# Light and the Electromagnetic Spectrum—The Basics

Louis Desmarais -September 13, 2013

3.1 The Nature of Light

As we all know, our most important source of visible light is the sun. Those of us who have stayed out in the sunlight on a bright summer's day a little bit too long also know that solar radiation contains damaging ultraviolet radiation. This energy somehow travels across the vacuum of space all the way to earth. But how does it get here? For a long time, many scientists thought that this energy was transmitted through a medium called the ether in a similar way that sound energy transmits through air. It was also proposed that this ether accounted for the finite velocity of light. This idea of an ether was needed to help explain how light energy could travel through the vacuum of space.

In the 1880s, two physicists, A. A. Michelson and E. W. Morley, performed the now famous experiment bearing their names to try to detect this ether. They used the earth itself as the frame of reference to detect its movement through the ether. On the earth, light was reflected back and forth between two mirrors for a total round trip of 22 meters. This design was first done parallel and then perpendicular to the direction of the earth's motion around the sun. To accomplish this, they performed these measurements at different times of the year, when the earth was moving in different directions with respect to the fixed stars. If this ether existed, there should be a relative difference in the speed of light for the two perpendicular directions at different times of the year.

After completing the experiments to detect the ether, Michelson came to the conclusion that it did not exist. No effect of the motion of the earth could be detected, thus the theory of an ether as a medium for the propagation of light had to be abandoned. This result troubled the scientists at the time because it seemed logical to them that some kind of physical medium was required to allow light to travel in the vacuum of space.

If the energy cannot be found in the proposed ether, then where is this energy stored during the transmission of light through a vacuum? In 1864, James Clerk Maxwell made the discovery that light energy is stored in the wave itself in a similar fashion that energy is stored in a water wave. He found that light energy has two components, an electric field and a magnetic field, that propagate together through space. This electromagnetic wave stores its energy in the electric and magnetic fields as described by Maxwell's equations.

Light energy does not need a physical medium such as the ether to propagate through space. Today we know that visible light is only one form of this electromagnetic energy. Maxwell wanted to write down what was known about electricity and magnetism at that time. This prompted him to combine these concepts into four equations known as Maxwell's equations. These equations describe the behavior of electric and magnetic fields in space and time. The first equation was obtained from Faraday's law of induction.

It was Michael Faraday who discovered that a changing magnetic field could produce an electric current. Faraday's experiment consisted of two separate wire windings around a piece of iron. When he placed battery contacts across one of the coils, he noticed a momentary current surge in the other coil. What Faraday witnessed was a changing magnetic field in one coil producing a current in the other coil of wire. Maxwell summarized this result in his first equation:

In this equation, E is the electric field strength, and H is the magnetic field strength, which changes with respect to time. The mathematical operations described in the above equation are the curl of the E field, and the partial derivative of the H field with respect to time. The curl operation can be thought of as a circulation per area. When no rotation is present, no curl exists. In the language of physics, as the angular velocity increases, so does the value of the curl. Since there are three physical dimensions in free space, the curl of E must be taken for all three. A derivative can be thought of as the rate of change of a function with respect to its variable. An example of a derivative is the time rate of change of speed, a description for acceleration. When we specify a partial derivative, as in the above equation, the derivative of the function can have several variables with respect to just one of them. The other variables are treated as constants. In the case of Maxwell's first equation, the partial derivative is taken with respect to time, t. The quantity µ0  in the above equation is the vacuum permeability. Putting these all together, the above equation basically says that a time varying magnetic field will produce an electric field, E. That's exactly what Faraday witnessed.

The second equation was obtained from Ampere's law. It was well known at the time that when a current flow occurred in a wire, magnetic effects were produced near it. This was demonstrated by placing a compass near a wire having a current flow. In this case, it was noticed that one point of the compass was attracted to the wire while the other compass point was repelled. Maxwell summarized this result by using the concept of fields:

In this equation, H is the magnetic field strength, E is the electric field strength. The mathematical operations are the same as described in Maxwell's first equation. You will notice that in this second equation, the curl operation is performed on H, and the partial derivative of E with respect to time is called for. The quantity e0 is the vacuum permittivity.

This equation basically says that a time varying electric field will produce a magnetic field, H. The third and fourth equations were obtained by using Gauss' laws for electricity and magnetism:

The third equation shows how the electric flux density is related to the electric charge density, pv . This flux density will vary with distance from the electric charge or by the number of electrons in a given space.

The fourth equation basically says that there is no such thing as a magnetic charge in nature. If you cut a magnet in half and in half again several times, you will get a smaller and smaller magnet with north and south poles. Magnetic flux lines always form closed loops. Unlike electric field lines, they do not diverge from a point.

Maxwell's first and second equations show a symmetry in nature between the electric and magnetic fields. A changing magnetic field will produce a changing electric field and visa versa. These fields are not independent of each other in the dynamic case. This fact impressed Maxwell, who believed that nature was truly beautiful and elegant. Thus, an important thing to realize from the first two equations is the symmetry involved with the production of the E and H fields of the electromagnetic wave. When all of the mathematical operations are performed as specified in the equations, time varying E and H fields can be described as illustrated in Figure 3.1.

These equations can be used to describe a transverse wave of energy with electric and magnetic field components that are orthogonal to each other as the wave propagates through space at the speed of light. Figure 3.1 gives a description of this wave. A changing electric field, E, traveling in the z direction induces a changing magnetic field, H.