Optics is the ideal subject for lecture demonstrations. Not only is the output of an optical experiment usually visible (and today, with the aid of closed circuit video, can be projected for the benefit of large audiences), but often the type of idea being put across can be made clear pictorially, without measurement and analysis being required. Recently, several institutes have cashed in on this, and offer for sale video films of optical experiments carried out under ideal conditions, done with equipment considerably better than that available to the average lecturer. Although such films have some place in the lecture room, we firmly believe that students learn far more from seeing real experiments carried out by a live lecturer, with whom they can interact personally, and from whom they can sense the difficulty and limitations of what may otherwise seem to be trivial experiments. Even the lecturer's failure in a demonstration, followed by advice and help from the audience which result in ultimate success, is bound to imprint on the student's memory far more than any video film can do.

The purpose of this appendix is to transmit a few ideas that we have, during the years, found particularly valuable in demonstrating the material covered in this book, and can be prepared with relatively cheap and easily available equipment. Need we say that we also enjoyed developing and performing these experiments?

Most optical systems are used to create images: eyes, cameras, microscopes, telescopes, for example. These image-forming instruments use lenses or mirrors whose properties, in terms of geometrical optics, have already been discussed in Chapter 3. But geometrical optics gives us no idea of any limitations of the capabilities of such instruments and indeed, until the work of Ernst Abbe in 1873, microscopists thought that spatial resolution was only limited by their expertise in grinding and polishing lenses. Abbe showed that the basic scale is the wavelength of light, which now seems obvious. The relationship between geometrical and physical optics is like that between classical and quantum (wave) mechanics; although classical mechanics predicts no basic limitation to measurement accuracy, it arises in quantum mechanics in the form of the Heisenberg uncertainty principle.

This chapter describes the way in which physical optics is used to describe image formation by a single lens (and by extension, any optical system). The theory is based on Fraunhofer diffraction (Chapter 8) and coherence (Chapter 11) and leads naturally both to an understanding of the limits to image quality and to ways of extending them. We shall learn:

• how Abbe described optical imaging in terms of wave interference;

• that imaging can be formulated as a double process of diffraction;

• what are the basic limits to spatial resolution;

• how microscopes are constructed to achieve these limits;

• […]

Why did it take so long for the wave theory of light to be accepted, from its instigation by Huygens in about 1660 to the conclusive demonstrations by Young and Fresnel in 1803–12? In retrospect, it may be that Huygens did not take into account the wavelength; as a result the phenomenon of interference, particularly destructive interference, was missing. Only when Huygens' construction was analyzed in quantitative detail by Young and Fresnel did interference fringes and other wavelength-dependent features appear, and when these were confirmed experimentally the wave theory became generally accepted. It was because the wavelength, as measured by Young, was so much smaller than the size of everyday objects that special experiments had to be devised in order to see the effects of the waves; these are called ‘diffraction’ or ‘interference’ experiments and will be the subject of this chapter. Even so, some everyday objects, such as the drops of water that condense on a car window or the weave of an umbrella, do have dimensions commensurate with the wavelength of light, and the way they diffract light from a distant street light is clearly visible to the unaided eye (Fig. 7.1).

The distinction between the terms diffraction and interference is somewhat fuzzy. We try to use the term diffraction as a general term for all interactions between a wave and an obstacle, with interference as the case where several separable waves are superimposed.

This book is intended to explain the physical basis of classical optics and to introduce the reader to a variety of wave phenomena and their applications. However, it was discovered at the end of the nineteenth century that the description of light in terms of Maxwell's classical electromagnetic waves was incomplete, and the notion of quantization had to be added. Since then, in parallel to the development of wave optics, there has been an explosive growth of quantum optics, much of it fuelled by the invention of the laser at the end of the 1950s, which also provided a great incentive to reconsider many topics of classical optics, such as interference and coherence theory. It would be inappropriate that this book should ignore these developments; on the other hand, the subject of quantum optics is now so wide that a single chapter can do no justice to the field. In this chapter, we therefore set out modestly to explain the way in which quantum optics is different from classical optics, and give a qualitative introduction to lasers, followed by a taste of some of the new phenomena that have developed in recent years and are currently at the forefront of optics research.

In this chapter we shall discuss:

• how the electromagnetic field can be quantized, by creating an analogy between an electromagnetic wave and a simple harmonic oscillator;

• the concept of the photon, and some of its properties;

• […]