Electromagnetic Radiation and Its Measurements

How a wave carries a disturbance

A wave transfers a disturbance through space. In electromagnetic radiation, the disturbance involves oscillating electric and magnetic fields. Maxwell’s theory connected these fields and showed how accelerating charges can produce electromagnetic waves. Hertz later confirmed electromagnetic-wave behaviour experimentally.

The electric field and magnetic field oscillate perpendicular to one another and to the direction in which the wave travels. Electromagnetic waves need no material medium: sunlight crosses the near-vacuum between the Sun and Earth. This distinguishes them from sound waves, which require matter to transmit their disturbance.

Different electromagnetic radiations are not fundamentally different kinds of stuff. Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays are different ranges of the same family. What changes is their wavelength and frequency.

Measuring repeating waves

Wavelength, $\lambda$, is the distance between successive points at the same stage of the wave cycle, such as neighbouring crests. Frequency, $\nu$, counts how many complete cycles pass a fixed point per second. Its unit is hertz, $\mathrm{Hz}={\mathrm{s}}^{-1}$. Period, $T$, is the time for one cycle, so a shorter period means a higher frequency.

Amplitude concerns the size of the field oscillation. It must not be confused with wavelength or frequency. In a given medium, changing wavelength does not mean changing how tall the wave is. In the next lesson, we will distinguish light intensity from the energy carried by one photon.

In vacuum, every electromagnetic wave travels at the same speed, approximately $3.00\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$. During one period, one wavelength moves past a point. Speed is therefore the number of wavelengths passing per second multiplied by the length of each wavelength.

Spectroscopy often uses wavenumber, written $\tilde{\nu }$. It is the number of wavelengths that fit into a unit distance, not the number passing in a unit time. Its units are inverse length. Although ${\mathrm{m}}^{-1}$ is the SI form, $\mathrm{c}{\mathrm{m}}^{-1}$ is common in spectroscopy.

Reading the electromagnetic spectrum

Moving from radio waves towards gamma rays, wavelength becomes shorter and frequency becomes larger. Visible light is only a narrow part of the spectrum. Within it, red has longer wavelength and lower frequency than violet. Our eyes cannot detect the surrounding infrared and ultraviolet bands, but appropriate instruments can.

Applications help make these ranges familiar: radio frequencies carry broadcasts, microwaves are used in radar and ovens, infrared is associated with thermal radiation, and ultraviolet is part of sunlight. X-rays penetrate materials and are useful in imaging. These names describe broad ranges; boundaries are conventional and some ranges overlap.

Converting units before calculating

Very small wavelengths are often written in nanometres, picometres, or angstroms. Convert them before substituting into a formula with $c$ in metres per second. The useful relations are $1\mathrm{nm}=10^{-9}\mathrm{m}$, $1\mathrm{pm}=10^{-12}\mathrm{m}$, and $1\mathring{\mathrm{A}}=10^{-10}\mathrm{m}$. A kilohertz is $10^3\mathrm{Hz}$.

Estimate the direction of the answer as well as calculating it. A shorter wavelength should give a larger frequency. If converting a visible wavelength gives a radio frequency, check the powers of ten. This simple physical check catches many arithmetic errors.