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Light and electromagnetic spectrum basics (Part 2)

17 Oct 2013  | Louis Desmarais

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We will be concerned with this phase constant starting with Chapter 5. For simplicity, we will consider this constant to be zero in Example 3.1 below:

Figure 2b: T is the times it takes the wave to make one complete cycle. The frequency of oscillation is 1/T = v.

Figure 3: This travelling wave moves with velocity v for time t. The distance travelled is vt.

The electric and magnetic field vectors are always perpendicular to the direction in which the wave travels and to each other. The E field vector lies in the yz plane and the magnetic field vector lies in the xz plane. The value of E depends upon z and t. As you can see from figure 1 of part 1, the E and H fields are in phase with each other at any particular point through which the wave moves. They reach maximum and minimum values at the same instant in time. The spatial pattern that these waves make when they travel through space can be described by Maxwell's equations.

A very important result obtained from Maxwell's equations is the speed of light itself. By using these equations, the following relationship can be worked out:

In this equation, u,0 and e0 are the same constants used in Maxwell's first two equations. Notice that the above relationship does not depend upon the wavelength of the electromagnetic wave but only on the two constants. This shows that the speed of light, c, relates to the electric and magnetic field components of the electromagnetic wave. These quantities, |^o and Eg, did not exist in Maxwell's day but he did however see a relationship between the speed of light and these two fields.

Up to now in our discussion, we have described light as a wave phenomenon. We used Maxwell's equations to help describe the propagation of light. This description treats light as a wave phenomenon. But this description turns out to be incomplete. By the beginning of the twentieth century, evidence began to appear that suggested light also has a particle-like nature. When the interaction of light and matter was considered by scientists at that time, this particle-like property of light could not be explained using classical wave theory.

Eventually, the quantum theory of light was first put forth by Max Planck, Albert Einstein, and Neils Bohr during the first two decades of the twentieth century. The acceptance of this theory occurred as a result of experiments with the interaction of light and matter. Neither a separate wave theory nor a particle theory of light could explain the observations.

According to the quantum theory of light, the electromagnetic energy is quantised. This means that energy can be added or taken from the electromagnetic field by discrete amounts called photons during this interaction. Each photon has a specified energy and momentum. When Maxwell's theory and the quantum theory were combined, the study of quantum electrodynamics began.

The modem view of light describes it as having a dual nature. Interference and diffraction effects support the wave-like nature, while the photoelectric effect supports the particle-like nature. There can be no simple description of light because no macroscopic model exists that can be used to explain this wave-particle duality. This wave-particle duality of light will be discussed later in this series.
Excerpted with permission from Pearson Publishing, Chapter 3, Light and the Electromagnetic Spectrum from Applied Electro Optics by Louis Desmarais.

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