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REOUETMEI1101X .130 1.35 1.40 545
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1.65 570 1.76
most valuable in distinguishing the See also:precious stones. It consists of a hemisphere of very dense See also:glass, having its See also:plane See also:surface fixed
at a certain See also:angle to the See also:axis of the See also:instrument. See also:Light is admitted by a window on the under See also:side, which is inclined at the same angle, but in the opposite sense, to the axis. The light on emerging from the hemisphere is received by a See also:convex See also:lens, in the See also:focal plane of which is a See also:scale graduated to read directly in refractive indices. The light then traverses a See also:positive See also:eye-piece. To use the instrument for a See also:gem, a few drops of methylene iodide (the refractive See also:index of which may be raised to 1.800 by dissolving See also:sulphur in it) are placed on the plane surface of the hemisphere and a facet of the See also: This law was discovered about eight years later by See also:Christian See also:Huygens. According to Huygens' fundamental principle, the law of refraction is determined by the See also:form and See also:orientation of the See also:wave-surface in the crystal—the See also:locus of points to which a disturbance emanating from a luminous point travels in unit See also:time. In the case of a doubly refracting See also:medium the wave-surface must have two sheets, one of which is spherical, if one of the pencils obey in all cases the ordinary law of refraction. Now Huygens observed that a natural crystal of spar behaves in precisely the same way which-ever pair of faces the light passes through, and inferred from this fact that the second See also:sheet of the wave-surface must be a surface of revolution See also:round a line equally inclined to the faces of the rhomb, i.e. round the axis of the crystal. He accordingly assumed it to be a See also:spheroid, and finding that refraction in the direction of the axis was the same for both streams, he concluded that the See also:sphere and the spheroid touched one another in the axis. So far as his experimental means permitted, Huygens verified the law of refraction deduced from this See also:hypothesis, but its correctness remained unrecognized until the See also:measures of W. H. See also:Wollaston in 18oz and of E. T. See also:Malus in 181o. More recently its truth has been established with far more perfect See also:optical appliances by R. T. Glazebrook, Ch. S. See also:Hastings and others. In the case of Iceland spar and several other crystals the extraordinarily refracted stream is refracted away from the axis, but See also:Jean See also:Baptiste See also:Biot in 1814 discovered that in many cases the See also:reverse occurs, and attributing the extraordinary refractions to forces that See also:act as if they emanated from the axis, he called crystals of the latter See also:kind " attractive," those of the former " repulsive." They are now termed " positive " and " negative " respectively; and Huygens' law applies to both classes, the spheroid being prolate in the case of positive, and oblate in the case of negative crystals. It was at first supposed that Huygens' law applied to all doubly refracting media. See also:Sir See also:David See also:Brewster, however, in 1815, while examining the rings that are seen round the optic axis in polarized light, discovered a number of crystals that possess two optic axes. He showed, moreover, that such crystals belong to the rhombic, See also:monoclinic and anorthic (triclinic) systems, those of the tetragonal and hexagonal systems being uniaxal, and those of the cubic See also:system being optically isotropic. Huygens found in the course of his researches that the streams that had traversed a rhomb of Iceland spar had acquired new properties with respect to transmission through a second crystal. This phenomenon is called polarization (q.v.), and the waves are said to be polarized—the ordinary in its See also:principal plane and the extraordinary in a plane perpendicular to its principal plane, the principal plane of a wave being the plane containing its normal and the axis of the crystal. From the facts of polarization Augustin Jean See also:Fresnel deduced that the vibrations in plane polarized light are rectilinear and in the plane of the wave, and arguing from the symmetry of uniaxal crystals that vibrations perpendicular to the axis are propagated with the same See also:speed in all directions, he pointed out that this would explain the existence of an ordinary wave, and the relation between its speed and that of the extraordinary wave. From these ideas Fresnel was forced to the conclusion, that he at once verified experimentally, that in biaxal crystals there is no spherical wave, since there is no single direction round which such crystals are symmetrical; and, recognizing the difficulty of a See also:direct determination of the wave-surface, he attempted to represent the See also:laws of double refraction by the aid of a simpler surface. The essential problem is the determination of the propagational speeds of plane waves as dependent upon the directions of their normals. These being known, the See also:deduction of the wave-surface follows at once, since it is to be regarded as the envelope at any subsequent time of all the plane waves that at a given instant may be supposed to pass through a given point, the See also:ray corresponding to any tangent plane or the direction of transport of See also:energy being by Huygens' principle the See also:radius-vector from the centre to the point of contact. Now Fresnel perceived that in uniaxal crystals the speeds of plane waves in any direction are by Huygens' law the reciprocals of the semi-axes of the central See also:section, parallel to the wave-fronts, of a spheroid, whose polar and See also:equatorial axes are the reciprocals of the equatorial and polar axes of the spheroidal sheet of Huygens' wave-surface, and that the plane of polarization of a wave is perpendicular to the axis that determines its speed. Hence it occurred to him that similar relations with respect to an See also:ellipsoid with three unequal axes would give the speeds and polarizations of the waves in a biaxal crystal, and the results thus deduced he found to be in accordance with all known facts. This ellipsoid is called the ellipsoid of polarization, the index ellipsoid and the indicatrix. We may go a step further; for by considering the intersection of a wave-front with two waves, whose normals are indefinitely near that of the first and See also:lie in planes perpendicular and parallel respectively to its plane of polarization, it is easy to show that the ray corresponding to the wave is parallel to the line in which the former of the two planes intersects the tangent plane to the ellipsoid at the end of the semi-See also:diameter that determines the wave-velocity; and it follows by similar triangles that the ray-velocity is the reciprocal of the length of the perpendicular from the centre on this tangent plane. The laws of double refraction are thus contained in the following proposition. The propagational speed of a plane wave in any direction is given by the reciprocal of one of the semi-axes of the central section of the ellipsoid of polarization parallel to the wave; the plane of polarization of the wave is perpendicular to this axis; the corresponding ray is parallel to the line of intersection of the tangent plane at the end of the axis and the plane containing the axis and the wave-normal; the ray-velocity is the reciprocal of the length of the perpendicular from the centre on the tangent plane. By reciprocating with respect to a sphere of unit radius concentric with the ellipsoid, we obtain a similar proposition in which the ray takes the place of the wave-normal, the ray-velocity that of the wave-slowness (the reciprocal of the velocity) and See also:vice versa. The wave-surface is thus the apsidal surface of the reciprocal ellipsoid; this gives the simplest means of obtaining its See also:equation, and it is readily seen that its section by each plane of optical symmetry consists of an See also:ellipse and a circle, and that in the plane of greatest and least wave-velocity these curves intersect in four points. The radii-vectors to these points are called the ray-axes. When the wave-front is parallel to either system of circular sections of the ellipsoid of polarization, the problem of finding the axes of the parallel central section becomes indeterminate, and all waves in this direction are propagated with the same speed, whatever may be their polarization. The normals to the circular sections are thus the optic axes. To determine the rays corresponding to an optic axis, we may See also:note that the rayand the perpendiculars to it through the centre, in planes perpendicular and parallel to that of the ray and the optic axis, are three lines intersecting at right angles of which the two latter are confined to given planes, viz. the central circular section of the ellipsoid and the normal section of the See also:cylinder touching the ellipsoid along this section: whence by a known proposition the ray describes a See also:cone whose sections parallel to the given planes are circles. Thus a plane perpendicular to the optic axis touches the wave-surface along a circle. Similarly the normals to the circular sections of the reciprocal ellipsoid, or the axes of the tangent cylinders to the polarization-ellipsoid that have circular normal sections, are directions of single-ray velocity or ray-axes, and it may be shown as above that corresponding to a ray-axis there is a cone of wave-normals with circular sections parallel to the normal section of the corresponding tangent cylinder, and its plane of contact with the ellipsoid. Hence the extremities of the ray-axes are conical points on the wave-surface. These peculiarities of the wave-surface are the cause of the celebrated conical refractions discovered by Sir See also: In the case of the monoclinic system one axis is in the direction of the axis of the system, and this is generally, though there are notable exceptions, either the greatest, the least, or the intermediate axis of the ellipsoid for all colours and temperatures. In the latter case the optic axes are in the plane of symmetry, and a variation of their acute See also:bisectrix occasions the phenomenon known as " inclined See also:dispersion ": in the two former cases the plane of the optic axes is perpendicular to the plane of symmetry, and if it vary with the colour of the light, the crystals exhibit " crossed " or " See also:horizontal dispersion " according as it is the acute or the obtuse bisectrix that is in the fixed direction.
The optical constants of a crystal may be determined either with a See also:prism or by observations of See also:total reflection. In the latter case the phenomenon is characterized by two angles—the See also:critical angle and the angle between the plane of incidence and the line limiting the region of total reflection in the field of view. With any crystalline surface there are four cases in which this latter angle is 9 0, and the principal refractive indices of the crystal are obtained from those calculated from the corresponding critical angles, by excluding that one of the mean values for which the plane of polarization of the limiting rays is perpendicular to the plane of incidence. A difficulty, however, may arise when the crystalline surface is very nearly the plane of the optic axes, as the plane of polarization in the second mean case is then also very nearly perpendicular to the plane of incidence; but since the two mean refractive indices will be very different, the See also:ambiguity can be removed by making, as may easily be done, an approximate measure of the angle between the optic axes and comparing it with the values calculated by using in turn each of these indices (C. M. See also:Viola, Zeit. See also:fur Kryst., 1902, 36, p. 245).
A substance originally isotropic can acquire the optical
properties of a crystal under the See also:influence of homogeneous See also:strain, the principal axes of the wave-surface being parallel to those of the strain, and the medium being uniaxal, if the strain be symmetrical. See also: 337). Not content with determining the laws of double refraction, Fresnel also attempted to give their See also:mechanical explanation. He supposed that the See also:aether consists of a system of distinct material points symmetrically arranged and acting on one another by forces that depend for a given pair only on their distance. If in such a system a single See also:molecule be displaced, the See also:projection of the force of restitution on the direction of displacement is proportional to the inverse square of the parallel radius-vector of an ellipsoid; and of all displacements that can occur in a given plane, only those in the direction of the axes of the parallel central section of the See also:quadric develop forces whose projection on the plane is along the displacement. In undulations, however, we are concerned with the elastic forces due to relative displacements, and, accordingly, Fresnel assumed that the forces called into See also:play during the See also:propagation of a system of plane waves (of rectilinear transverse vibrations) differ from those See also:developed by the parallel displacement of a single molecule only by a See also:constant See also:factor, See also:independent of the plane of the wave. Next, regarding the aether as incompressible, he assumed that the components of the elastic forces parallel to the wave-front are alone operative, and finally, on the See also:analogy of a stretched See also:string, that the propagational speed of a plane wave of permanent type is proportional to the square See also:root of the effective force developed by the vibrations. With these hypotheses we immediately obtain the laws of double refraction, as given by the ellipsoid of polarization, with the result that the vibrations are perpendicular to the plane of polarization. In its dynamical See also:foundations Fresnel's theory, though of considerable See also:historical See also:interest, is clearly defective in rigour, and a strict treatment of the aether as a crystalline elastic solid does not lead naturally to Fresnel's laws of double refraction. On the other See also:hand, See also:Lord See also:Kelvin's rotational aether (Math. and Phys. Papers, iii. 442)—a medium that has no true rigidity but possesses a quasi-rigidity due to elastic resistance to See also:absolute rotation—gives these laws at once, if we abolish the resistance to See also:compression and, regarding it as gyrostatically isotropic, attribute to it aeolotropic inertia. The equations then obtained are the same as those deduced in the electro-magnetic theory from the circuital laws of A. M. See also:Ampere and See also:Michael See also:Faraday, when the specific inductive capacity is supposed aeolotropic. In order to See also:account for dispersion, it is necessary to take into account the interaction with the See also:radiation of the See also:intra-molecular vibrations of the crystalline substance: thus the total current on the electro-magnetic theory must be regarded as made up of the current of displacement and that due to the oscillations of the electrons within the molecules of the crystal. See also:Optics (1904) ; R. W. See also:Wood, See also:Physical Optics (1905) ; E. Mascart, Traite d'optique (1889) ; A. See also:Winkelmann, Handbuch der Physik. (J. WAL.*) The refraction of a ray of light by the See also:atmosphere as it passes from a heavenly See also:body to an observer on the See also:earth's surface, is called "astronomical." A knowledge of its amount is a necessary datum in the exact determination of the direction of the body. In its investigation the fundamental hypothesis is that the strata of the See also:air are in See also:equilibrium, which implies that the surfaces of equal See also:density are horizontal. But this See also:condition is being continually disturbed by aerial currents, which produce continual slight fluctuations in the actual refraction, and commonly give to the See also:image of a See also:star a tremulous See also:motion. Except for this slight motion the refraction is always in the See also:vertical direction; that is, the actual See also:zenith distance of the star is always greater than its apparent distance. The refracting See also:power of the air is nearly proportional to its density. Consequently the amount of the refraction varies with the temperature and barometric pressure, being greater the higher the See also:barometer and the See also:lower the temperature. At moderate zenith distances, the amount of the refraction varies nearly as the tangent of the zenith distance. Under ordinary conditions of pressure and temperature it is, near the zenith, about 1" for each degree of zenith distance. As the tangent increases at a greater See also:rate than the angle, the increase of the refraction soon exceeds 1" for each degree. At 450 from the zenith the tangent is 1 and the mean refraction is about 58". As the See also:horizon is approached the tangent increases more and more rapidly, becoming See also:infinite at the horizon; but the re-fraction now increases at a less rate, and, when the observed ray is horizontal, or when the See also:object appears on the horizon, the refraction is about 34', or a little greater than the diameter of the See also:sun or See also:moon. It follows that when either of these See also:objects is seen on the horizon their actual direction is entirely below it. One result is that the length of the See also:day is increased by refraction to the extent of about five minutes in See also:low latitudes, and still more in higher latitudes. At 6o° the increase is about nine minutes. The atmosphere, like every other transparent substance, refracts the blue rays of the spectrum more than the red; consequently, when the image of a star near the horizon is observed with a See also:telescope, it presents somewhat the See also:appearance of a spectrum. The edge which is really highest, but seems lowest in the telescope, is blue, and the opposite one red. When the atmosphere is steady this atmospheric spectrum is very marked and renders an exact observation of the star difficult. Among the tables of refraction which have been most used are See also:Bessel's, derived from the observations of See also:Bradley in Bessel's Fundamenta Astronomiae; and Bessel's revised tables in his Tabulae Regiomontanae, in which, however, the constant is too large, but which in an See also:expanded form were mostly used at the observatories until 187o. The constant use of the Poulkova tables, Tabulae refractionum, which is reduced to nearly its true value, has gradually replaced that of Bessel. Later tables are those of L. de See also:Ball, published at See also:Leipzig in 1906. (S. Additional information and CommentsThere are no comments yet for this article.
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