Light

R. W. Ditchburn

• Publisher: Dover Publications
• Year: 2013
• ISBN:
  9780486173320
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This classic study, available for the first time in paperback, clearly demonstrates how quantum theory is a natural development of wave theory, and how these two theories, once thought to be irreconcilable, together comprise a single valid theory of light. Aimed at students with an intermediate-level knowledge of physics, the book first offers a historical introduction to the subject, then covers topics such as wave theory, interference, diffraction, Huygens' Principle, Fermat's Principle, and the accuracy of optical measurements.
Additional topics include the velocity of light, relativistic optics, polarized light, electromagnetic theory, and the quantum theory of radiation. The more difficult mathematics has been placed in appendixes, or in separated paragraphs in small type, intended to be omitted on first reading. Examples and/or references follow each chapter to assist the student in absorbing the material and to suggest additional resources.

CHAPTER I

Introduction

1.1. The Scientific Picture.

New experimental data nearly always cause some alteration in scientific theories, but in certain periods of history the changes are very gradual. The new material is assimilated by extending and modifying the theories while leaving unchanged certain fundamental ideas on which all the theories are based. Progress of this kind went on during most of the nineteenth century, but near the end of the century it became impossible to modify the current theories so as to accept the new experimental results. Certain fundamental difficulties affecting the whole basis of physical science were revealed and, in order to overcome these difficulties, it has been necessary to clarify our views concerning the nature and purpose of scientific inquiry. It would not be appropriate to discuss this matter at length in a book on one branch of science. On the other hand, it would be very difficult to give an adequate account of the modern theory of light without some reference to these general considerations. It therefore appears desirable to state, at the outset, the objective which the author has in mind during the development of the theory of light. Later, the reader may be able to judge for himself whether the objective has been attained. He may also decide whether he feels that the objective is satisfactory both from the practical and from the intellectual point of view.

1.2.—The practical scientific worker makes observations with the senses of sight and hearing, and also with scientific instruments which increase the range, delicacy and number of his observations. The theoretical worker accepts these observations as given data which he has to co-ordinate. In order to be able to reason about them, he first collects them into groups. Each group is then organized in a system which exhibits relations between the members of the group. A system of this kind is called a scientific theory. The whole body of scientific theories and the connections between them constitute a scientific picture of the world. In the process of making scientific theories, words like “electron”, “energy”, “organism” are introduced. These words are symbols invented in order to create a language capable of describing the results of observation in a logical and elegant way.

1.3.—The construction of a scientific theory may be compared to the preparation of a weather map at a central meteorological station. A large number of observations of pressure, temperature, etc., are received and recorded, at the appropriate places, on a large chart. When all the data are entered, the meteorologist inserts isobars, etc., and proceeds to make predictions. In discussing the map, he uses terms like “depression” or “cold front”. These terms form a convenient way of summarizing certain aspects of the observations. They help him to think quickly and clearly about the meteorological situation. The weather map is, however, primarily a representation of the observations. The isobars are useful only in so far as they represent the observations. In a similar way, in the theory of light, we use terms like “waves” and “particles” for the description and discussion of the results of experiments. We need to remember that the meaning of these words is derived from the experiments which they describe. We must not attempt to deduce the special properties of light waves or light particles from any preconceived ideas about waves or particles in general. All that we can say about light must be deduced from experimental observation.

1.4.—New scientific theories usually begin by relating new observations to familiar concepts, based upon older observations. For a long time the theory of light was discussed in terms of waves or particles, because it is easy to form mental pictures of waves and particles. Recent advances have forced us to accept the fact that a complete theory of light cannot be expressed in terms of simple analogies of this type. We are, however, able to construct a summary of our observations in mathematical terms. This mathematical theory is precisely defined and enables us to make certain kinds of predictions concerning the probable results of future observations. It is logically consistent within itself. We often find it convenient to “translate” part of this theory into words, but the translation is never quite perfect, though it may frequently be very useful. A wave picture of light furnishes an adequate description of a wide range of observations just as a set of isobars expresses the results of certain meteorological observations. The wave theory is unsuited to describe certain other types of observations and these may be discussed in terms of light particles or “photons”. In a similar way certain types of meteorological observations cannot be described simply by drawing isobars, but can be included in the weather map in other ways. Any attempt to make a complete theory of light in terms of waves or particles must lead to confusion and error. We must admit that the results of our experiments on light are, in some ways, so different from the results of observations on things like waves on water, or moving particles, that analogies break down. They cease to be useful and become a burden. At this point it is necessary to leave the analogies and revert to the mathematical equations. When all this has been said, it still remains true that most people think more readily in terms of words than in terms of equations. We therefore use the analogies as far as possible —like a man who travels as far as possible by train even though he knows that none of the places he wishes to visit lies exactly on the railway line.

1.5.—In the historical development of a subject ideas are gradually introduced in order to include fresh observations within the theoretical description. In the treatment given in a textbook it is often convenient to disregard the historical order and to introduce many of the current ideas as hypotheses to be tested by experiment. The author knows, in advance, that most of the hypotheses which he introduces are going to be “approved” by the experimental results which he subsequently describes. In this way he avoids the necessity of burdening the reader with details of theories which have been found to be unsatisfactory and are now only of historical interest. The formal treatment of the subject, in this book, follows this plan. It begins in Chapter II. In the remainder of the present chapter our object is to consider the theory of light more from the historical point of view and to show how each of the more important types of experimental observation has been incorporated in, and has led to alterations in, the theory of light. A summary of this process is given in fig. 1.6 which will be considered in detail at the end of the chapter. In the course of this review of the progress of the theory of light we also seek to indicate the general relations of the theory of light to other departments of science.

1.6. Light in Relation to Biological Science.

The scientific picture of the world would be seriously incomplete if it did not include an account of the physical and physiological processes by which man makes his observations. The scientific picture must include an account of the link or links between the human brain and the things—atoms, molecules, etc.—whose existence is postulated in order to describe the observations. Historically, it has been recognized from the earliest times that a very important set of our observations involves light and vision. Early theories of light were therefore theories of vision. One school postulated that the eye sends out invisible antennae or sensitive probes and is thus able to feel objects which are too distant to be touched by hands or feet. This theory may be called the “tactile” theory. Another view was that something is emitted by bright objects and that when this thing enters the eye it is able to affect some sensitive part of the eye and so give rise to the sensation of sight. This theory was called the “emission” theory. Both these theories were current among Greek thinkers about 500 B.C.*

1.7.—The tactile theory is inherently simple because it describes the unknown in terms of the known. The more mysterious sense of vision is directly related to the simpler and more obvious sense of touch. The tactile theory has some difficulty in explaining why things can be felt, but not seen, in the dark, and why bodies can be made visible in the dark by heating them. The fact that certain bright bodies are able to make neighbouring bodies visible also receives no obvious explanation.

The tactile theory can include this type of observation by postulating that the visual probes are able to feel only certain kinds of surfaces and then making a series of assumptions that surfaces can be modified under various conditions. When this is done, the simple relation to the sense of touch has been lost. The theory becomes intolerably complicated. These observations are described in a simple and satisfactory way by the emission theory if it be assumed that some bodies emit a radiation to which the eyes are sensitive, and that others are able to reflect or scatter this radiation so that it enters the eye. For these and similar reasons, the emission theory gradually displaced the tactile theory. The process was very slow and it was not until about 1000 A.D. that, under the influence of the Arabian astronomer Alhazen, the tactile theory was finally abandoned.

1.8.—The emission theory being accepted, light may be defined as “visible radiation”, and we may give the following general account of the visual process. Light, being emitted, reflected, or scattered, enters the eye and is focused by the lens of the eye on a surface situated at the back of the eye. This surface is called the retina. It contains a large number of nerve endings. When light falls on one of them, a chemical and physical action takes place. As a result, a series of electrical impulses is sent along an appropriate nerve fibre to the brain.

A complete theory of vision thus involves many sciences. The description of the emission, reflection and scattering of light and of its transmission to the eye is a part of physical science. The description of the structures of the eye, of the optic nerve and of the associated parts of the brain, belongs to the anatomist. The description of the processes by which the eye lives and transmits its messages to the brain is within the science of physiology. The description of the way in which the mind interprets a pattern of visual sensation and relates it to other visual and non-visual experience falls within the domain of psychology. Most of the theory of vision is clearly outside the scope of a book which is primarily concerned with the physical properties of light, though knowledge of some of the non-physical aspects of vision is necessary in order to understand the subject of photometry and the physical specification and measurement of colour.

1.9. Light in Relation to Physical Science.

Although the theory of light started as the study of vision, this is not, to the physicist, the most important part of the subject. He can detect light through its heating effect on a thermopile or through its electrical effect on a photocell. He can also detect it as an agent capable of causing chemical action or through its effect on a photographic plate. To him, light is a form of energy which travels from one place to another. It can interact with matter and can be transformed into thermal, electrical or chemical energy. The physical equations would be incomplete and the energy conservation law would fail if the transfers and transformations of energy due to the action of light were not taken into account. To the physicist the effect of light on the retina is only one example of photo-chemical action.

1.10. Waves or Corpuscles.

If light is a form of energy which can be transferred from one place to another, it is reasonable to seek to describe it by analogy with other methods of transport of energy. Moving bodies possess kinetic energy. This energy accompanies the body in its movement and thus passes from one place to another. Another mechanical mode of transfer of energy is by means of the propagation of waves. This mode is not, in general, accompanied by any bodily movement of the medium. Many physicists of the seventeenth and eighteenth centuries sought to describe light either in terms of moving particles or of waves. To them, these forms of moving energy were sharply differentiated, in that particle energy is highly localized. The kinetic energy of a rifle-bullet travels from one well-defined, small region of space to another, and does not spread during transit. If, however, a wave is started by dropping a stone into a pond, the energy quickly spreads over the...