any point and time is the sum of all individual fields at that point and time, these arguments are easily extended to any number of superposing waves. One finds constructive, destructive, or partial interference for waves having the same frequency and given phase relationships.

Propagation and coherence

Once generated, an electromagnetic wave is self-propagating because a time-varying electric field produces a time-varying magnetic field and vice versa. When an oscillating current in an antenna is switched on for, say, eight minutes, then the beginning of the electromagnetic train reaches the Sun just when the antenna is switched off because it takes a few seconds more than eight minutes for electromagnetic radiation to reach the Sun. This eight-minute wave train, which is as long as the Sun–Earth distance, then continues to travel with the speed of light past the Sun into the space beyond.

Except for radio waves transmitted by antennas that are switched on for many hours, most electromagnetic waves comes in many small pieces. The length and duration of a wave train are called coherence length and coherence time, respectively. Light from the Sun or from a lightbulb comes in many tiny bursts lasting about a millionth of a millionth of a second and having a coherence length of about one centimetre. The discrete radiant energy emitted by an atom as it changes its internal energy can have a coherence length several hundred times longer (one to 10 metres) unless the radiating atom is disturbed by a collision.

The time and space at which the electric and magnetic fields have a maximum value or are zero between the reversal of their directions are different for different wave trains. It is therefore clear that the phenomenon of interference can arise only from the superposition of part of a wave train with itself. This can be accomplished, for instance, with a half-transparent mirror that reflects half the intensity and transmits the other half of each of the billion billion wave trains of a given light source, say, a yellow sodium discharge lamp. One can allow one of these half beams to travel in direction A and the other in direction B, as shown in Figure 4. By reflecting each half beam back, one can then superpose the two half beams and observe the resultant total. If one half beam has to travel a path 1/2 wavelength or 3/2 or 5/2 wavelength longer than the other, then the superposition yields no light at all because the electric and magnetic fields of every half wave train in the two half beams point in opposite directions and their sum is therefore zero. The important point is that cancellation occurs between each half wave train and its mate. This is an example of destructive interference. By adjusting the path lengths A and B such that they are equal or differ by λ, 2λ, 3λ…, the electric and magnetic fields of each half wave train and its mate add when they are superposed. This is constructive interference, and, as a result, one sees strong light.

The interferometer discussed above and represented in Figure 4 was designed by the American physicist Albert A. Michelson in 1880 (while he was studying with Hermann von Helmholtz in Berlin) for the purpose of measuring the effect on the speed of light of the motion of the ether through which light was believed to travel (see below The electromagnetic wave and field concept).

Speed of electromagnetic radiation and the Doppler effect

Electromagnetic radiation—or, in modern terminology, the photons hν—always travels in free space with the universal speed c—i.e., the speed of light. This is actually a very puzzling situation which was first experimentally verified by Michelson and Edward Williams Morley, another American scientist, in 1887. It is the basic axiom of Albert Einstein’s theory of relativity. Although there is no doubt that it is true, the situation is puzzling because it is so different from the behaviour of normal particles—that is to say, for little or not so little pieces of matter. When one chases behind a normal particle (e.g., an airplane) or moves from the opposite direction toward it, one certainly will measure very different speeds of the airplane relative to oneself. One would detect a very low relative speed in the first case and a very high one in the second. Moreover, a bullet shot forward from the airplane and another toward the back would appear to be moving with different speeds relative to oneself. This is not at all the case when one measures the speed of electromagnetic radiation: irrespective of one’s motion or that of the source of the electromagnetic radiation, any measurement by a moving observer will result in the universal speed of light. This must be accepted as a fact of nature.

What happens to pitch or frequency when the source is moving toward the observers or away from them? It has been established from sound waves that the frequency is higher when a sound source is moving toward the observers and lower when it is moving away from them. This is the Doppler effect, named after the Austrian physicist Christian Doppler, who first described the phenomenon in 1842. Doppler predicted that the effect also occurs with electromagnetic radiation and suggested that it be used for measuring the relative speeds of stars. This explains why a characteristic blue light emitted, for example, by an excited helium atom as it changes from a higher to a lower internal energy state no longer appears blue when one looks at this light coming from helium atoms that move very rapidly away from Earth with, say, a galaxy. When the speed of such a galaxy away from Earth is high, the light may appear yellow; if the speed is still higher, it may appear red or even infrared. Hence, the speed of galaxies as well as of stars relative to Earth is measured from the Doppler shift of characteristic atomic radiation energies hν.