26 Opties: The prineiple of Least Time 26-1 Light This is the first of a number of chapters on the subject of electromagnet 26-1 Light 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 26-2 Reflection and refraction different values of a certain quantity which varies. This variable quantity could 26-3 Fermat's principle of least time 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 26-4 Applications of Fer long wavelengths toward shorter ones, we would begin with what are usually called principle adiowaves. Radiowaves are technically available in a wide range of wavelengths, 26-5 a more precise statement of some even longer than those used in regular broadcasts; regular broadcasts bave Fermats principle 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 26-6 How it works 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 all 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 10-8m,or10-2μ. These are“‘soft”x-rays; then there are ordinary x- rays and very hard x-rays; then y-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 equip ment. Under these conditions we can make a rough first approximation by a method called geometrical optics. If, on the other hand, the wavelengths are com parable 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 negligi- bly 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 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 hich 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 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 e shall have to"unlearn"again. But we shall very quickly unlearn it, because we shall almost immediately go on to a more accurate method