Light
This is the first of a number of chapters on the subject of                         electromagnetic radiation. Light, with which we                         see, is only one small part of a vast spectrum of the same kind of                         thing, the various parts of this spectrum being distinguished by                         different values of a certain quantity which varies. This variable                         quantity could be called the “wavelength.” As it                         varies in the visible spectrum, the light apparently changes color from                         red to violet. If we explore the spectrum systematically, from long                         wavelengths toward shorter ones, we would begin with what are usually                         called radiowaves. Radiowaves are technically available in a wide                         range of wavelengths, some even longer than those used in regular                         broadcasts; regular broadcasts have wavelengths corresponding to about                         $500$ meters. Then there are the so-called “short waves,” i.e., radar                         waves, millimeter waves, and so on. There are no actual boundaries                         between one range of wavelengths and another, because nature did not                         present us with sharp edges. The number associated with a given name for                         the waves are only approximate and, of course, so are the names we give                         to the different ranges. Then, a long way down through the millimeter waves, we come to what we                         call the infrared, and thence to the visible                         spectrum. Then going in the other direction, we get into a region which                         is called the ultraviolet. Where the ultraviolet                         stops, the x-rays begin, but we                         cannot define precisely where this is; it is roughly at $10^{-8}$ m, or                         $10^{-2}$ $\mu$m. These are “soft” x-rays; then there are ordinary                         x-rays and very hard x-rays; then $\gamma$-rays, and so on, for smaller                         and smaller values of this dimension called the wavelength.                          Within this vast range of wavelengths, there are three or more regions                         of approximation which are especially interesting. In one of these, a                         condition exists in which the wavelengths involved are very small                         compared with the dimensions of the equipment available for their                         study; furthermore, the photon energies, using the quantum theory, are                         small compared with the energy sensitivity of the equipment. Under                         these conditions we can make a rough first approximation by a method                         called geometrical optics. If, on the other hand, the                         wavelengths are comparable to the dimensions of the equipment, which is                         difficult to arrange with visible light but easier with radiowaves, and                         if the photon energies are still negligibly small, then a very useful                         approximation can be made by studying the behavior of the waves, still                         disregarding the quantum mechanics. This method is based on the                         classical theory of electromagnetic radiation, which will be                         discussed in a later chapter. Next, if we go to very short wavelengths,                         where we can disregard the wave character but the photons have a very                         large energy compared with the sensitivity of our equipment,                         things get simple again. This is the simple photon picture, which                         we will describe only very roughly. The complete picture, which unifies                         the whole thing into one model, will not be available to us for a long                         time. In this chapter our discussion is limited to the geometrical optics                         region, in which we forget about the wavelength and the photon                         character of the light, which will all be explained in due time. We do                         not even bother to say what the light is, but just find out                         how it behaves on a large scale compared with the dimensions of                         interest. All this must be said in order to emphasize the fact that                         what we are going to talk about is only a very crude approximation;                         this is one of the chapters that we shall have to “unlearn”                         again. But we shall very quickly unlearn it, because we shall almost                         immediately go on to a more accurate method. Although geometrical optics is just an approximation, it is of very                         great importance technically and of great interest historically. We                         shall present this subject more historically than some of the others                         in order to give some idea of the development of a physical theory or                         physical idea. First, light is, of course, familiar to everybody, and has been                         familiar since time immemorial. Now one problem is, by what process do                         we see light? There have been many theories, but it finally                         settled down to one, which is that there is something which enters the                         eye—which bounces off objects into the eye. We have heard that idea                         so long that we accept it, and it is almost impossible for us to                         realize that very intelligent men have proposed contrary                         theories—that something comes out of the eye and feels for the                         object, for example. Some other important observations are that, as                         light goes from one place to another, it goes in straight                             lines, if there is nothing in the way, and that the rays do not seem                         to interfere with one another. That is, light is crisscrossing in all                         directions in the room, but the light that is passing across our line                         of vision does not affect the light that comes to us from some                         object. This was once a most powerful argument against the corpuscular                         theory; it was used by Huygens.                         If light were like a lot of arrows shooting along, how could other                         arrows go through them so easily? Such philosophical arguments are not                         of much weight. One could always say that light is made up of arrows                         which go through each other!