# 1.5 The Electromagnetic Spectrum

Visible light belongs to a family of waves arranged according to frequency and wavelength along a continuum called the electromagnetic spectrum (Fig. 1-16). Other members of this family include gamma rays, X-rays, infrared waves, and radio waves. Generically, they all are called EM waves because they share the following fundamental properties:

- A monochromatic (single frequency) EM wave consists of electric and magnetic fields that oscillate at the same frequency f.

- The phase velocity of an EM wave propagating in a vacuum is a universal constant given by the velocity of light c, defined earlier by Eq. (1.14).

- In a vacuum, the wavelength λ of an EM wave is related to its oscillation frequency f by

Whereas all monochromatic EM waves share these properties, each is distinguished by its own wavelength λ, or equivalently by its own oscillation frequency f.

# Figure 1-16 The electromagnetic spectrum.

Figure 1 16 Full Alternative Text

The visible part of the EM spectrum shown in Fig. 1-16 covers a very narrow wavelength range extending between λ=0.4 μ m (violet) and λ=0.7 μ m (red). As we move progressively toward shorter wavelengths, we encounter the ultraviolet, X-ray, and gamma-ray bands, each so named because of historical reasons associated with the discovery of waves with those wavelengths. On the other side of the visible spectrum lie the infrared band and then the microwave part of the radio region. Because of the link between λ and f given by Eq. (1.34), each of these spectral ranges may be specified in terms of its wavelength range or its frequency range. In practice, however, a wave is specified in terms of its wavelength λ if λ<1 mm, which encompasses all parts of the EM spectrum except for the radio region, and the wave is specified in terms of its frequency f if λ>1 mm (i.e., in the radio region). A wavelength of 1 mm corresponds to a frequency of 3×10 11 Hz=300 GHz in free space.

The radio spectrum consists of several individual bands, as shown in ‘the chart of Fig. 1-17. Each band covers one decade of the radio spectrum and has a letter designation based on a nomenclature defined by the International Telecommunication Union. Waves of different frequencies have different applications because they are excited by different mechanisms, and the properties of an EM wave propagating in a nonvacuum material may vary considerably from one band to another.

# Figure 1-17 Individual bands of the radio spectrum and their primary allocations in the U.S. [See expandable version on book website: em8e.eecs.umich.edu.]

Individual bands of the radio spectrum and their primary allocations in the U.S. [See expandable version on book website: em8e.eecs.umich.edu.] Source: U.S. Department of Commerce

Figure 1 17 Full Alternative Text

Although no precise definition exists for the extent of the microwave band, it is conventionally regarded to cover the full ranges of the UHF, SHF, and EHF bands. The EHF band is sometimes referred to as the millimeter-wave band because the wavelength range covered by this band extends from 1 mm (300 GHz) to 1 cm (30 GHz).

Concept Question 1-9: What are the three fundamental properties of EM waves?

Concept Question 1-10: What is the range of frequencies covered by the microwave band?

Concept Question 1-11: What is the wavelength range of the visible spectrum? What are some of the applications of the infrared band?