Discoveries and Inventions of the Nineteenth Century

About two hundred years ago, a traveller, returning from Iceland, brought to Copenhagen some crystals, which he had obtained from the Bay of Roërford, in that island. These crystals, which are remarkable for their size and transparency, were sent by the traveller to his friend, Erasmus Bartholinus, a medical man of great learning, who examined them with great interest, and was much surprised by finding that all objects viewed through them appeared double. He published an account of this singular circumstance in 1669, and by the discovery of this property of Iceland spar, it became evident that the theory of refraction, the laws of which had been studied by Snell and by Huyghens a few years before, required some modification, for these laws required only one refracted ray, and Iceland spar gave two. Huyghens studied the subject afresh, and was able, by a geometrical conception, to bring the new phenomena within the general theory of light. Iceland spar is chemically carbonate of lime (calcium carbonate), and hence is also called calc spar, and, from the shape of the crystals, it has also been termed rhombohedral spar. The form in which the crystals actually present themselves is seen in Fig. 204, which also represents the phenomenon of double refraction. Iceland spar splits up very 400readily, but only along certain definite directions, and from such a piece as that represented in Fig. 204 a perfect rhombohedron, such as that shown in Fig. 206, is readily obtained by cleavage; and then we have a solid having six lozenge-shaped sides, each lozenge or side having two obtuse angles of 101° 55´, and two acute angles of 78° 5´. Of the eight solid corners, such as A B C, &c., six are produced by the meeting of one obtuse and two acute angles, and the remaining two solid corners are formed by the meeting of three obtuse angles. Let us imagine that a line is drawn from one of these angles to the other: the diagonal so drawn forms the optic axis of the crystal, and a plane passing through the optic axis, A B, Fig. 205, and through the bisectors of the angles, E A D and F B G, marks a certain definite direction in the crystal, to which also belong all planes parallel to that just indicated. Any one of such planes forms what is termed a “principal section,” to which we shall presently refer. Fig. 204. Fig. 205. Fig. 206. It will be observed that in Fig. 204 the white circle on a black ground seen through the crystal is doubled; but that, instead of being white as the circle really is, the images appear grey, except where they overlap, and there the full whiteness is seen. If we place the crystal upon a dot made on a sheet of paper, or having made a small hole with a pin in a piece of cardboard, hold this up to the light, and place the crystal against it, we see apparently two dots or two holes. The two images will, if the dot or hole be sufficiently small, appear entirely detached from each other. Now, if, keeping the face of the crystal against the cardboard or paper, the observer turn the crystal round, he will see one of the images revolve in a circle round the other, which remains stationary. The latter is called the ordinary image, and the former the extraordinary image. Let us place the crystal upon a straight black line ruled on a horizontal sheet of paper, Fig. 205, and let us suppose, in order to better define the appearance, that we place it 401so that the optic axis, A B, is in a plane perpendicular to the paper, A being one of the two corners where the three obtuse angles meet, and B the other, and the face, A B C D, parallel to E G H B, which touches the paper. Then, according to the laws of ordinary refraction, if we look straight down upon the crystal, we should see through it the line I K, unchanged in position—that is, the ray would pass perpendicularly through the crystal as shown by L M—and, in fact, a part of the ray does this, and gives us the ordinary image, O O´; but another part of the ray departs from the laws of Snell and Descartes, and, following the course L N Y´, enters the eye in the direction N Y´, producing the impression of another line at L´, which is the extraordinary ray, E E´. If the crystal be turned round on the paper, E E´ will gradually approach O O´, and the two images will coincide when the principal section is parallel to the line I K; but the coincidence is only apparent, and results from the superposition of the two images—for a mark placed on the line drawn on the paper will show two images, one of which will follow the rotation of the crystal, and show itself to the right or left of the ordinary image, according as C is to the right or left of A. So that there are really in every portion of the crystal two images on the line, one of which turns round the other, and the coalescence of the two images twice in each revolution is only apparent, for the different parts of the lengths of the images do not coincide. On continuing the revolution of the crystal after they apparently coincide, the images are again seen to separate, the extraordinary one being now displaced on the other side, or always towards the point, C. Thus, then, the ray, on entering the crystal, bifurcates, one branch passing through the crystal and out of it in the same straight line, just as it would in passing through a piece of glass, while the other is refracted at its entrance into the crystal, although falling perpendicularly upon its face, and again at its exit. And again, when a beam of light, R r, Fig. 206, falls obliquely on a crystal of Iceland spar, it divides at the face of the crystal into two rays, R O, and r E; the former, which is the ordinary ray, follows the laws of ordinary refraction—it lies in the plane of incidence, and obeys the law of sines, just as if it passed through a piece of plate-glass. The extraordinary ray, on the other hand, departs from the plane of incidence, except when the latter is parallel to the principal section, and the ratio of the sines of the angles of incidence and refraction varies with the incidence. The reader who is desirous of studying these curious phenomena of double refraction, and those of polarization, is strongly recommended to procure some fragments of Iceland spar, which he can very easily cleave into rhombohedra, and with these, which need not exceed half an inch square, or cost more than a few pence, he can demonstrate for himself the phenomena, and become familiar with their laws. He will find very convenient the simple plan recommended by the Rev. Baden Powell, of fixing one of the crystals to the inside of the lid of a pill-box, through which a small hole has been made, and through the hole and the crystal view a pin-hole in the bottom 402of the box, turning the lid, and the crystal with it, to observe the rotation of the image. The same arrangement will serve, by merely attaching another rhomb of spar within the box, to study the very interesting facts of the polarization to which we are about to claim the reader’s attention. The curious phenomena which have just been described, although in themselves by no means recent discoveries, have led to some of the most interesting and beautiful results in the whole range of physical science. The examination and discussion of them by such able investigators as Huyghens, Descartes, Newton, Fresnel, Malus, and Hamilton, have largely conduced to the establishment of the undulatory hypothesis—that comprehensive theory of light, which brings the whole subject within the reach of a few simple mechanical conceptions. It was at first supposed that it was only one of the rays which are produced in double refraction that departed from the ordinary laws, and Iceland spar was almost the only crystal known to have the property in question. At the present day, however, the substances which are known to produce double refraction are far more numerous than those which do not possess this property, for, by a more refined mode of examination than the production of double images, Arago has been able to infer the existence of a similar effect on light in a vast number of bodies. Crystals have also been found which split up a ray of light entering them into two rays, neither of which obeys the laws of Descartes. It may, in fact, be said that, with the exception of water, and most other liquids, of gelatine and other colloidal substances, and of well-annealed glass, there are few bodies which do not exercise similar power on light. Fig. 207. On examining the two rays which emerge from a rhomb of Iceland spar, on which only one ray of ordinary light has been allowed to fall, we find that these emergent rays have acquired new and striking properties, of which the incident ray afforded no trace; for, if we allow the two rays emerging from a rhomb of the spar to fall upon a second rhomb, we shall find, on viewing the images produced, that their intensity varies with the position into which its second crystal is turned. Thus, if we place a rhomb of the spar upon a dot made on a sheet of white paper, we shall have, as already pointed out, two images of equal darkness. But, in placing a second rhomb of the spar upon the first, in such a manner that their principal sections coincide, and the faces of one rhomb are also parallel to the faces of the other, we shall still see two equally intense images of the dot, only the images will be more widely separated than before, and no difference will be produced by separating the crystals if the parallelism of the planes of their respective principal sections be preserved. Here, then, is at once a notable difference between a ray of ordinary light and one that emerges from a rhomb of Iceland spar; for, in the case of rays of ordinary light, we have seen that the second rhomb would divide each ray into two, whereas it is incapable (in the position of crystals under consideration) of dividing either the ordinary or the extraordinary ray which emerges from the first rhomb. If, still keeping the second rhomb above the other, we make the former rotate in a horizontal plane, we may observe that, as we turn the upper crystal so that the planes of the principal sections form a small angle with each, each image will be doubled, and, as the upper crystal is turned, each pair of images exhibits a varying difference of intensity. The ordinary ray in entering the second crystal is divided by it into a second ordinary ray and a second extraordinary ray, the intensities of which vary according to the angle between the principal sections. When the two principal 403sections are parallel to one plane, that is, when the angle between them is either 0° or 180°, the extraordinary image disappears, and only the ordinary one is seen, and with its greatest intensity. When the two principal sections are perpendicular to each other, that is, when the second crystal has been turned through either 90° or 270°, the extraordinary has, on the contrary, its greatest intensity, and the ordinary one disappears. When the principal section of the second crystal has been turned into any intermediate position, such as through 45° and 135°, or any odd multiple of 45°, both images are visible and have equal intensities. This experiment shows that the two rays which emerge from the first crystal have acquired new properties, that each is affected differently by the second