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The Principles of Physical Optics
An Historical and Philosophical Treatment
By Ernst Mach, John S. Anderson, A.F.A. Young
Dover Publications, Inc.Copyright © 2003 Dover Publications, Inc.
All rights reserved.
1. BRIGHTNESS, darkness, light, and colour cannot be described. These sensations, experienced by people with normal sight, can only be named, that is, designated by means of a generally recognized arbitrary convention or one that suggests itself naturally.
A piece of copper, which in a dark room can only be felt, can also be seen, though of course only by a non-defective, open, eye directed towards it, in sunlight, in the neighbourhood of a burning lamp, or, if it is heated until it glows, in a dark room.
The appearance of the feature red in copper, therefore, depends on the concurrence of a variety of conditions which, for the sake of convenience and uniformity, are classified as physical and physiological.
The colour red can also appear under quite different physical conditions and on other objects, also when a galvanic current is passed through the eye, or when pressure is exerted on the eye, and, indeed, at times, without any external stimulus or presence of a body other than the organ of sight, as an hallucination (both in dreams and when awake).
Red can therefore be regarded as the terminal link of a chain of interrelated circumstances. The appearance of red presupposes as a rule, but not always nor necessarily, the existence of the whole chain.
With particular reference to the way in which the feature (red), which differentiates the visible from the merely tangible body, depends on the last (physiological) links of the chain, we call it a light- sensation.
The object which to us appears red can also be seen by others. It also brings about physical changes in its surroundings (see below). Presupposing the physiological conditions to be given as invariable, we may now regard the red also as a (physical) feature of the behaviour of the object in relation to other objects, or to the eye, etc. With respect to another object, for example, the red object exerts a reflex action.
A piece of chalk is white in the presence of a bright white flame, and yellow when near a sodium flame. The white and the yellow are in this case a physical feature of the behaviour of the flame, the feature determining the white or yellow of the chalk. The chalk and the flame which previously appeared white also, however, appear yellow when we take a dose of santonin. In this case we regard the yellow which we see, but others do not see, as determined physiologically by a condition appertaining to the more limited sensory complex of the body. Thus the same elements which we observe—white, yellow, red, etc.—are, according to circumstances, sometimes physical, sometimes physiological, sometimes features of bodies and of their behaviour towards other bodies, and sometimes sensations.
2. The sum total of the occurrences observable in common by all people with normal sight we shall call physical optical data (Tatsachen). When investigating these, we pay no attention to the conditions present in the organ as being known, invariable, and given, but examine the relations of the occurrences among themselves. If, conversely, we pay attention to the dependence of the occurrences as observed by individuals on the conditions in their organs, we enter the field of physiological optical data. The circumstance that the distinction between these two lines of investigation has not always been sufficiently realized has often led to great confusion; it has, for example, led such distinguished men as Goethe and Schopenhauer to ideas which were quite one-sided.
Moreover, it is obvious that in physical optical investigations a knowledge of the organ of vision is as useful as a knowledge of physical optical data is in physiological optical researches. In this book, therefore, the connexion between the two classes of data cannot be quite ignored, although the physical data form the particular object of our investigation.
3. The data of physical optics exhibit certain general and permanent characteristic properties, gradually elucidated during the historical development of optics, which correlate the data and draw attention to their points of similarity. We shall now give a resume of these properties.
Certain objects, such as the sun, a flame, or glowing iron, are observed to be visible in themselves, whilst others, such as a piece of chalk, wood, (cold) copper, are visible only in the presence of the former. We call the first class of objects self-luminous, or, for short, luminous, the second class, dark. A dark body, then, becomes luminous in the neighbourhood of a luminous one, just as a piece of iron assumes magnetic properties in the neighbourhood of a magnet, or as a cold object is warmed by a hot one. The illuminated object can again illuminate a third (in itself dark) object by reflected light, and so on. We call the sum total of the physical relations between one object and another, determined by the feature of the visibility of the first object, the condition of illumination. The mechanism imagined to be involved, conditioned by the first object, is designated briefly as light. reference books (see below).
4. When the sun illuminates a misty atmosphere through a rift in the clouds, or shines over a roof into a dusty or smoky street, or through a hole in a window shutter into the dusty air of a dark room, the rectilinear nature of the rays is so obvious as not to escape the most casual observation. The phenomenon may be grasped more accurately as follows. If an extensive, opaque screen S containing an aperture O is placed between a luminous object A and a dark object B, then B can be illuminated by A only at points which lie on the line AO produced. A, B, and the cross-section of the aperture can be made very small without affecting the nature of the effect. Disregarding the spreading that takes place, the ray ultimately becomes a geometrical straight line and it is this ideal ray with which geometrical optics is concerned. The rectilinear property of the rays was well known to Euclid (300 B.C.), who made it the basis of a number of laws of perspective, which, however, he was unable to systematize.
5. When the line of dust particles, illuminated by light passing through a small hole in the window shutter of a dark room, is examined, another property of the ray, apart from its rectilinearity, reveals itself. Let O be the small hole and B an illuminated object lying in the dark room. If an opaque object C is introduced in the path of the ray between O and B, the dust particles in the portion CB become invisible, but not those in the portion OC. Thus the physical state of the portions of the ray nearer to O conditions the reappearance of the same state in portions of the ray farther from O, but the contrary is not the case. Here the one-sidedness (polarity in the Maxwellian sense) manifests itself also as a continuous connexion (continuity) between the states at the different points of a ray. Wrong or inaccurate conceptions of this relation are allied to those mentioned above (footnote, p. 2).
6. Direct observation shows that a dark object becomes illuminated immediately a neighbouring self-luminous object is uncovered. Thus not only does the latter determine the illumination of the former, but also the conveyance of the attribute requires apparently no time. Objections to such a conception must appear on carefully considering even the data previously mentioned. Galileo conjectured that the propagation of the process of illumination has a very great velocity, but Römer (1644-1676) was the first to prove that the propagation of light from luminous objects is a function of time, and to measure its velocity. By this means the polarity and continuity of the ray as portrayed above could now receive a more exact definition, and the disclosure really gives us for the first time a full right to speak of light processes. Subsequent observers introduced the view that the velocity of propagation depends on the medium and on the colour of the light.
7. The undisturbed rectilinear propagation of light takes place only in a Physically homogeneous transparent medium. At the boundary of two different media a ray undergoes division and deflection, giving rise to what are known as reflection and refraction. The equality of the angles of incidence and reflection was known to Euclid, who utilized this knowledge as the basis of a number of catopric laws which, however, are partly defective. Hero expressed the law of reflection in an elegant mathematical form.
Although refraction was already known to Euclid (300 B.C.), Descartes (1596-1650) was the first to give the correct quantitative form of the law of refraction. He held that, for a given pair of media, the ratio sin α/sinβ = μ, the refractive index, is constant, where α, β denote the angles of incidence and refraction respectively.
There is another case in which light does not follow a simple rectilinear motion, namely, when it passes the edges of objects or through small slits. This is the phenomenon of diffraction, which was discovered by Grimaldi, and further investigated by Hooke, Newton, and others.
8. The colour effects which are associated with refraction have caused considerable difficulty. So long as it was thought that, for a given pair of media, the value of sin α/sin β, or the index of refraction, was the same for every colour, attempts at an explanation of the phenomenon were unsuccessful. Such nearly always took the form of a representation of the colours as mixtures of light and darkness.
Descartes endeavoured to picture colour as analogous to musical tone. Marcus Marci (1595-1667) was of the opinion that the colours originate in refraction, and that the degree of refraction determines the colour. Grimaldi (1613-1663) held that light possibly consisted of a combination of coloured components. Newton (1642-1727) was the first to demolish all these vague conjectures, and as the result of his work the science of optics made a great advance. He showed (1666) that a great number of hitherto unintelligible facts immediately become explicable, if it is assumed that there is an infinite number of kinds of light, different in colour, to which, for a given pair of media, there correspond as many different refractive indices. Colour and refractive index are interdependent.
9. Newton, however, advanced an important step farther than this in that he recognized the periodicity of light. The ground was prepared beforehand by Grimaldi, who, on observing the fringes in the shadow of a hair, was led to the idea that light depends upon a kind of wave motion. Newton observed the colours of very thin layers of air, and from the periodic variation of colour and brightness with continuously increasing thickness of layer elucidated the periodic nature of light. Considering it in conjunction with Römer's discovery, the periodicity must necessarily be regarded as relevant to space and time. The lengths of the periods, and their dependence on the colour and the refractive index, and therefore also on the medium, were determined by Newton. The ray, which had hitherto been regarded as uniformly constituted throughout, thus presented quite a number of new properties.
What Newton had overlooked, namely, that the colour phenomena referred to only occur when two rays combine, was discovered by Thomas Young. In his principle of interference the periodic properties of the rays are regarded as positive and negative magnitudes capable of algebraic summation. For the view that the periodicity of light is not perfectly regular (as in the case of a vibrating tuning-fork), but is subject to frequent disturbances, we are indebted principally to Fresnel.
10. Newton prepared the way for another great advance by recognizing that rays of light may exhibit different properties in different directions, that is, polarization. Huygens became acquainted with the phenomena in question in his observations on calcite, but was unable to give a complete explanation. A further study of them was first prosecuted by Malus, to whom new aspects presented themselves. Finally, Fresnel 15 recognized an analogy between the periodic properties of a ray of light and geometrically additive distances in a two-dimensional space (a plane at right angles to the ray), and also the dependence of the properties on the direction in the (anisotropic) medium.
II. The fundamentals of physical optics may therefore be summarized as follows :—
(a) In a physically homogeneous space, light from a luminous object proceeds outwards in straight lines with a definite velocity (depending on the medium).
(b) At the boundary between two regions of space which are differently filled, reflection and refraction take place.
(c) For a given pair of media, the index of refraction is different for each colour.
(d) When light passes the edges of objects or through narrow slits, diffraction (i.e. a considerable deviation from rectilinear propagation) takes place.
(e) Light exhibits a periodicity in space and time (subject, however, to frequent disturbances). For a given medium, the length of the period depends on the colour.
(f) The periodic properties of a ray of light are representable geometrically only by distances drawn perpendicular to its direction.
These six propositions comprise properties exhibited by every physical optical phenomenon. Having once recognized them in one particular case, we find that they may be readily detected under different combinations, arrangements, and degrees of conspicuity in any other, so that the latter case appears to comprise something at least partially known and familiar. The rectilinear propagation of light is apparent with every shadow, and in each case of perspective, as something already known; periodicity follows as a consequence of every interference experiment and, once acknowledged, enables us to understand any of the similar cases. The establishment of such general properties helps in the elucidation and leads to the discovery of known elements in new phenomena.
12. The above six propositions are evidently descriptions ; they are not, however, descriptions of a single case, but comprehensive descriptions of analogous cases. When they can be expressed in the hypothetical form "if the phenomenon responds to the reaction A, it will also respond to the reaction B," they comprehend all cases corresponding to the condition A and attribute to them the property B, and exclude all cases not corresponding to A. If I bring between a luminous object L and a dark one K an opaque screen with a hole O in it (reaction A), K will be illuminated only where the lines LO produced meet it (reaction B). If we superpose two rays from the same light source (reaction A), they alternately strengthen and weaken each other (reaction B). Such hypothetical propositions have a high practical and academic value in that they enable us mentally to associate with the given reaction A the anticipated reaction B and so to supplement the phenomenon with facts not included in what has already been observed.
13. From practical and academic standpoints it is desirable to discover propositions in which the reaction A implies a perfectly unique definition of the reaction B. Quite consistent with the desire for such propositions and the belief that these have been found is the fact that new experiences teach us the necessity of determining B not only by means of A but also by means of a complement C. The rectilinear propagation of light is demonstrated by experience: new experiences introduce refraction and reflection and limit rectilinear propagation to the case of homogeneous space: other experiences convey the notion of diffraction and limit the case of rectilinear propagation still further. The progress of science consists in a continual modification and restriction of propositions of the form indicated. The termination of this process is as little ascertainable as the termination of experience.
Excerpted from The Principles of Physical Optics by Ernst Mach, John S. Anderson, A.F.A. Young. Copyright © 2003 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
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