Light, that force in nature which, acting on the retina, produces the sensation of vision. It also has an important influence upon chemical affinity, as may be instanced in the union of hydrogen and chlorine gases, which in diffused light takes place gradually, hut in the direct rays of the sun instantly. The manifestation of vitality in plants is almost entirely dependent upon it, and most animals cannot maintain their health for any considerable time without its presence. The sources of light are self-luminous bodies, such as the sun, the fixed stars, certain meteors, those planets which have not cooled below the point of redness, and terrestrial bodies in a state of incandescence and phosphorescence. The ancient Greeks were aware that rays of light proceeded from illuminated objects in straight lines, which were reflected as well as refracted by surfaces according to certain definite laws. But all the ancient philosophers had very inconsistent notions in regard to its connection with vision, believing this vital function to be performed by something which proceeded from the eye to the object; and it is remarkable that this illogical idea was entertained until the early part of the 11th century, when it was refuted by the Arabian astronomer Alhazen, who seems to have been the first to perceive that vision is produced by rays of light proceeding from the object to the eye. - Two principal theories have been advocated to account for the phenomena of light, the emission or corpuscular theory, and the undulatory theory.
The emission theory, which was the first to be connected with optics on mechanical principles, originated with Descartes, who was the founder of modern mechanical philosophy. He conceived light to consist of small particles emitted by luminous bodies, capable like elastic balls of bounding from or being reflected by surfaces; and he explains the production of colors by assuming that a rotary motion is given to these particles under certain circumstances. But Newton was the founder of the emission theory, because he developed nearly all the doctrines by which it was maintained for more than a century, and also discovered many of the laws of optics by its means. The principal distinguishing hypotheses of this theory will be noticed in the course of this article. The undulatory theory assumes that the space between the celestial bodies is occupied by a kind of imponderable matter, which is infinitely elastic and of extreme tenuity, so that it not only occupies the space between bodies, but also enters into them and performs its function of undulation within them and between their particles.
This subtile matter is called the lumi-niferous or cosmic ether (see Ether), and the luminousness of a body is assumed to be due to a rapid vibratory motion of its molecules which is propagated in the ether in the form of waves. These waves proceed in all directions from every luminous point, resembling in that respect the waves of sound; the luminous point, like that of the origin of sound, being the centre of a sphere. The waves, however, are propagated in different ways in the two cases. The sphere of sound is formed by alternate expansions and condensations of the air, the waves consisting of concentric shells of alternate density and rarity, and the motion of the aerial particles being to and fro in the direction of the radii of the sphere. In the case of light the propagation is also in the direction of the radii, but the motion of the particles of ether is supposed to be in a transverse direction, as represented in section in fig. 1. The transverse oscillations in a line of ether particles proceeding in a right line from the source of light, as from c to a, is called a ray, and that length of a ray which at any instant includes all the phases of an oscillation is called a wave; while the form of that part of the wave which is presented toward the direction of propagation is called a wave front.
In the figure the vibrations are represented as taking place in one plane. Some regard each ray as cylindrical in form, and made up of a number of transverse vibrations which cross each other like the diameters of a cylinder; but it is only necessary to suppose that each ray vibrates in one plane, and that there are innumerable parallel rays with planes at every inclination to each other, as well as rays crossing each other in all directions. The velocity of light is known to be about a million times as great as that of sound, so that upon the undulatory theory air, or any other ponderable form of matter with which we are acquainted, would not be a sufficiently subtile medium for its propagation. For the purpose of explanation it therefore becomes necessary to assume some other medium which possesses adequate mechanical properties. Such a medium had been imagined by the ancients, and Hooke in 1664 proposed a theory that "light is propagated by a quick, short, and vibratory motion, in a homogeneous medium, in such a way that every pulse or vibration of the luminous body will generate a sphere which will continually increase and grow bigger, as the waves or rings on the surface of water do swell into bigger and bigger circles about a point in it." His theory, however, contained many erroneous hypotheses, and was unsupported by experimental or mathematical proof; but in the hands of Huygens it soon assumed a form capable of explaining most of the phenomena of light in accordance with established mathematical principles, and of standing the test of experimental demonstration to the present time.
No better idea of the inception of the undulatory theory can be given than by quoting a few -words from Huygens's Traite de la lumiere (1690; Tractates de Lumine, 1728). It will also thus be seen that he had formed views in regard to molecular physics winch have but recently been adopted, and that he had a pretty clear idea of the doctrine of dissociation almost a century and a half before the birth of Sainte-Claire-Deville, its commonly reputed author. "No one will question," says Huygens, " but that light consists of a motion of a certain matter as regards its effects. It appears that light, when gathered into a focus by a concave mirror, has the property of burning like fire, that is to say, it dissociates the particles of bodies (quod disjungat partes corpormn); and this most certainly indicates motion, at least according to that philosophy wherein the causes of all natural effects are conceived by means of mechanical reasons. ... If we consider with what great velocity the rays of light are propagated on all sides, and how, setting out from various and even opposite quarters, they intersect without interfering with one another, we will easily understand that lucid bodies are not seen by means of a certain luminous matter coming from them to us, as a ball or an arrow passes through the air. ... It therefore moves in another way, and to understand this it will be well to know how sound passes through the air." He then gives the explanation of the propagation of sound in a manner scarcely equalled by any modern writer, and proceeds: "There is no doubt but that light reaches us from luminous bodies by means of motion given to the interposed matter. . . . Light and sound, though they possess successive motion in common, yet differ very widely in other respects, as the motion which is the cause of each is differently produced, and the matter is different in which the motion takes place, and the mode different whereby the motion is communicated.
For sound has for its cause a sudden concussion of the whole body, or of a large part of it, which puts the contiguous air in motion; but light must arise from the separate parts of the luminous body, so that they are all plainly seen. ... In luminous bodies the motion is produced by a violent concussion of the particles, whereby an impulse is given to the ethereal matter. If we now inquire what is that ethereal matter wherein that motion springs, it will be seen that it is not the same as that which serves for the propagation of sound; for this is no other than the air we breathe, which being removed, the other still remains, a fact proved by placing the sonorous body in a glass vessel and removing the air by Boyle's machine." It is sometimes said that Huygens entertained the idea that light was propagated in the luminiferous ether in the same manner that sound is in the air, that is, by to and fro vibrations in the lino of propagation; but according to the above quotation, and for other reasons, this conclusion is scarcely well founded. He does indeed compare the action to that which accompanies the impact of elastic bodies, but does not suggest any definite method of production of the vibrations.
He concerns himself more with the forms of the wave fronts which are produced by the vibrations, and in that way arrives at mathematical results which, by the most rigid experimental and theoretical tests, have been found true. The composition of light by the union of rays of different degrees of refrangi-bility was not then known, and the cause of this difference of refrangibility not till more than a century after; several other of the phenomena of light, as interference and diffraction, had not been well observed, and required some additional hypotheses for their explanation; but the fundamental principles which enter into the explanation of all the phenomena, then as well as recently observed, were laid down by him, and will never be affected by any changes of hypothesis in regard to the precise mode of motion of the individual particles of ether. The additional hypotheses by which the theory has been brought to more completeness, the most important of which is that of transverse vibrations and the deduced principle of interference, were proposed (1801-'3) by Dr. Thomas Young of England, and hence many of his countrymen regard him as really the founder of the undulatory theory.
The principle of interference, however, was not perfectly established and generally applied until Fresnel brought to bear upon the subject the analytical powers of his great mathematical genius. Euler, Malus, Cauchy, Arago, Biot, Sir David Brewster, Sir William Hamilton, Sir G. B. Airy, and other investigators have also added many important contributions. The definite conception of transverse vibrations of different lengths by which the rays of different refrangibility were propagated must, however, be considered as an important part of the undulatory theory as it now stands, and the principal hypothesis upon which a great share of the physical explanations depends. It may seem remarkable that this theory, whose fundamental laws were so clearly stated nearly two centuries ago, should not have been sooner accepted, as it is thought the emission theory can be put to the test of direct experiment. Experiments made by Mr. Bennet are pointed to as being conclusive. He suspended a slender straw horizontally by means of a spider's web, and attached a piece of white paper to one end of the delicate balance.
He then introduced it into the receiver of an air pump, exhausted the air, and brought the focus of a powerful lens to bear upon it, but without producing any motion in the ponderable matter of the balance. It is asserted that on the emission theory the immense velocity of the luminous particles, although they might be infinitesimally small, would possess sufficient momentum to impart a sensible degree of motion to light bodies; and the position cannot well be denied. If a single molecule of light weighed 1/2400 of a grain, it would have a momentum equal to that of an ounce ball moving with a velocity of 1,000 ft. a second; and if it he assumed that the light molecules are many millions of times lighter than this, it may also be assumed that as many millions of molecules may be made to act together. It may be answered, on the other hand, that if the luminif-erous ether is composed of particles so small as to be able to easily pass between the particles of ponderable matter, as some suppose they do, they have not the power to impart momentum. But this position fails when we consider the immensely greater velocity of light than that of any ponderable bodies that are supposed to be traversed by the ethereal particles in consequence of the. motion of such ponderable bodies.
It must be admitted, however, that the experiments of Mr. Bennett, although they add difficulty to the emission theory, do not amount to a demonstration; that is, after all, more nearly reached by the perfect competency of the undulatory theory to explain all the various phenomena of radiation. But the velocity and momentum of the luminous particles are held to be no greater objection to the emission theory than that offered by the fact that the velocity of light in a homogeneous medium is uniform; which, it is maintained, could not be the case if the luminous particles were emitted by the force of the self-luminous body, which must be admitted to be a variable force. - Velocity of Light. The velocity of light is so great that no sensible space of time is occupied in its passage between any two points on the surface of the earth. The first determinations of this velocity were made from observations on the heavenly bodies. Roemer, a Danish astronomer, in 1675 made the first estimation by means of observations on the eclipses of Jupiter's first satellite. This body passes into the planet's shadow at equal intervals of 42 h. 28 m. 36 s. Let m, fig. 2, represent the satellite, e and e' the earth, and S the sun.
When the earth is travelling in that part of its orbit between a and b, the distance between it and the satellite varies but little, and therefore the intervals between successive occultations do not sensibly change; but when the earth has reached the opposite part of its orbit, as at e' a retardation has taken place in all the occultations amounting to about 16 m. 40 s., the precise time varying as the points e and e' vary with respect to the elliptical orbit. Calculations from data furnished in this way show the velocity of light to be about 190,000 m. per second. Another method which has been employed is that of aberration, or an apparent change in the position of the fixed stars, caused conjointly by the velocity of light coming from them and that of the earth in its orbit. (See Aberration.) The velocity of light has also been determined by observations upon distances between places on the surface of the earth, machinery being used to mark the otherwise insensible periods of time. In 1849 M. Fizeau measured the time it took for light to travel from Suresnes to Montmartre and back again.
A toothed wheel, having the teeth and the intervals between them of equal width, is made to revolve rapidly in a plane at right angles to a beam of light, with such a velocity that the beam, having passed through an interval, and having been reflected back by a mirror placed at the other station, will be intercepted by a tooth which has in the mean time taken the place of the interval. The main apparatus was placed at Suresnes and the mirror at Montmartre, a distance of 28,516 ft. With a certain velocity of the wheel the beam of light would be intercepted and no reflection observed; with twice the velocity it would reappear; and with three times the velocity it would again be obscured. The velocity of light deduced from recent observations with this apparatus is 185,000 m. a second, which accords pretty closely with results of astronomical observations. Another method only requires a distance of less than 12 ft., and employs the principle of the revolving mirror first used by Wheatstone in his experiments on the duration of the electric spark. (See Electricity.) This method was proposed by Arago, and carried out independently by Foucault, Fizeau, and Breguet. An important feature in the experiment is the passing of a beam of light through a long tube containing a liquid, in which its velocity is found to be retarded; a fact which is strongly confirmatory of the truth of the undulatory theory, one of whose consequences is that light has a greater velocity in air and gases than in liquids, while the emission theory leads to an opposite conclusion. - Intensity. The intensity of light may be estimated by an amount which is received on a unit of surface, and depends upon the degree of luminosity, upon the distance from the source, and upon the obliquity to the rays of the surface illuminated.
The intensity of light emanating from a point is inversely proportional to the square of the distance. This agrees with a similar law in regard to heat, and is proved by considering the internal surfaces of two spheres to be illuminated from points at the centre. If the sources of light are equal to the surfaces, they will each receive the same amount of light; but if one has a radius twice as great as the other, it will have four times the area, and therefore .an equal area would receive only one fourth as much light. In regard to the effect resulting from obliquity of the receiving surface, the law is that the intensity of light received is proportional to the cosine of the angle which the incident rays make with a perpendicular to the surface. Let a b, fig. 3, be a surface receiving a beam of parallel rays, c b a d. The quantity of light falling on a b will be the same as that which would fall upon a surface e b, perpendicular to c b and d e; therefore the intensity of light received by these surfaces is inversely proportional to their areas. But e b=a b x cos. a b e=a b x cos. c b f, the angle included between the incident rays and the perpendicular to the surface.
The same law has been applied to heat, and is true as to the number of rays falling upon the surface, but not strictly so as to the amount of heat absorbed. (See Heat.) The intensity of light emitted from a luminous surface obeys the same law. For the comparison of the intensity of different sources of light, see Photometry. - Absorption and Emission. In regard to the properties of bodies by which they allow light to be transmitted through them, or cause its absorption, they are classified as transparent, translucent, and opaque. Transparent bodies are those which transmit light with little or no perceptible loss, and through which objects may be distinguished. Translucent bodies allow much of the light to pass through them, but prevent objects from being viewed through them, such as ground glass, oiled paper, and horn. Opaque bodies are those which absorb the rays of light, or prevent most of them from passing through them. These properties of bodies depend upon their molecular constitution. Some bodies have the power of transmitting the non-luminous but not the luminous rays of the spectrum; such are called diathermanous bodies. (See Diathermancy.) Dry air and rock salt are bodies that are almost perfectly transparent as well as diathermanous; or, as it is sometimes said, transparent to all the rays, visible and invisible.
Rock salt is the only known solid having this property nearly perfect. Those bodies which permit the ether within them to transmit undulations of medium wave length from and to the ether around them are transparent to the luminous rays; those whose molecular constitution causes the ether undulations to be broken up are opaque. There are no bodies which are perfectly opaque, as is shown by cutting them in very thin slices, or hammering them into thin films, when most of them will bo found slightly translucent. Foucault has coated the object glass of a telescope with so thin a film of silver that the sun can be viewed through it. - Reflection and Refraction, "When a beam of light meets the surface of a new medium, a portion of it is always turned back or reflected, while another portion is propagated onward in the second medium, and is also turned out of its original course, or refracted. The angles which are made by the incident and reflected rays with a perpendicular to the surface are called the angles of incidence and reflection respectively, and are always equal to each other. Light is said to be regularly and irregularly reflected.
The image formed in a mirror is regularly reflected, but the rougher surfaces of ordinary objects reflect light irregularly in all directions without forming an image. The intensity of reflected light varies with the reflecting surface and with its position. The differences also in the reflecting powers of different substances are greater for small than for large angles of incidence. Thus water reflects only 1/50 part of a perpendicular beam, while mercury reflects two thirds; but when the incident angle is 89 1/2°, they each reflect 721/1000 of the incident light. The refracted rays are deflected in a direction either to or from the perpendicular, depending upon the refracting power of the second medium. When its refracting power is greater, the direction is toward the perpendicular, and when it is less, from it. Ptolemy measured the refraction of glass and water at various angles, and he observed that the angle of incidence was greater than the angle of refraction; but he erred in supposing the proportion to be invariable for different angles, it being left for Willebrord Snell, about 1621, to demonstrate that in refraction there is an exact proportion between the sines of the angles of incidence and refraction, instead of between the angles themselves.
Alhazen had long before shown that the angles vary as the incident rays are more or less oblique, but failed to discover the natural law. Alhazen's discovery, however, had not prevented mathematicians from generally adhering to the old notion of Ptolemy down to the time of Kepler, who again saw the error, and published an approximate correction in 1604. The laws of single refraction may be stated as follows: 1. At any angle of incidence the ratio of the sines of the angles of incidence and refraction is constant for the same two media, but varies with different media, and this ratio is called the index of refraction. 2. The incident and the refracted rays are in the same plane, which is perpendicular to the plane separating the two media. These have been generally known as Descartes's laws, but, as stated above, their discovery is due to Willebrord Snell. The index of refraction, as will be seen further on, also varies somewhat with the nature of the light, whether red, green, or violet; and in exact experiments homogeneous light alone is used, but this does not affect the general law. The index of refraction from air to water is 4/3, and is called the index of refraction for water. In calculating the indices of refraction for media generally, air is considered as the first medium.
The indices of refraction for various substances are given in the following table, and are calculated for yellow light, except those marked *, which are for extreme red:
Fig. 2. - Roemer's Observations.
Ind. of refr.
Canada balsam ..
Ind. of refr.
Oil of turpentine*.
The phenomena of reflection and refraction are explained on the emission theory by supposing that the projected luminous particles and the particles of bodies exert a mutual action, either repulsive or attractive. In certain positions the particles of light are suffered to be repelled, and therefore reflected; in other positions they are attracted, and therefore pass into the medium and are refracted. In the wave theory it is supposed that when a wave of light reaches the surface of a second medium whose elasticity is different, it gives rise to two waves, one in each medium, both differing in position from the original wave. But the several portions of the incident wave will reach the surface at different moments of time, and each of these portions will be the centre of two new waves, one of which will be propagated in the first medium with the velocity of the incident ray, and the other in the second medium with a velocity depending on the density of the ethereal particles within it; so that an infinite number of partial waves will be reflected and refracted, forming by their union grand or primary wave fronts at right angles with the reflected or refracted rays.
The following is a condensation of the elegant demonstration of Huygens. Let a e, fig. 4, be the front of a plane wave meeting the reflecting surface at a. As each portion of this wave reaches the surface, it becomes the centre of a spherical wave in the first medium having the same velocity. Therefore, when the portion e has reached the surface at c, the portion a will have formed a spherical wave whose radius a m is equal to e c, and the portion b will also have formed a wave whose radius b o is equal to d c. The surface n m c, which touches all these partial wave fronts, is the front of the reflected wave; but since a e and b o are proportional to a c and b c, it follows that this surface is plane; and furthermore, since a m = e c, and the angles at e and m are right angles, the angles e a c and m c a are equal, or the incident and reflected waves fronts (and therefore the rays) are equally inclined to the reflecting surface. The demonstration of the law of refraction is similar. If a e, fig. 5, is the front of a plane wave, when the portion a reaches the surface a partial wave is generated, which will proceed a certain distance, while the portion e passes on to c, and the portion g will arrive at b, where a partial wave is also generated, with the same velocity as that formed at a.
As these partial waves form a plane wave front in the refracting medium, their direction must be such that they will reach the plane c n in the same time that the portions g and c reach b and c respectively; and as sin e a c: sin a c o:: e c: a o (the angles at e and o being right angles), it follows that the sines of the angles are in the constant ratio of the velocities of propagation in the two media. The composition of the primary wave by the union of the several secondary waves in this demonstration has been called the "principle of Huygens," and is frequently employed in explaining many of the phenomena of light. Refraction produces some well known effects. "When an object immersed in water is viewed obliquely, it appears nearer the surface than it really is, because the light in passing from the denser to the rarer medium, or to that whose refractive index is the less, takes a direction from the perpendicular, or more inclined to a horizontal direction. When a ray of light enters a less refracting medium, there is always a value of the angle HOB, fig. 6, which causes the angle of refraction A O C to be a right angle. If the angle of incidence H O B is increased, as to E O B, the ray cannot emerge from the first medium, but will be reflected from its internal surface.
The angle HOB is therefore called the critical angle, and its sine is the reciprocal of the index of refraction of the medium. From water to air this critical angle is 48° 35', and from glass to air it ranges from 38° to 42°. From the diamond to air it is only 24°, leaving a range of 66° in which reflection takes place from the internal surfaces of the faces of the crystal; to which circumstance this gem owes its brilliancy and splendid play of colors. The phenomenon of mirage depends upon the unequal refractive powers of the different strata of the atmosphere in consequence of the different quantities of vapor which they contain. (See Mirage.) The phenomena of reflection and refraction, such as the formation of images, the production of caustics by means of lenses, and mirrors, are treated in the article Optics. - Dispersion. Thus far light has been considered as homogeneous, that is, composed of rays having the same wave length; but most of the light with which we are acquainted is compound, consisting of innumerable rays of different degrees of refrangibility, a discovery which we owe to Newton. If a beam of solar light is received into a darkened chamber through a small circular aperture at D, fig. 7, it will produce a luminous spot upon a screen at F, and the diameter of the image will be equal to that of the aperture.
If the light is passed through a prism, ABC placed horizontally, the rays will all be bent toward the base of the prism, but not in an equal degree. Upon the screen M N there will be depicted an elongated spectrum, of a width equal to that of the diameter of the original beam, and composed of innumerable rays of different degrees of refrangibility, and of an infinity of tints, of which seven principal ones are capable of being distinguished by the human eye, viz., violet, indigo, blue, green, yellow, orange, and red, the violet being refracted the most and the red the least. They do not all occupy an equal space, the violet having the greatest and the orange the least extent. Newton proved that white light is composed of these various colors, not only by decomposing it, but also by recombining the colored rays and reproducing white light. He also showed that the rays in each portion of the spectrum always retain their characteristic color when isolated and passed singly through prisms, and that they will not be dispersed as in the case of white light.
According to the theory of Young, which has lately been ably supported by Helmholtz, color results from the impression made by rays of different refrangibility upon three kinds of nerve elements in the retina, one of which alone is impressed by red, another by green, and another by violet light. When these nerves are simultaneously impressed by varying quantities of rays of different degrees of refrangibility, the sensation of a variety of tints is the result. According to the wave theory, the intensity of light depends upon the amplitude of the vibrations, that is to say, upon the distance the ether particles travel and which is in a direction perpendicular to the time of propagation. The color of a ray, which varies with its refrangibility, depends upon the wave length, that is, upon the distance of the wave crests from each other, in the direction of the line of propagation. The solar beam also contains invisible rays of different wave lengths. When the rays in the beam are dispersed by a prism, these invisible rays are also dispersed, those which are the most refrangible being found beyond the violet, and those which are the least refrangible beyond the red. The most refrangible invisible rays are called actinic, and the least refrangible calorific or heat rays.
That portion of the spectrum which is visible is also illuminated in different degrees in different parts, the greatest proportion of light being in that part corresponding to the yellow rays. According to Fraunhofer, the amount of light contained in each part of the spectrum is as follows: red, 94; orange, 640; yellow, 1,000; green, 480; blue, 168; indigo, 31; violet, 6. All the rays possess the property of more or less affecting the temperature of bodies on which they impinge, but those of a certain degree of refrangibility possess it in a far greater degree than the others. When a diathermanous substance, as rock salt, is used as the dispersing medium, by far the greatest amount of heat is contained in that part of the spectrum which lies beyond the red. The violet rays have the power of exciting a faint degree of heat, and the actinic rays are not totally devoid of it; and all the rays possess more or less actinic power, but the least refrangible only in an extremely small degree. The rays which produce vision, however, have a limited degree of refrangibility, and in the spectrum lie within certain bounds. They have relation to a vital function, and are therefore confined to those whose wave lengths are capable of exciting the nerves of vision.
Newton supposed the spectrum to be continuous, but it has been found on careful examination to be interrupted by certain dark bands or lines representing vacant spaces, which have fixed positions. A prism of low dispersive power does not exhibit these lines, because the colors are superimposed; but when a succession of prisms is used, the spectrum is lengthened out, so that they are easily seen and their places noted. When the refracting substance is varied, the dark lines may have their positions with regard to one another changed; but with regard to the colors they are not changed, the refracting substance having the same effect upon the extent of the colors that it has upon the position of the lines. A diffraction grating, as will be seen further on, may be advantageously substituted for a prism for the purpose of showing the position and counting the number of the lines. The vacant spaces or lines are caused by the absorption of rays given out by the incandescent body in some part of their passage to the eye.
It has been found that the vapor of a substance has the power of absorbing rays which that substance in a state of incandescence emits; so that, there being in the solar atmosphere vapors of various incandescent bodies, some of the rays originating in the incandescent mass are absorbed, leaving dark lines in their places. These dark lines, having a definite position with regard to the refrangibility of rays, are employed as a means of marking the wave lengths of the different rays. The following table gives the lengths of undulations in parts of an inch, and also the number of undulations performed in a second, corresponding to the different dark lines and other places in the spectrum, as computed by Fraunhofer:
Fig. 7. - Solar Spectrum.
PLACE IN SPECTRUM.
Length of undulations.
No. of undulatiom per second.
Several of these dark lines were first observed by Wollaston in 1802; but as they have since been more completely studied by Fraunhofer, they are called Fraunhofer's lines. He counted over 600 of them, and assigned fixed positions to 354 He selected seven of these as standards of comparison, designating them by the letters B, C, D, E, F, G, H, of which some are single, some are double, and others composed of a group of fine lines, as at E. Sir David Brewster counted about 2,000, and since then Kirchhoff, Bunsen, and others have extended the number to more than 3,000. In other kinds of light, as that of the fixed stars, flames, and the electric spark, analysis discovers similar bands, but differing in position and magnitude, so that each species of light has its own system of bands, which are distinct physical characteristics. The subject will be treated in the article Spectrum Analysis. - Double Refraction. In what has thus far been said about refraction it has been supposed to take place in one direction only for the same medium and the same angle of incidence; but this is not true for the majority of refracting media, but only of those having a homogeneous or a crystalline structure alike in all directions.
Liquids, annealed glass, and crystals whose fundamental form is the cube, possess only the pro'perty of single refraction. All transparent substances of regular form, in which there is an unequal state of compression or cohesion of molecules, possess the property of refracting a beam of light in two directions. Such are crystals of the dimetric and hexagonal systems, and glass which is subjected to unequal pressure in different directions. There is one direction, called the optic axis, in which a beam of light is not divided by these crystals, and this is also the crystallographic axis. They are therefore called uniaxial crystals. Some crystals have two optical axes, or axes through which there is no double refraction. Such belong to the trimetric, monoclinic, and triclinic systems of crystallization, and are called biaxial crystals. The phenomenon of double refraction was first discovered by Erasmus Bartholinus, a Danish philosopher, in Iceland spar, and his account was published in 1669. A few years afterward the subject was investigated by Huygens, who succeeded in establishing the general laws under which double refraction takes place.
Iceland spar, which possesses the property of double refraction in the most remarkable degree, is a variety of carbonate of lime, which substance crystallizes in a great variety of forms, all of which may be reduced by cleavage to the rhonibohedron. If a transparent crystal of the spar be laid upon a printed page, all the letters seen through it will appear double, but of less depth of color, except where the images overlap. (See fig. 8.) If a line be drawn from one of the solid angles in which three of the obtuse plane angles meet, this line, or any line parallel to it, will be the optic axis of the crystal, which is a direction, and not a particular line. See fig. 9, where a b, or any line parallel to it, is the optical axis. A ray of light entering the crystal in the direction of any of these lines will not be divided by refraction, but in any other direction it will be split into two rays separated by an angle of 6° 12', one of which was called by Huygens the ordinarv, and the other the extraordinary ray; and these possess remarkable properties, as we shall see further on.
If a crystal of the spar is laid upon its side over a dot, and rotated on an axis perpendicular to the surface on which it lies, one of the images of the dot (the ordinary image) will remain stationary, while the other (the extraordinary) will revolve around it. A line drawn between the two images is always in the direction of the shorter diagonal of the face of the crystal, supposing its edges to be of equal length. The ordinary ray follows the law of sines as in single refraction, but the extraordinary ray does not, except when the plane of incidence is perpendicular to the axis of the crystal; in which case, however, the indices of refraction differ, the ordinary index being 1.66, while the extraordinary is 1.52. Huygens's explanation of double refraction is contained in the fifth chapter of the Tractatus de Lumine, and one of the remarkable geometrical constructions contained in it may be briefly stated as follows: Let A C, fig. 10, be the incident ray, and C F the surface of the crystal. Produce AC to B, and draw B F perpendicular to it, meeting the surface in F. Let C D: C B:: sine of refraction: the sine of incidence of the ordinary ray; and from the centre C, with a radius CD, describe the spherical surface DOG. Describe the spheroid of revolution G E with the same centre, its axis of revolution being in the direction of the optic axis of the crystal and equal to the diameter of the sphere, the other axis being greater in the ratio of the ordinary to the extraordinary index.
If from a line perpendicular to the plane of the diagram at F tangent planes F O and F E be drawn to the sphere and spheroid, the lines C 0 and C E drawn from the centre to the points of contact will be the directions of the ordinary and extraordinary rays. In Iceland spar and many other crystals the index of refraction of the extraordinary is less than that of the ordinary ray, but there are other crystals which refract the extraordinary ray the most. The class of crystals to which Iceland spar belongs are called negative, while those which refract the extraordinary ray the most are called positive crystals, both classes being uniaxial. The following is a list of double-refracting crystals: negative uniaxial crystals - Iceland spar, spath-ose iron, tourmaline, sapphire, ruby, emerald, apatite, pyromorphite, ferrocyanide of potassium; positive uniaxial crystals - zircon, quartz, apophylite, titanite, boracite, ice; biaxial crystals - nitrate of potash, sulphate of iron, sulphate of barium, Brazilian topaz, sugar, selenite, aragonite, strontianite, kyanite, epidote, mica. - Interference. The important principle now known under the name of interference of light was first proposed by Dr. Thomas Young more than half a century ago.
This class of phenomena result from the mutual interference of waves of light when they proceed from two neighboring sources and meet each other under a very small angle, and may be shown by the experiment of Gri-maldi, which is described further on in connection with diffraction. The experiment of Grimaldi is not however satisfactory, as interference takes place in consequence of diffraction from the action of the edge of the aperture. Young modified the experiment so far as to afford him the means of establishing the law of interference, but it was not freed from the objections which might be urged, that the effects were also produced, as in Grimaldi's experiment, by the edge of the aperture. Fres-nel afterward made the experiment in such a way that interference took place without the possibility of diffraction, and his experiment is regarded as one of the most instructive and elegant in the range of physics, and as a demonstration of the truth of the undulatory theory. He employed two mirrors placed together at a very obtuse angle (a very little less than 180°), and reflected from their surfaces upon a screen light from the focus of a lens, in such a manner that on reaching the screen some of the undulations of two converging rays should correspond and intensify one another, while others should be separated by half a wave length and destroy one another. - Diffraction. A divergence of the rays of light in passing the edge of an opaque body in such a way as to produce interference is called diffraction.
The phenomena were first observed and partially explained by Grimaldi, an Italian physicist, and published in a work entitled Physico-mathesis de Lumine, Coloribus et Iride alisque Anuexis, in 1665, two years after his. death. He noticed that the circle of light formed upon a screen when rays were passed through a minute orifice into a dark chamber was bounded by fringes which extended into the shadow beyond the geometrical projection. Again, admitting light through two small apertures sufficiently near together to cause the pencils of light projected upon a screen to overlap each other, he further observed that although the space occupied by the overlapping was more brightly illuminated, its borders were darkened by bands or fringes to a greater degree than the other parts of the spectrum. From these discoveries was deduced the proposition that light added to light may produce darkness. To observe the phenomena of diffraction with greater advantage than was possible with Grimaldi, who was not aware of the compound nature of light, monochromatic light should be employed. Let a beam of light be received into a dark room, fig, 11, and place a plate of red glass in the aperture.
Pass the homogeneous beam through a convex lens of short focal distance, converging the beam to a physical point at a, and place an opaque screen b, having a sharp edge, beyond the focus to intercept the lower portion of the luminous cone, allowing the upper portion to be projected upon a second screen, still further removed. Below the right line c d the second screen will not be entirely in shadow, but will be faintly illuminated for a short distance, the light gradually passing into obscurity. That portion of the cone which is above the edge of the first screen and which falls upon the second will not be uniformly illuminated, as might be supposed; but there will be an alternate series of light and dark bands, proceeding from the intersection of the line c d, and extending upward until they gradually disappear. The light and dark bands are not clearly separated, but their edges are more or less blended. If, instead of red, violet light is employed, both dark and light bands, as well as the whole spectrum, will be narrower. Careful observation will also discover that the fringes are not straight lines, but are sensibly curved, the concavity of the curvature being turned downward toward the shadow.
By using an eyepiece with a micrometer, Fres-nel accurately determined the distances of the bands from the shadows at different points, and found these curves to be hyperbolas. If in this experiment the light proceeds from a source which has any considerable cross section, instead of from a point or a very minute orifice, each line in it parallel to the first screen will tend to produce a different system of fringes, the dark band of one coinciding with the light band of the next, and thus the phenomena of diffraction will not be produced. If, instead of employing an edge, the light is allowed to pass the opposite edges of a very narrow opaque body, as a hair or a fine wire, the phenomena observed by Grimaldi will appear; but the use of monochromatic light will render them more distinct. On each side of the geometrical projection there will appear a set of parallel bands or fringes, like those produced without the geometrical projection by the single edge; but within it, instead of the gradually shaded light, there will also be a series of dark and light bands similar to those outside, only narrower and more clearly marked. These are called the interior fringes, and they also have the form of hyperbolas, but of less curvature.
Newton explained the phenomena of diffraction by supposing that the rays of light in passing the edges of bodies are inflected, in consequence of the attraction or repulsion between their particles and the matter composing the edges of the bodies so passed; an explanation similar to that which he offered for reflection and refraction. He supposed that the particles of light in passing the edge of an opaque body are repelled when they arrive at a certain point; and therefore that those passing nearest the edge are inflected the most, and so made to intersect others less inflected, thus producing a caustic (see Optics), within which no rays will pass, and which forms the boundary of the visible shadow. He explained the appearance of the fringes by supposing the attractive and repulsive forces between the particles of each ray and the matter of the edge of the body to alternate, and thus throw them into a serpentine course, the intersections of the rays producing a series of caustics which diminish in intensity from the edge of the shadow. To explain the appearance of the prismatic colors, it was only necessary to apply his theory of the decomposition of white light, which supposes that the various colored rays are unequally attracted by the refracting body through which they pass.
That the explanations of Newton are insufficient, aside from other evidence, appears from a consideration of the fact that no difference in the degree of diffraction is produced by increasing the density and therefore the attraction of the matter composing the diffracting edge. The supposition of Mairan and Du Tour that diffraction is caused by refraction of the rays of light in passing through a prismatic film of air condensed by the inflecting body is equally open to objection, for these atmospheric prisms would necessarily vary in form with the nature and density of the body, and would consequently possess different refractive powers. To Young and Fresnel we owe the explanation of the phenomena of diffraction according to the principle of the interference of waves. The formation of the exterior fringes was ascribed by Young to the interference of two portions of light, one of which passes by the body and is slightly deflected, while the other is thrown further out of its course by being obliquely reflected by the edge. The production of the inferior fringes he ascribed to the bending of the waves inward, and the consequent interference which takes place between the rays that intersect each other from the opposite sides.
That this latter explanation is correct is shown by the fact that the bands do not appear unless the obstruction is sufficiently narrow to allow rays coming from the opposite sides of the body to intersect each other; when the body is not narrow, the same effect is produced on either side as when a single edge is employed. The explanation of the formation of the exterior fringes, however, does not agree with certain observed facts. Fresnel allowed the rays of light to pass both the back and the edge of a razor, and produced fringes which were alike in breadth and intensity; which could not have been the case if the interference were caused by the reflection of a portion of light by the body, because then there would be a greater condensation by the back than by the edge. Fresnel ascribed the effects to partial or secondary waves, which are separated from the principal wave by meeting an obstacle, and are subdivided into an indefinite number of equal portions, each portion becoming, according to the principle of Huygens, the centre of a system of partial waves; a theory whose correctness was demonstrated by the agreement which was found to exist between the calculation of the resultant of all the forces, according to the mathematical laws of interference and the intensities of light in the dark and light bands. - Diffraction Spectrum. If a piece of glass is ruled with very fine parallel lines, which may be done by a dividing engine and a diamond point, at the rate of from 1,000 to 5,000 or 6,000 to the inch, and it be looked through in the direction of a slit parallel with the grating, a number of spectra will be seen which will be so pure in color as to exhibit several of Fraunhofer's lines.
The spectra may be viewed with advantage by employing a telescope; or an image of the slit, which must be highly illuminated, may be thrown upon a screen by a convex lens. Diffraction spectra are of great use in furnishing a uniform standard of reference in the comparison of spectra, and as affording the most accurate method of determining the wave lengths of the different elementary rays of light. Fraunhofer was the first to employ diffraction spectra. The first were made with fine wire stretched between the threads of screws about 1/250 of an inch apart. This was comparatively a coarse grating, but he soon ruled lines on glass much closer, and others have since executed them with great nicety. Mr. Rutherfurd of New York has ruled 12,960 lines to the inch, but finds that for practical purposes about half this number is preferable. - Colors of Thin Plates; Newton's Rings. The phenomena known under these names were first examined by Boyle and Hooke, but were afterward more completely investigated by Newton. They are observed in soap bubbles, plates of mica and selenite, and other crystals, in thin plates or films of glass or other transparent substances, or in the films of air held between two transparent plates.
Any arrangement by means of which a ray of light may be reflected from two adjacent surfaces, or transmitted through two plates in such a manner as to produce interference of the rays, will exhibit the colors of thin plates. If the mouth of a small cylindrical vessel is dipped into water made viscid with soap, a film will remain across it after its removal, which will exhibit the phenomena of these colors. Holding the film in a vertical position, it will at first, if thick enough, appear white; but growing thinner by evaporation and descent of particles, it will soon present, commencing at the top, a brilliant play of iris-colored bands, arranged horizontally. After a while the top of the film loses its color and appears black, and growing thinner bursts. If a drop of oil or of spirits of turpentine is spread over the surface of water, a film of the proper thickness soon forms, which presents the same play of iris colors as the soap bubble. A finely grooved surface, which has the power to reflect the rays of light in such a way as to produce interference, will also exhibit the same appearance. Newton examined the subject experimentally by placing a glass plate having a spherically convex surface of great focal length upon a plane glass, and applying a certain degree of pressure.
When the system is held toward the light a series of colored rings is observed, whose dimensions change with the amount of pressure. On looking attentively it will be observed that at the centre there is a circle of uniform color. If pressure is increased, this central circle dilates and at last forms a ring, and a new circle of a different color springs from its centre. This will in turn dilate and form a new ring, while another new circle will form within it, till at last a black spot appears at the centre of the system. After this no further pressure will produce a new circle, because we have now obtained a plate of air so thin as to be incapable of reflecting light. Newton traced seven colored rings around this central spot, which are called the first, second, third, etc, order. Each order, when white light is used, contains all the primary colors; thus, the red of the third order is the red in the third ring from the central black spot. The whole system of colors is called Newton's scale, and the principal laws of the phenomena are: 1. In homogeneous light the rings are alternately bright and black; the thickness corresponding to the bright rays of succeeding orders being as the odd numbers of the natural series, and those corresponding to the black rings as the intermediate even numbers. 2. The thickness corresponding to the ring of any given order varies with the color of the light, being greatest in the red light, least in the violet, and of intermediate magnitude in light of intermediate refrangibility. 3. The thickness corresponding to any given ring varies with the obliquity of the incident light, being very nearly proportional to the secant of the angle of incidence. 4. The thickness varies with the substance of the reflecting plates, and in the inverse ratio of its refractive index.
To explain the effect of interference in producing the ring, let us consider a section of fig. 12. Let A C B represent the convex plate, and D E the plane plate. There will be a film of air between them, whose thickness increases from the point of contact, 0, in proportion to the square of the distance. If a beam of light is received upon either surface, a portion will be reflected by the surface of the film of air, and another portion by the surface of the glass beyond it. There will thus be formed two systems of waves intersecting each other, and increasing or destroying each other according to whether they conspire together or not. At a certain distance from C, as at F, the difference of the paths of the two beams is equal to a half undulation, and the waves interfere with and destroy one another, producing a dark ring. At a greater distance, as at G, the difference of the paths is equal to one whole undulation; therefore the waves conspire together and increase the amount of light, which also is decomposed, producing rainbow colors. With homogeneous light there is simply alternate increase of light and darkness.
Now as the thickness of the plate of air at the distance from the centre where any ring is formed is in proportion to the square of this distance, or to the square of the diameter of the ring, it is only necessary to measure these diameters in order to determine the law of thickness. This was done by Newton with great accuracy, who found that the squares of the diameters were in an arithmetical progression; consequently the thicknesses of the plates corresponding to the successive rings form a similar progression. He moreover measured the absolute thickness of the plate of air at which each ring was formed, and found that at the dark ring of the fifth order it was 1/17,800 of inch, this being ten times the thickness at the first bright ring. The successive orders of bright rings are therefore formed at the thicknesses 1/178,000, 3/178,000, 5/178,000, etc., the intermediate dark rings at the thicknesses 2/178,000,4/178,000, etc. - Polarization of Light. While making his researches on the law of double refraction, Huygens found that the rays divided by passing through a rhomb of Iceland spar possessed remarkable properties; that on passing them through a second rhomb the two portions did not remain equally intense; that their relative brightness depended on the position of the second rhomb, and that there were two positions in which one of the rays completely disappeared.
Each of the rays has therefore acquired characteristic properties, or, it may be said, has lost properties. It is said to have acquired sides, but in fact it is reduced to vibrations in one plane. At Newton's suggestion it was said to be polarized. The phenomenon discovered by Huygens remained for more than a century an isolated fact in science, and other phenomena with which it is associated also remained unnoticed till the beginning of the present century. In 1808, while Malus was engaged in researches upon the subject of double refraction, he happened to turn a double-refracting prism toward the windows of the Luxembourg palace, which then reflected the rays of the setting sun. On turning round the prism the ordinary image of the window nearly disappeared in two opposite positions, while in two others at right angles to the former the extraordinary image nearly vanished. He at first ascribed this phenomenon to some influence of the atmosphere upon the ray similar to that produced by a second rhomb of Iceland spar, but he soon found that it was caused by reflection at a particular angle.
This therefore was the second important discovery in regard to polarization: that it was not only produced by transmission, but by reflection; a discovery of great value in investigating the properties of light. A beam of light from a self-luminous source when passing through a homogeneous medium exhibits the same properties on all sides so long as it does not meet with an obstacle; such a beam is composed of ordinary or natural light. But after it has been reflected or refracted, it has lost some of its properties; some of its rays have been quenched. When the reflection takes place at a certain angle, nearly all the rays except those lying in a certain plane will have been obliterated. If the ray, having been thus reflected from a glass mirror, be received obliquely upon another glass mirror, and the latter turned around the ray, care being taken not to change the angle of incidence, the intensity of the twice-reflected beam will vary as the position of the mirror is changed. Let a ray of light A 0, fig. 13, fall upon a plate of glass at 0, making an angle of 54° 35' with the perpendicular; it will be reflected in the direction 0 D. Let the ray be received upon a second plate of glass, at the same angle with the perpendicular as before.
If the second mirror is so placed that its plane of reflection is parallel to the plane of reflection from the first surface, it will be reflected in the direction D E without being diminished. But if the second mirror has its plane of reflection perpendicular to that of the first, as in fig. 14, then the ray will not be reflected, or its intensity will be greatly reduced. In intermediate positions at the same angle of incidence it will be partly reflected, the quantity of light being greater in proportion as the planes of reflection become more nearly parallel. The plane in which a polarized ray is most easily reflected is called the plane of polarization, and it coincides with the plane of incidence and reflection. The angle of reflection at which polarization becomes most complete with any surface is called the polarizing angle for that surface, and varies with the substance, according to the following law discovered by Brewster: "The polarizing angle of a substance is that angle of incidence for which the reflected polarized ray is at right angles to the refracted ray." Thus, in fig. 15, if s i is the incident, i r the refracted, and if the reflected ray, the polarization is most complete when f i is at right angles to ir.
It is still an unsettled question as to whether the vibrations of the polarized ray take place in the plane of polarization or at right angles to it. It is sometimes assumed for convenience of explanation that they take place within it, but it is the opinion of Fres-nel and Cauchy that they are perpendicular. Mac-Cullagh and Neumann regard them as taking place within the plane. Fig. 16 will serve to represent the manner in which the vibrations take place according to Fresnel and Cauchy, where a c b, b c d is the plane of polarization. The majority of physicists are inclined to regard this as the more probable mode of motion. The following table shows the polarizing angles of a few transparent substances, chiefly according to the observations of Biot and Arago:
Fig. 8. - Double Refraction.
Fig. 11. - Diffraction.
Fig. 12. - Explanation of Newton's Rings.
When a ray of light from a luminous source falls upon a glass plate at the polarizing angle, that portion of it which is refracted is also partially polarized. If that which has passed through one plate is afterward transmitted through several in succession having their surfaces parallel, the polarization may be made tolerably complete. The planes of polarization of the reflected and the refracted rays are at right angles to each other, as are the planes of polarization of the ordinary and extraordinary rays in Iceland spar. If two plates of tourmaline, a negative uniaxial crystal, which has been cut in sections parallel to its axis, are laid at right angles upon each other, as in rig. 17, the combination will be opaque; if placed diagonally, as in fig. 18, the opacity will be partial; and if they are placed parallel to each other, as in fig. 19, the light will pass through both as if they formed one piece. The light in passing through the first plate of tourmaline has been polarized, its vibrations having been reduced to one plane; or, as it is sometimes explained, all the rays except those which vibrate in one plane have been sifted out by the crystalline structure of the tourmaline, which has the property when not too thin of destroying the vibrations in the ordinary ray, and allowing only the extraordinary ray to pass through.
Therefore, in order that all the rays which have passed through the first plate may pass through the second, the axes of the two must be parallel. - Polarizing Apparatus. There are various pieces of apparatus used in investigating the properties of polarized light, and they always consist of two parts, a polarizer and an analyzer. In the experiment with the reflecting glass plates, fig. 14, the first plate is the polarizer and the second the analyzer. In the case of the tourmaline plates, figs. 17, 18, and 19, that through which the light first passes is the polarizer, and the other the analyzer; and in the original experiment with Iceland spar, the first rhomb was the polarizer and the second the analyzer. Iceland spar, as has been said, is one of the most perfect of polarizing substances, but it does not in its natural form separate the two rays far enough for convenience. The desired separation has been accomplished by a very ingenious device of Ni-col, a London optician, in the construction of a prism which bears his name. A rhombohedron of Iceland spar has its natural faces, which make an angle with the obtuse edges a and b, fig. 20, of 71°, cut to an angle of 68°. It is then cut in a section ef at right angles to the new faces a b and c d.
The two parts are again joined together in their original position with Canada balsam, and mounted in a manner convenient for use. The index of refraction in Iceland spar for the ordinary ray is 1.654, and for the extraordinary 1.483. The refractive index of Canada balsam is 1.549, so that when a ray of light m o enters the crystal at o and is divided into two rays, o i and o h, the ordinary ray o i is totally reflected by the surface of the Canada balsam in the direction i g, and refracted out of the crystal in g k; while the extraordinary ray o h passes through the balsam in the direction h n, and is refracted in the direction n p, parallel to m o. A beam of light therefore, passed through a Nicol's prism in this direction, will cast but one image upon a screen. This combination has been improved by Fou-cault by dispensing with the Canada balsam, thus having nothing between the divided surfaces except a film of air. If the length of the prism is such that the two rays may fall upon the divided surface at angles intermediate to those corresponding to the indices of refraction, the ordinary ray will be wholly reflected, while the extraordinary ray will be refracted, and therefore transmitted.
Malus's polarioscope, figs. 21 and 22, consists of two reflectors, A, the analyzer, and B, the polarizer. They are each composed of a pile of glass plates which may be turned about a horizontal axis, the analyzer also turning about a vertical axis, the angle of rotation being measured on the horizontal circle C C, which also holds the substance to be experimented upon. The polarizer is set so that a beam of light reflected at the polarizing angle shall be thrown vertically upward. If the analyzer is set at an angle of about 35° 25' from the perpendicular (the precise angle depending on the refractive index of the glass), the polarized ray will be reflected when the angles of incidence and refraction of the two mirrors are in the same plane, as shown in fig. 22, but will not be reflected when they are at right angles to each other, as in fig. 21. It is not necessary that both mirrors should have the same inclination to the vertical, the position given in the cut; that will depend on the direction of the incident ray. - Elliptic and Circular Polarization; Interference of Polarized Light. So far we have been considering cases in which the particles of ether in the polarized ray move in parallel straight lines at right angles to the direction of the ray, so that this lies in one plane; such is called plane polarized light.
But when the ethereal particles are acted on by forces tending to alter their planes of vibration, they are supposed to describe curves which may be either ellipses or circles, depending on the components forming the resultant. An elliptic vibration may result from the action of two rectilinear vibrations at right angles to each other which differ in phase, as in the ordinary and the extraordinary ray; therefore, when a plane polarized ray is reflected from a surface, or passed through a double-refracting plate cut parallel to its axis and placed in certain positions, it is either elliptically or circularly polarized. In the case of polarization by reflection, when the azimuth of the plane of polarization of the incident ray is 45°, we may conceive this resolved into two rays, one in the plane of incidence and the other in the perpendicular plane, which are equal to each other; and if they differ in phase by one quarter of an undulation, the light will be circularly polarized. According to the theory of Fresnel, the change of phase is produced at the moment of reflection, and the amount of change has been deduced by him through the most ingenious mathematical reasoning.
In reflection from St. Gobain glass Fresnel found the difference of phase in the two rays was one eighth of an undulation when the angle of incidence was 54° 37'. Therefore, if a rhomb of this glass is formed with its faces of incidence and emergence inclined to the other faces at this angle, and a ray is sent into it perpendicular to one of the faces, it will take the direction abcd, fig. 23, being reflected at the inner surfaces of the crystal at b and c, and emerge perpendicularly at the oppposite face, with a difference in phase of a quarter of an undulation. If therefore the incident ray is polarized in a plane inclined at an angle of 45° to the plane of reflection, the emergent light will be circularly polarized. This theory, the result of pure mathematical reasoning, was verified by experiment. If this circularly polarized ray is transmitted through a second rhomb parallel to the first, it will become plane-polarized.
Fig. 20. Nicol's Prism.
Fig. 22. Malus's Polariscope.
Fig. 23. - Fresnel's Rhomb.
If a plate of a double-refracting crystal, cut parallel to its axis, is interposed between the polarizer and analyzer of any polarizing apparatus, certain effects are produced when a strong beam of light is sent through it, "which depend upon the position of the interposed plate as well as upon the relative positions of the polarizer and analyzer. When the interposed plate has its axis parallel or perpendicular to the plane of the polarizer or analyzer, and these have their planes crossed at right angles, no change will take place in the phenomena, although in fact, when the axis of the interposed plate is perpendicular to the polarizer, it becomes itself an analyzer, and intercepts the polarized ray. When turned through an angle of 90°, it allows it to pass and be intercepted by the analyzer proper; but if it is turned around gradually, a portion of light will pass through the analyzer, which increases in quantity till it has been turned through an angle of 45°, when on further turning the light will gradually diminish till the plate has been turned through an additional angle of 45°, when it will vanish.
This phenomenon has been called depolarization, though improperly, and has been made use of by Malus to detect double-refracting substances in which no bifurcation of the rays could in any other way be detected. When the interposed plate is moderately thick, the transmitted light is white; but when reduced to a very thin plate or film, the most gorgeous colors appear, which vary with every change of inclination of the interposed plate. Thin plates of mica or selenite, from 1/30 to 1/60of an inch thick, are the most convenient for exhibiting these effects. If the thickness of the plate is uniform, the transmitted light will be of a uniform color, differing however with plates of different thickness, the intensity being greatest when the axis of the plate is inclined at an angle of 45° with the plane of primitive polarization, and the color vanishing altogether when the axis of the plate coincides with the plane of primitive polarization or is perpendicular to it. But if the interposed plate be fixed and the analyzer turned, the color will change through every grade of tint into the complementary color.
Suppose the position of the plate to be that in which the color is the brightest, viz., at an angle of 45°, and suppose the color to be red; now on turning the analyzer the color will grow fainter till it has moved through an angle of 45°, when it disappears, and no light is transmitted; on continuing to turn the analyzer, the complementary color green makes its appearance, increasing in intensity till a further angle of 45° is reached, when it will also begin to diminish, and finally vanish at a further angle of 45°, or 135° from the first position, when the red will again appear and attain its greatest brightness at 180° from the first position. Whatever may be the color at one position of the analyzer, the complementary color will appear on turning it through an angle of 90°. To prove that the colors are complementary, a double-refracting prism may be used as the analyzer, in which two rays will be transmitted, each of which will exhibit alternately the same changes of color; and if they are near enough together to overlap, the overlapping space will exhibit white light. When a plate is used which varies in thickness, the tints follow the laws of the colors of Newton's rings.
The thickness producing corresponding tints, however, is much greater in crystalline plates exposed to polarized light than in thin plates of air or any other uniform medium. The black of the first order appears in a plate of sulphate of lime when its thickness is 1/2000 of an inch, and between that and 1/50 of an inch is contained the whole succession of colors of Newton's scale. The color produced by a plate of mica in polarized light is the same as that reflected from a plate of air only 1/400 as thick. With Iceland spar the same color is produced when the thickness is about 13 times that of the plate of air. The physical explanation of these phenomena may be briefly stated as follows: A ray of light striking a double-refracting crystal is divided into two of unequal velocities, thus seemingly affording the conditions of interference if the plate is sufficiently thin; but if these conditions were sufficient, the phenomena of interference ought to be produced without the polarizing apparatus. But in polarized light the case of interference is different from that in ordinary light. In the latter the rays lie in. planes of all azimuths, while in polarized light they lie only in two planes at right angles, and therefore they cannot interfere with each other.
The subject was examined with reference to this point by Fresnel and Arago, who found that two rays polarized in the same plane interfere like two rays of ordinary light, and produce fringes, and that when the planes of polarization are inclined to each other the interference will be diminished until the angle between them is 90°. It was further found that two oppositely polarized rays will not interfere when their planes are made to coincide, unless they are derived from a pencil originally polarized in one plane, and which has lost or gained half an undulation in passing from one plane to the other. If now the planes of polarization of two rays which have been made to differ in length by half an undulation, or any odd number of half undulations, can be brought to coincide, interference will follow; and this is accomplished by interposing the thin plate of double-refracting crystal which causes the light that has been reduced to one plane by the polarizer to be divided into two rays, one ordinary and the other extraordinary, and differing in phase by half a wave length. - Colored Rings. If a thin plate of a double-refracting crystal, as Iceland spar, cut perpendicular to its axis, be substituted for the thin plate cut parallel with its axis used in the experiment last described, and a cone of converging or diverging rays is passed through it, or if the analyzer is brought so near to the eye that the visual rays converge toward its optic centre, brilliant colored rings are produced, differing in form according as the plate is uniaxial or biaxial.
A simple mode of viewing the phenomena is by employing the tourmaline pincetto, tig. 24, a small instrument made by placing two tourmalines cut parallel to their axes in two metallic disks, a 5, so that they may be turned in parallel planes and their axes given any angle to each other. A spring presses them together, by which means the substance to be examined may be held in position. When the plate of Iceland spar or other uniaxial crystal cut perpendicular to its optic axis is placed between the crossed tourmalines, and held near to the eye and toward the light, the rings above mentioned, intersected by a black cross, fig. 25, will be observed. If the tourmalines are placed with their axes parallel, the cross will be white, as shown in fig. 26, while the order of colors will be complementary. If homogeneous light is used, as for instance red, the rings will be simply red and black. If the light is violet, the rings will be violet and black, and they will be smaller, their size varying with the increase of refrangibility from red to violet.
To understand the formation of these rings, it must be remembered that rays of light which travel through the axis of a uniaxial crystal are alike in velocity, and therefore no chromatic effects will be produced in the centre; but the converging polarized rays, being inclined to the axis, will be divided into ordinary and extraordinary rays, with sufficient difference in phase to produce fringes by interference when reduced again to the same plane by the polarizer. The thickness of plate which the rays traverse increases with the divergence, so that at equal distances from the centre they will alternately conspire together or destroy each other, producing bright and dark rings. The explanation of the cause of the appearance of the crosses requires abstruse mathematical reasoning. The conclusions arrived at, however, are that in the two planes passing through the axis of the interposed plate, which are parallel and perpendicular to the axis of the polarizing tourmaline, the polarized ray is not resolved into two components, and consequently there are in those directions no conditions for interference. Therefore, when the tourmalines have their axes at right angles the cross will be black, and when they are parallel it will be white.
In biaxial crystals colored rings are produced having more complicated forms, the colored bands having the form of curves with two centres corresponding to the two optic axes of the crystal. If a plate of a biaxial crystal which has its optic axes inclined at a small angle, not exceeding 5° or 6°, is cut at right angles to the medial line and held between the tourmalines in such a manner that the plane of the optic axes is parallel to the axis of one of the tourmalines, an appearance represented in fig. 27 will be presented when the tourmalines are crossed. When the double-refracting plate is turned around in its plane, the rings turn in the same direction, while the cross separates into two branches, as seen in fig. 28; and when the plane of the axes makes an angle of 45° with the axes of the tourmalines, the appearance seen in fig. 29 results, the branches of the cross having the form of hyperbolas. When the axes of the tourmalines are parallel, the colors are complementary and the cross is white.
When a biaxial crystal is cut perpendicularly to one of its optic axes, it will present the appearance shown in fig. 30.
Fig. 24. - Tourmaline Pincetto.
Rotation of Plane of Polarization.
In the cases which have been considered the changes of plane which take place when a polarized ray is reflected or refracted are definite and independent of the distances through which it passes in either medium; but there are substances which change the plane of polarization in proportion to their thickness. If a ray of polarized light is sent through a plate of Iceland spar or other uniaxial crystal in the direction of its axis, its plane is not changed; hut when a plate of rock crystal is cut in the same direction and a polarized ray of homogeneous light is passed through its axis, its plane will be found changed on emergence. It will have rotated on its axis, and this rotation may he either to the right or to the left, and the amount of rotation will depend upon the thickness of the plate. The direction of the rotation serves to classify such crystals into right-and left-handed. If the prisms of the polarizing apparatus are crossed so as to produce extinction of light, and the substance to he examined then introduced, there will be, if it possesses the properties above mentioned, a partial restoration of light.
If now the analyzer is turned through a certain number of degrees, the light will again disappear, and the angle through which the analyzer has been turned will be the measure of the rotating power of the substance. The principal laws of rotatory polarization, the discovery of which is due to Biot, embrace the following facts: 1. With the same substance the rotation of the plane of polarization is in proportion to the thickness of the substance traversed. 2. When two plates are placed together, the effect is nearly the same as that of a single plate whose thickness is equal to the sum or difference of the two plates, according as they rotate the ray in the same or opposite directions. 3. The degrees of rotation of the plane of polarization vary with the different rays of the spectrum, and increase with their refrangibility. For a given plate the angle of rotation is inversely as the square of the length of the wave. Therefore, as the rays of different colors emerge polarized in different planes, if a beam of white light is sent through a rotating crystal or substance and then received by the analyzing prism or plate, as this is turned the different colored rays of polarized light will make their appearance in succession.
Sir David Brewster discovered that amethyst or violet quartz is made up of alternate layers of right- and left-handed quartz; and the structure may be distinguished in the fracture of the crystal, which presents a peculiar undulating appearance. Biot and Seebeck discovered that many liquids and vapors have, like quartz, the power of rotating the plane of polarization. Oil of lemon, solution of sugar in water, and solution of camphor in alcohol rotate the polarized ray to the left; oil of turpentine rotates it to the right. The power of these liquids is, however, much feebler than that of quartz, and therefore greater thicknesses are required to be employed. When liquids having this property are mixed, the rotation produced by the mixture is equal to the sum or difference of that of the ingredients, and Biot made an application of this principle to the analysis of compounds containing a substance having rotatory power, combined with others which are neutral. Polarized light, therefore, has a practical application as a test for a variety of substances; many cases of doubtful identity in chemical analysis being alone decided by its use. The saccharometer of M. Soleil is constructed in accordance with these properties of light.
It is used in the arts for ascertaining the percentage of sugar in solutions, and in medicine for testing its presence, as well as determining its quantity in the fluids of the body. It may also be applied in detecting albumen and other organic bodies. Arago employed polarization by double refraction in the construction of a photometer; and he has also shown how rocks beneath the surface of water may be discovered by using a Nicol's prism to extinguish the reflected rays by which the submerged rocks are prevented from being seen. Chromatic polarization may be employed with advantage in crystallography, to indicate whether a crystal has one or two axes of symmetry, and also the positions of these axes. By the use of the polariscope we may ascertain whether the light which comes to us from the heavenly bodies is reflected from their surfaces, as from the moon and planets, or whether the bodies are self-luminous. - Faraday made the discovery that the plane of polarization can be rotated by the action of magnetism.
If a cylin-drical or rectangular bar of "heavy" or "Faraday's glass " (silico-borate of lead) is placed longitudinally between the poles of a powerful electro-magnet which is hollow in its axis (to admit of observation), and a Nicol's prism is placed in one end of the magnet as polarizer, and another in the other end as analyzer, and they be so turned that no light passes through both, then, as long as no current passes around the temporary magnet, the interposition of the glass bar will have no effect; but when a current is passed around the magnet, rotation of the plane of polarization takes place, and in the direction of the current. The degree of rotation is in proportion to the length of the bar and the strength of the current. Flint glass is acted on with about half as great effect as heavy glass, and all transparent solids and liquids are more or less affected in the same manner. Faraday thought that the magnetism had a direct action on the light, but others have since believed that the rotation is produced by a molecular change induced in the glass by the magnet. It has been stated that when glass is subjected to strain or unequal pressure its homogeneous texture is altered, and the particles are so disposed that it acquires the property of double refraction.
It consequently has the power of producing polarization of light transmitted through it, analogous to that possessed by natural double-refracting crystals. The compression or strain may be produced by rapid cooling of fused glass, or the glass may be compressed in a vice. - From the fact that polarization always takes place when rays of light are reflected from surfaces at particular angles, it follows that much of the light that is transmitted through the air is more or less polarized in consequence of being reflected from the surfaces of the numerous contained particles of atmospheric dust and vapor. If the sky is examined through a Ni-col's prism, it will be found that the greatest amount of polarization is in rays that come from directions at right angles to the sun; that is to say, when the sun is in the horizon, from an arc passing through the zenith, each end meeting the horizon 90° from the position of the sun. If the sun were in the zenith, the greatest amount of polarization would be in the circular horizon.
It is evident, therefore, that if a polarizing apparatus is held with its axis perpendicular to the path of the sun, an interposed selenite plate or other double-refracting crystal, by causing interference of polarized light, will afford an indication of the time of day. An instrument based upon this principle invented by Sir Charles Wheatstone, called a polar clock, is another of the practical applications of the more refined discoveries in molecular physics. (See Polar Clock.) Prof. Tyndall, in making experiments upon minute quantities of gaseous vapors, found that when condensation commenced, if a powerful ray of light was sent through the experimental tube, an " incipient cloud " was illuminated, which upon examination was found to reflect polarized light. This at first would be a very pure blue, and nearly perfectly polarized in a direction perpendicular to the beam of light; but as the vapory particles became larger the cloud became whiter, and the amount of polarization diminished till at last it was not perceptible. The vapor which gave the greatest effect was that of nitrite of butyle.
He concludes that at the first formation of the cloud the vapory particles are less in diameter than the length of a wave of light, so that the most refrangible rays are the first to be scattered, the addition of the others producing white light. It is therefore concluded that the blue color of the heavens is owing to the scattering of the more refrangible rays of light by the minute particles of aqueous vapor held in the atmosphere before any visible condensation has taken place, and that the white color of clouds is owing to the scattering of all the rays. It appears that the polarizing angle for matter in a state of vapor does not follow the ordinary law and change with the substance, but that it is always 45°, so that the polarized is always at right angles to the reflected beam. Several facts in regard to atmospheric polarization were observed many years ago by Sir David Brewster, Sir John Hersehel, and others. - The verification of Fresnel's prediction in regard to circular polarization was one of the great tests of the un-dulatory theory of light, as well as an example of the transcendent power of genius. An equally remarkable example was the deduction from Fresnel's theory of double refraction of a result which that mathematician had not himself foreseen.
This deduction was made by Sir William Hamilton, and experimentally verified by Dr. Lloyd of Dublin. According to Fresnel's theory of double refraction in biaxial crystals, the wave surface intersects the plane of the crystal in a circle and an ellipse whose magnitude is such that they intersect at four points, as represented in fig. 31. Dr. Lloyd's explanation is as follows: "When two rays pass within the crystal in any common direction, as O A B, their velocities are represented by the radii vec-tores of the two parts of the wave O A and O B, and their directions at emergence are determined by the positions of the tangent planes at the points A and B. But in the case of the ray 0 P, whose direction is that of the line joining the centre with one of the four cusps which are formed by the intersections of the circle and ellipse, the two radii vectores unite, and the two rays have the same velocity. There are still, however, two tangents to the plane section at the point P; so that it might be supposed that the rays proceeding with this common velocity within the crystal would still be divided at emergence into two, and two only, whose directions are determined by the tangent planes; and this seems to have been Fresnel's view.
But Sir William Hamilton has shown that there is a cusp at each of the four points just mentioned, not only in this particular section, but in every section of the wave surface passing through the line O P, or that there is a conoi-dal cusp on that surface at the four points of the intersection of the circle and ellipse, and consequently an infinite number of tangent planes which form a tangent cone of the second degree. Hence a single ray, such as 0 P, proceeding within the crystal in one of these directions, should be divided into an infinite number of rays at emergence, whose directions and planes of polarization are determined by the tangent planes. Again, it is evident that the circle and ellipse have four common tangents, such as M N; and the planes passing through these tangents, and perpendicular to the plane of the section, are perpendicular to the optic axis of the crystal. Fresnel seems to have thought that these planes touched the wave surface in the two points just mentioned, and in these only; and consequently that a single ray (incident upon a biaxial crystal in such a manner that one of the refracted rays should coincide with an optic axis O M) will be divided into two within the crystal, O M and O N, determined by the points of contact.
But Sir William Hamilton has shown that the four planes touch the wave surface, not in two points only, but in an infinite number of points, constituting each a small circle of contact; and consequently that a single ray of common light, incident externally in the above mentioned direction, should be divided into an infinite number of refracted rays within the crystal. Here are two singular and unexpected consequences of Fresnel's theory, not only unsupported by any facts hitherto observed, but even opposed to all the analogies derived from experience; here are two remote conclusions of that theory deduced by the aid of a refined analysis, and in themselves so strange that we are inclined at first to reject the principles of which they are the necessary consequences. They accordingly furnish a test of the truth of that theory of the most trying nature that can be imagined.'1 Dr. Lloyd, at Sir William Hamilton's request, made the following experiments: There were two cases in which it was expected cones of light would be produced. The first was that of external conical refraction.
A plate of aragonite, a biaxial crystal, was prepared with its faces perpendicular to the line o p, fig. 32, bisecting the optic axis, which in aragonite contains an angle of about 20°. "A thin metallic plate perforated with a very minute aperture was placed on each face of the crystal, with one aperture at o and the other at m. The flame of a lamp was then brought near one of the apertures, and in such a position that the central ray of the converging beam should have an incidence of 15° or 16°. When the adjustment was completed a brilliant an-nulus of light (fig. 33) appeared on looking through the aperture in the second surface. When the aperture in the second plate was very slightly changed so that the line connecting the two apertures no longer coincided with the line m o. the phenomena rapidly changed and the annulus resolved itself into two separate pencils." It was found that the rays composing the emergent cone were all polarized in different planes, which are connected by the following law: " The angle between the planes of polarization of any two rays of the cone is half the angle between the planes containing the rays themselves and the axis." The law was discovered by observation, but may be deduced from Fresnel's theory. "The other case, that of internal conical refraction, was expected to take place when a single ray has been incident externally upon a biaxial crystal in such a manner that one of the refracted rays may coincide with an optic axis.
The incident ray in this case should be divided into a cone of rays within the crystal, the angle of which, in the case of aragonite, is 1° 55'. The rays comprising this cone will be refracted at the second surface in directions parallel to the incident ray so as to form a small cylinder of rays in air whose base is the section of the cone made by the surface of emergence. This is represented in fig. 34, in which n o is the incident ray, a o b the cone of refracted rays within the crystal, and a a' b b' the emergent cylinder." This experiment was more difficult than the other. Suffice it to say that when the required position was attained the two rays into which the incident ray was divided "suddenly spread out into a continuous circle." The experiment was repeated with the sun's light, and the cylinder received on a screen at various distances, but with no change in the size of the section. The observed angle of the cone was 5' less than the theoretical, 1° 55'. The rays of the internal cone are all polarized in different planes, and governed by the same laws as in the other case. - Polarization of Heat. The rays of heat being identical in nature with those of light, it might be supposed that they would be governed by similar laws of double refraction and polarization, and this has been found to be the case.
The first experiments were made by Malus and Berard in 1810. By using a piece of rock salt formed in the shape of a rhombohedron similar to Fresnel's rhomb, of St. Gobain glass, Forbes found that heat, like light, is circularly polarized. It has also been shown by Knoblauch and others that the rays of heat suffer diffraction and interference like those of light. - Chemical Action of Light. A great many substances undergo chemical change when exposed to the light of the sun, or to that of certain artificial sources. This is explained upon the undulatory theory by supposing that the kinetic energy of the molecules of ether is transferred to the molecules of the substance in such a degree as to cause them to be shaken asunder. The measurement of the chemical action of light and the investigation of its laws were successfully commenced by Dr. John W. Draper of New York about the year 1840. He employed for the purpose of measurement a reaction originally observed by Gay-Lussac and Thenard, which takes place in a mixture of chlorine and hydrogen - gradually in diffuse, explosively in direct sunlight.
His apparatus enabled him to determine the amount of hydrochloric acid which would be produced in a given time with given volumes of the gases; and although these were pioneer experiments, they led him to the first great law of photo-chemical action, viz.: " that the chemical action of light varies in direct proportion to its intensity, and to the time of the exposure." The subject has been since examined by others, particularly by Bunsen and Roscoe, whose experiments, together with other matter pertaining to the subject, will be found in the articles Photometry and Photography. - For a more extended consideration of the subject of light, see the treatise on the undulatory theory of light by President F. A. P. Barnard, published in the Smithsonian report for 1862; an "Essay on the Velocity of Light," by M. Delaunay, translated by Alfred M. Mayer, in the Smithsonian report for 1864; CEuvres completes d'Augnstin Fresnel (3 vols., Paris, 1867-'70); Wullner's Lehrbuch der Experimental Physik (vol. ii., Leipsic, 1871); and " The Wave Theory of Light," by Humphrey Lloyd, 1). D., D. C. L. (London, 1873).