610 LIGHT Refrac tion by Iceland spar. with the results of direct observation. There can be no question that the whole investigation was, for the age in which it was made, of an exceedingly high order. But it must not be left unsaid that far more accurate measure ments than those of Huygens were necessary before it could be asserted that the form of the extraordinary wave is an ellipsoid of revolution, and not merely a surface closely resembling such an ellipsoid. These improved measurements were made 1802 by Wollaston, and they have recently been repeated vdth far more perfect optical means by Stokes, Mascart, and Glazebrook. The result has been the complete verification of Huygens s conjecture. The generating ellipse of the extraordinary waves is found to have its minor axis, which is that of revolution, equal to the diameter of the corresponding sphere for the ordinary ray. Its major axis is to the minor nearly in the ratio 1-654:1-483. We are now in a position to trace the paths of the two rays into which a ray falling in any direction on a surface of the crystal is divided by refraction. Let fig. 34 represent a plane wave front AB (in air) falling on the surface AC of a piece of Iceland spar cut in any way. The figure is a section perpendicular to the surface, and parallel to the incident ray. The wave-front AB cuts the surface of the spar in a line (not shown) at right angles to the plane of the paper. Draw from A the axis Aa (not necessarily in the plane of the paper) and the sphere and ellipsoid of revolution which have Aa for a common axis. Then, if C be taken such that BC is to Aa a:i the velocity of light in air is to that of ths ordinary ray in Images seen through Iceland spar. Fig. 34. the crystal, the vave-front of the ordinary ray is found by drawing a tangent plane to the sphere, passing through C and perpendicular to the plane of the paper. This touches the sphere in a point o (in the plane of the paper) and AoO is the ordinary ray. 1 To find the direction of the extraor dinary ray, a plane perpendicular to the paper, and passing through C, must be drawn so as to touch the ellipsoid. Let e be the point of contact, which will in general not be in the plane of the paper unless Aa is in or perpendicular to that plane ; then AcE is the extraordinary ray. Thus, in general, the extraordinary ray is not in the plane of incidence. Also the ratio of the sines of the angles of incidence and refraction is generally different for different directions of incidence, in the case of the extraordinary ray. In an elementary article we cannot attempt more fully to study these phenomena ; so we merely state that all the observed appearances, so far as the directions of the 1 This is merely a repetition of the construction we have already given for singly refracting bodies. refracted rays are concerned, are explained by supposing the wave-surface in the crystal to be made up of the sphere and the ellipsoid of revolution above described. Thus, when both eyes are used, the two images of a plane object seen through a crystal of Iceland spar appear in general to be situated at different distances above the plane. One of them maintains its apparent position as the crystal is made to rotate about a perpendicular to the two faces employed ; the other s position varies as the crystal is turned. But we have now to inquire why the incident ray is divided into two, and why one of them follows the ordinary law of refraction. Here another experimental result of Polariza- Huygens comes to our assistance. We paraphrase the t} 011 ot author s description : " I will, before conchiding, mention another remarkable pheno- Huy- menon which I discovered after the above was written. For, gens s although I have not yet been able to find the cause of it, I do not dis- wish on that account to refrain from pointing it out, in order that covery, others may have an opportunity of seeking to explain it. It appears that it will be necessary to make hypotheses additional to those already given, though these will lose none of their proba bility, confirmed as they have been by so many tests. The pheno menon is that, taking two fragments of the crystal (Iceland spar) and laying them on one another, or even holding them apart, if all the faces of tlie one be parallel to those of the other, a ray of light divided into two by the first fragment will not be farther subdivided by the second. The ordinary ray from the first will be refracted ordinarily by the second, the extraordinary ray extraordinarily. And the same thing happens not only in this arrangement but in all others in which, the principal sections 2 of the two fragments are in the same plane, whether the surfaces turned towards one another be parallel or not. It is, in fact, marvellous that these rays, fall ing on the second fragment, do not divide like the ray incident on the first. One would say that the ordinary ray from the first frag ment had lost what is necessary for the production of extraordinary refraction, and the extraordinary ray that which is necessary for ordinary refraction ; but there is something else which upsets this view. For when one places the fragments so that their principal sections are at right angles, whether the opposed surfaces be parallel or not, the ordinary ray from the first suffers only extraordinary refraction by the second, and vice versa. " But in all the infinite number of positions other than those named, both rays from the first fragment are divided into two by the second. Thus the single incident ray is divided into four, sometimes equally sometimes unequally bright, according to the varying relative position of the crystals. But all together do not seem to have more light than has the single incident ray. " When we consider that, the two rays given by the first crystal remaining the same, it depends upon the position of the second crystal whether they shall be divided into two or not, while the in cident ray is always divided, it appears that we must conclude that the waves of light which have traversed the first crystal have acquired a form or disposition which in some positions enables them to excite the two kinds of matter which give rise to the two kinds of lefraction, in other positions to excite only one of them. But I have not yet been able to find any satisfactory explanation of this." So far Huygens. His statements are perfectly in accord ance with fact; and they were reproduced by Newton 3 in very nearly the same form. Newton adds : " The un- Newton usual refraction is, therefore, performed by an original conjee- property of the rays. And it remains to be enquired, ture - whether the rays have not more original properties than are yet discovered. Have not the rays of light several sides, endued with several original properties 1 " It is very curious to notice how near each of these great men came to the true explanation, and yet how long time elapsed before that explanation was found. The date of Huygens s work is 1690, that of Newton s 1704. It was not till 1810 that farther information on the subject was obtained. Then one brilliant observation opened the way for a host of discoveries in a new and immense field of optics. 8 Defined as passing through the shorter diagonal of one of the rhombic faces of the crystal, and through the edge formed by the two adjacent faces. 3 Optics, Queries 25, 26.
