Double refraction

“ Having done this for the sake of Polarization, we turn to the phenomena of Double Refraction, and inquire what new hypothesis they require. But the answer is, that they require none: the supposition of transverse vibrations, which we have made in order to explain Polarization, gives us also the law of Double Refraction. Truth may give rise to such a coincidence; falsehood cannot. Again, the facts of Dipolarization come into view. But they hardly require any new assumption ”

“ It follows from these assumptions that a crystal will produce double refraction and polarisation of electric waves which fall upon it, and, further, that the laws of double refraction will be those given by Fresnel for light waves in a doubly refracting medium. ”

“ THE FitzGerald-Lorentz [2] "Contraction" Hypothesis to explain the negative results of the Michelson-Morley [3] experiment of interference between two rays, at right angles and parallel to the earth's motion, has been tested by Rayleigh [4] in his experiments on the double refraction of liquids and of glass. He assumes the contraction to be , and also the excess of the index above unity to be proportional to the density. ”

“ Again, if the rays be transmitted in two directions, as with certain crystals, “double refraction” (see Refraction, Double) takes place, and the emergent rays have undergone Polarization. A Shadow is cast by light falling on an opaque object, the complete theory of which involves the phenomenon of Diffraction. ”

“ It was soon seen that the explanation of refraction was arbitrary, and that of double refraction illusory; while polarization entirely eluded the grasp of this machinery. Centers of force would no longer represent the modes of causation which belonged to the phenomena. Polarization required some other contrivance, such as the undulatory theory supplied. No theory of light can be of any avail in which the fundamental idea of Polarity is not clearly exhibited. ”

“ If the suggested double refraction, due to the earth's motion, were large enough, it would suffice to set the analysing nicol to extinction in one position of the board, and to observe the revival of light consequent on a rotation of the latter through 90°. But a more delicate method is possible and necessary. Between the polarizing nicol and the liquid column we introduce a strip of glass whose length is horizontal and transverse to the board. ”

“ No Body has this Construction except Spar; therefore no other natural or artificial Substance has this Power of double Refraction. Even Sir Isaac Newton has said, Crystal has something of this Power; in vain: For no Authority can stand against the Testimony of the Senses. All different Mediums vary in Refraction; but this peculiar Power resides only in a pellucid Body formed of connected Rhombs. ”

“ Since only crystals possessing the property of double refraction show polarisation, it follows that those of the 1st, or cubic system—in which the diamond stands a prominent example—fail to become polarised, so that when such a stone is placed in the polariscope and [Pg 28] rotated, it fails at every point to transmit light, which a double-refracting gem allows to pass except when its optical axis is placed in the axis of the polariscope, but this will be dealt with more fully when the methods of testing the stones come to be considered. ”

“ But there is between its double refraction and that of the spar, this capital difference, observed by M. Biot, that in the spar the deviation of extraordinary rays from the axis, is greater than that of the ordinary, whereas in quartz crystals it is less. All crystals with one axis, that he has examined, have been found to possess one or other of these modes of action, which has occasioned their distinction, by him, into crystals of attractive and repulsive double refraction ”

“ He then proceeded to consider the relation of the direction of vibration to the plane of polarization. "Apply these ideas to double refraction, and regard a uniaxal crystal as an elastic medium in which the accelerating force which results from the displacement of a row of molecules perpendicular to the axis, relative to contiguous rows, is the same all round the axis; while the displacements parallel to the axis produce accelerating forces of a different intensity, stronger if the crystal "repulsive," and weaker if it is "attractive." ”

“ There is no part of the optical labours of Newton which is less satisfactory than that which relates to the double refraction of light. In 1690, Huygens, published his admirable treatise on light, in which he has given the law of double refraction in calcareous spar, as deduced from his theory of light, and as confirmed by direct experiment. ”

“ If, therefore, a beam that has been rendered conical by a converging lens be sent through the spar so that the central ray of the cone passes along the axis, this ray only will escape double refraction. Each of the others will be divided into an ordinary and an extraordinary ray, the one moving more slowly through the crystal than the other; the one, therefore, retarded with reference to the other. Here, then, we have the conditions for interference, when the waves are reduced by the analyzer to a common plane. ”

“ Much experimental work has been done on the production of polarized rays by double refraction and on the reflection of polarized light, either by isotropic or by anisotropic transparent bodies, the object of inquiry being in the latter case to determine the position of the plane of polarization of the reflected rays and their intensity. ”

“ It may be added that the subject does admit of perfect experimental treatment, since glass, when compressed in one direction, becomes capable of doubly-refracting light, and as there is probably no alteration in the glass but change of elasticity, we learn that the power of double refraction is probably due to a difference of elasticity in different directions. ”

“ If this retardation amounted to 1⁄2λ, λ being the wave-length, the effect would be the same as of a rotation of the nicol through 90°. In general, a retardation of phase ε, in place of π, gives a revival of light measured by sin2 (1⁄2ε) . If the revivals of light in the two cases be the same, we may equate θ to 1⁄2ε. Hence if we find that rotation θ produces a sensible effect in lessening the darkness at the darkest place, we may infer that there is delicacy sufficient to detect a relative retardation of 2θ due to double refraction. ”

“ When a ray of light has undergone polarization in a certain direction, by the process above described, it carries that property with it, and preserves it without sensible alteration, when made to pass perpendicularly through even considerable thicknesses of air, water, and, in general, any substance that exerts only single refraction, but double refracting media alter, in general, the polarization of a ray, and in a manner, to all appearance, sudden, communicating to it a new polarization of the same nature in a different direction. ”

“ The liquid, held in a horizontal tube closed at the ends by plates of thin glass, was placed, of course, between the nicols. When at 12 o'clock the board stands north and south, the earth's motion is transverse and the situation is such as to exhibit any double refraction which may ensue. It might be supposed, for instance, that luminous vibrations parallel to the earth's motion, i. e. east and west, are propagated a little differently from those whose direction is transverse to the earth's motion, i. ”

“ It will readily be conceived that the unequal refrangibility of light must give rise to a good deal of confusion in all images produced by refraction. For instance, a pencil of rays diverging from a point on the axis of a convex-lens will be collected, not to one single focus, but to a series of foci lying at different distances from the lens along its axis, and there will consequently be a confusion analogous to that arising from the aberration which we found to be produced by the spherical form of a refracting surface. ”

“ I have hitherto preferred the null method in my experiments, as it possesses many advantages. The sensitiveness of the receiver can be pushed to the utmost extent, and observations taken when no effect is produced on the receiver. The total reflection method also dispenses with the difficulty of making accurate measurement of the deviation produced. After obtaining the value of the index by the method described above, I was desirous to see whether it was not possible to obtain fairly good results by measuring the angle of refraction corresponding to a given angle of incidence. ”

“ Having thus cleared away the kinematic interpretation of the coin-in-the-bowl phenomenon, we may pass on to discuss the optical effect through which the so-called law of refraction was first established in science. Instead of picturing to ourselves, as is usually done, light-rays which are shifted away from or towards the perpendicular at the border-plane between two media of different optical properties, we shall rather build up the picture as light itself designs it into space. ”

“ A ray of light may, for our purposes, be presented to the mind as a luminous straight line. Let such a ray be supposed to fall vertically upon a perfectly calm water-surface. The incidence, as it is called, is then perpendicular, and the ray goes through the water without deviation to the right or left. In other words, the ray in the air and the ray in the water form one continuous straight line. But the least deviation from the perpendicular causes the ray to be broken, or "refracted," at the point of incidence. What, then, is the law of refraction discovered by Snell? ”

“ If the ray after emergence from the refracting substance, that we have just been considering, meet with another with surfaces parallel to those of the former, whose thickness is and for which the ratio of refraction is its direction will, after the second emergence, be of course parallel to the former, and its intersection with will be removed by an additional distance so that the whole deviation will be and if there were more refracting substances of the same description, their effects would, in like manner, be all added together. ”

“ Luminous undulations ought to produce a similar effect when the medium in which they are excited is terminated by a body in which the density of the ethereal fluid is different; that is to say, there must be produced a reflected wave and one transmitted; which is, in fact, what we call reflexion and refraction. In this system, the intensities of rays of light must be measured by the vis viva of the fluid in motion, that is, by the product of the density of the fluid by the square of the proper velocity of its particles. ”

“ The denser the medium is, the less is the angle and sine of refraction. If a ray of light MC, were to pass from air into water, or from empty space into air, in the direction MC perpendicular to the plane NO which separates the two mediums, it would suffer no refraction, because one of the essentials to that effect is wanting, namely, the obliquity of the incidence. ”

“ Although a ray when passing from one medium to another is refracted at different angles depending upon its obliquity, yet the phenomenon is governed by one law and capable of being expressed in one formula. This is called the index of refraction, and was discovered by Willebrod Snell, a Dutch philosopher, about the year 1621. Fig. 5 will illustrate it. A circle is described around the point I, at which the ray R is incident upon the refracting surface. As the angle of the incident ray R varies with the normal, the angle of the refracted ray S will vary also. ”

“ Opacity due to Multiple Refraction and Reflexion.—An experiment analogous to the opacity of powdered glass to light is shown by filling a long trough with irregular-shaped pieces of pitch, and interposing it between the radiator and the receiver. The electric ray is unable to pass through the heterogeneous media, owing to the multiplicity of refractions and reflexions, and the receiver remains unaffected. But on restoring partial homogeneity by pouring in kerosene, which has about the same refractive index as pitch, the radiation is easily transmitted. ”

“ When rays pass perpendicularly from one medium into another, they are not bent; and experience shows, that in the same surface, though the sines of the angles of incidence and refraction retain the same ratio, the refraction increases with the obliquity of incidence (N. 189) . Hence it appears that the refraction is greatest at the horizon, and at the zenith there is none. But it is proved that, at all heights above ten degrees, refraction varies nearly as the tangent of the angular distance of the object from the zenith, and wholly depends upon the heights of the barometer and thermometer. ”

“ Some media are clearly more dense, more compact or solid—dense is the proper [42] word—than others. Water is more dense than air and glass than either. The bending of light rays is known as refraction. So now we may state our second law a little more concisely, thus:—When light passes from a medium into one more dense, or vice versa, it is refracted, and the more dense the medium into which or from which the light passes the greater the refraction.
A diagram and an experiment should make matters clear. ”

“ By refraction is meant the property possessed by every transparent medium of bending, under particular circumstances, the rays of light which enter it out of their original course. The science of physics teaches us that if a ray of light passes from any transparent medium into another which is denser, and if the path of this ray is not perpendicular to the surface of the second medium, it will be turned from its original course in such a way as to make it more nearly perpendicular. ”