This chapter is devoted to the physical effects and methods that are available to measure electromagnetic flux as a function of its frequency or its wavelength. The content of the present chapter will form the basis for the following chapters, in which the technical realization and the practical use of these methods will be described.

In the literature, the term light is often reserved for radiation at visual or optical wavelengths. However, there exists no qualitative difference between the basic properties of electromagnetic waves of different frequencies. Therefore, in the following text, the shorter term “light” will be used for all types of electromagnetic radiation.

Electromagnetic Radiation

That light is composed of electromagnetic waves has been known since the nineteenth century. Along their paths these waves produce variations of an electric and a magnetic field, which are periodic in time and space. A complete treatment of the theory of electromagnetic waves can be found in the textbooks on electrodynamics and on optics. (For a concise introduction to the subject see, e.g., Chapter 2 of Wilson et al. (2009).) In the present chapter, some of the optical effects and important relations that are essential for practical spectroscopy will be summarized briefly.

Monochromatic Plane Waves

We first consider the special case of a monochromatic (or single-frequency) plane light wave propagating in a nonconducting medium in the positive x direction. Because the electric and magnetic fields are coupled, a light wave can be characterized by either its electric or its magnetic component. In the following text we discuss the electric field only.

With the exception of a few objects that have been successfully identified as sources of highly energetic charged particles or of neutrinos, all our knowledge about the universe outside the inner solar system is based on the analysis of electromagnetic radiation. Some valuable information has been derived by measuring the flux, the time variations, or the polarization of astronomical radiation sources. By far the most important tool for investigating cosmic objects, however, has been the analysis of their energy distributions and of their line spectra. There are obvious reasons for this predominance of spectroscopic methods in modern astronomy. First, spectra contain a particularly large amount of physical information. If properly analyzed, spectra allow us to determine the chemical composition, local physical conditions, kinematics, and presence and strength of local physical fields. Second, apart from the cosmological redshift and the reduced observed total flux of faraway objects, spectra are independent of the distance, making spectroscopy a particularly valuable remote-sensing tool. Finally, there exists a well-developed theory of the formation of continua and line spectra.

The gathering of information on distant objects by means of spectral observations requires several steps. First, suitable instruments must be designed that allow us to measure the spectra of the faint astronomical sources. Then, these instruments must be employed to obtain spectra of optimal quality. Finally, the spectra must be analyzed and physical information on the observed objects must be extracted.

Electromagnetic waves have, as light and radio waves, been recurring examples for many of the phenomena that we have met throughout this book, from reflection and refraction to diffraction and interference, and for many of the technological applications, from antireflection coatings to Doppler radar. Using Maxwell's equations of electromagnetism, we can describe in exquisite detail how each of these processes occurs; and, since in characterizing the wave by the electric field strength E we refer directly to the force that the wave will exert on a static point-like test charge, we can see quite directly the processes by which electromagnetic waves are detected. The accompanying magnetic field, and its effects and detection, require only small steps further; and even the extension of our classical treatment into a quantum-mechanical description proves to be straightforward. The detailed processes by which moving charges give rise to electromagnetic waves, however, prove to hold many subtleties, and to yield some elegant but somewhat startling results.

Our general approach throughout this book has been to determine the characteristics of wave propagation in each case from the physical mechanisms by which a disturbance at one point affects that at its neighbours. This allows us to write and solve a wave equation for the system, and to determine amongst other properties the phase velocity Up of the propagating wave. We showed in Section 1.3, however, that wave propagation can be approached in a different order, and that the propagation of a disturbance from an emitter to an observer or receiver may be regarded as a version of the static interaction between the source and detector when the finite propagation speed is taken into account.

When we revised our Southampton undergraduate programme to draw into a single course the wave phenomena hitherto distributed among optics, electromagnetism, thermal physics, quantum mechanics and solid-state physics, there seemed to be no single text to recommend. This book is an expanded version of the lecture notes that resulted, and its aim, beyond covering wave physics in its own right, is to introduce the common phenomena and analytical methods that are encountered in these individual fields as well as in the disciplines such as oceanography from which we have always drawn a further audience.

There were nonetheless some excellent textbooks for individual aspects. Coulson's classic [15] provides a concise and elegant mathematical introduction; French's once ubiquitous volume [29] is admirable for its clarity and brevity; and Crawford's brilliant and popularly acclaimed approach through everyday examples [16] suffers only from being long out-of-print. Many other texts are highly satisfactory in the areas they cover, and references to their recent editions are included throughout the following chapters.

One privilege for the author of any new volume is to have a new range of scientific and technological examples upon which to draw. Oscillations in the circulations of the oceans have been quite recently recognized; the extraction of power from ocean waves and tides is only now emerging as practical and necessary; the electronic control of holographic arrays has been possible for just a few years; and the quantum mechanics of coherent systems now underpins major research fields and devices that not long ago appeared impossible.