24.2

The Electromagnetic Spectrum

An electromagnetic wave, like any periodic wave, has a frequency f and a wavelength that are related to the speed v of the wave by (Equation 16.1). For electromagnetic waves traveling through a vacuum or, to a good approximation, through air, the speed is , so .
As Figure 24-10 shows, electromagnetic waves exist with an enormous range of frequencies, from values less than Hz to greater than Hz. Since all these waves travel through a vacuum at the same speed of m/s, Equation 16.1 can be used to find the correspondingly wide range of wavelengths that the picture also displays. The ordered series of electromagnetic wave frequencies or wavelengths in Figure 24-10 is called the electromagnetic spectrum. Historically, regions of the spectrum have been given names such as radio waves and infrared waves. Although the boundary between adjacent regions is shown as a sharp line in the drawing, the boundary is not so well defined in practice, and the regions often overlap.

Figure 24-10 The electromagnetic spectrum.

Beginning on the left in Figure 24-10, we find radio waves. Lower-frequency radio waves are generally produced by electrical oscillator circuits, while higher-frequency radio waves (called microwaves) are usually generated using electron tubes called klystrons. Infrared radiation, sometimes loosely called heat waves, originates with the vibration and rotation of molecules within a material. Visible light is emitted by hot objects, such as the sun, a burning log, or the filament of an incandescent light bulb, when the temperature is high enough to excite the electrons within an atom. Ultraviolet frequencies can be produced from the discharge of an electric arc. X-rays are produced by the sudden deceleration of high-speed electrons. And, finally, gamma rays are radiation from nuclear decay.
The human body, like any object, radiates infrared radiation, and the amount emitted depends on the temperature of the body. Although infrared radiation cannot be seen by the human eye, it can be detected by sensors. An ear thermometer, like the pyroelectric thermometer shown in Figure 24-11, determines the body’s temperature by measuring the amount of infrared radiation that emanates from the eardrum and surrounding tissue. The ear is one of the best places to measure body temperature because it is close to the hypo-thalamus, an area at the bottom of the brain that controls body temperature. The ear is also not cooled or warmed by eating, drinking, or breathing. When the probe of the thermometer is inserted into the ear canal, infrared radiation travels down the barrel of the probe and strikes the sensor. The absorption of infrared radiation warms the sensor, and, as a result, its electrical conductivity changes. The change in electrical conductivity is measured by an electronic circuit. The output from the circuit is sent to a microprocessor, which calculates the body temperature and displays the result on a digital readout.

Figure 24-11 A pyroelectric thermometer measures body temperature by determining the amount of infrared radiation emitted by the eardrum and surrounding tissue.

The physics of a pyroelectric ear thermometer.

Of all the frequency ranges in the electromagnetic spectrum, the most familiar is that of visible light, although it is the most narrow (see Figure 24-10). Only waves with frequencies between about Hz and Hz are perceived by the human eye as visible light. Usually visible light is discussed in terms of wavelengths (in vacuum) rather than frequencies. As Example 1 indicates, the wavelengths of visible light are extremely small and, therefore, are normally expressed in nanometers (nm); m. An obsolete (non-SI) unit occasionally used for wavelengths is the angstrom (); m.

| Example 1 | | | The Wavelengths of Visible Light

Find the range in wavelengths (in vacuum) for visible light in the frequency range between Hz (red light) and Hz (violet light). Express the answers in nanometers. Reasoning According to Equation 16.1, the wavelength (in vacuum) of a light wave is equal to the speed of light c in a vacuum divided by the frequency f of the wave, .
Solution The wavelength corresponding to a frequency of is

Since , it follows that

The calculation for a frequency of is similar:

The eye/brain recognizes light of different wavelengths as different colors. A wavelength of 750 nm (in vacuum) is approximately the longest wavelength of red light, whereas 380 nm (in vacuum) is approximately the shortest wavelength of violet light. Between these limits are found the other familiar colors, as Figure 24-10 indicates.
The association between color and wavelength in the visible part of the electromagnetic spectrum is well known. The wavelength also plays a central role in governing the behavior and use of electromagnetic waves in all regions of the spectrum. For instance, Conceptual Example 2 considers the influence of the wavelength on diffraction.

| Conceptual Example 2 | | | The Diffraction of AM and FM Radio Waves

As we have seen in Section 17.3, diffraction is the ability of a wave to bend around an obstacle or the edges of an opening. Based on the discussion in that chapter, would you expect AM or FM radio waves to bend more readily around an obstacle such as a building?

The physics of AM and FM radio reception.

Reasoning and Solution Section 17.3 points out that, other things being equal, sound waves exhibit diffraction to a greater extent when the wavelength is longer than when it is shorter. Based on this information, we expect that longer-wavelength electromagnetic waves will bend more readily around obstacles than will shorter-wavelength waves. Figure 24-10 shows that AM radio waves have considerably longer wavelengths than FM waves. Therefore, AM waves have a greater ability to bend around buildings than do FM waves. The inability of FM waves to diffract around obstacles is a major reason why FM stations broadcast their signals essentially in a “line-of-sight” fashion and why FM reception is more degraded by hills and buildings than AM reception is.

The picture of light as a wave is supported by experiments that will be discussed in Chapter 27. However, there are also experiments indicating that light can behave as if it were composed of discrete particles rather than waves. These experiments will be discussed in Chapter 29. Wave theories and particle theories of light have been around for hundreds of years, and it is now widely accepted that light, as well as other electromagnetic radiation, exhibits a dual nature. Either wave-like or particle-like behavior can be observed, depending on the kind of experiment being performed.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.