654 OPTICS approximation. The actual relation, known as the "law of the sines," was discovered by Willebrord Snell, about 1621. Descartes, who unjustly claimed this discovery, has really the merit of having applied it so as to explain the general formation and the angles of the rain- bow. Newton in 1672 published his remark- able discoveries in connection with the decom- position of light by aid of the prism, with the doctrine and measure of the refrangibilities of the different colors, and the agreement of the phenomena with those of the rainbow. His discoveries resulted in improvements in the telescope, and also in explaining a prominent defect in the refracting telescope, that of the colored borders of images, due to chromatic ab- erration. Dollond about 1757 discovered the possibility of achromatic combinations of lens- es, and produced the first of these. The first notice of double refraction is that of Bartho- lin, 1669; but Huygens first satisfactorily ex- plained the phenomena, by means of his since renowned undulatory theory of light, his trea- tise upon which was written in 1678, and first published in 1690. He also first observed the fact of polarization; though the distinct dis- covery of this phenomenon was not made until more than a century later, namely, by Malus in 1808, who commenced a thorough study of the subject ; and this was much ex- tended by Young, Fresnel, Arago, Brewster, Biot, and Seebeck. Hooke appears first to have studied the colors of thin plates, which he described in 1664 ; and these colors Newton and Young afterward turned to very impor- tant use. Diffraction and the fringes of shad- ows were discovered by Grimaldi in 1665 ; de- polarization, with the production of periodi- cal colors in polarized light, by Arago in 1811 ; the relation of optical properties to the sym- metry and axes of crystals, by Brewster in 1818. The general explanation of most of these phenomena by the undulatory theory is due to the labors of Young and Fresnel, from 1802 to 1829; and these have since been car- ried forward and corrected by the labors of Airy, Hamilton, Lloyd, Cauchy, and many others. Still other discoveries in optics, espe- cially the more recent, as those made in con- nection with color, the velocity and physical modifications of light, the various optical in- struments, and photography, will be found mentioned under the proper heads. I. CATOP- TRICS. When rays of light fall on a surface of an opaque, and in some degree smooth or pol- ished body, a portion of those rays, greater or less, but never the whole, is thrown off again from such surface, and this light is said to be reflected. Opaque surfaces reflecting in a high degree are termed specula, or mirrors. Sup- pose a ray or minute beam incident on a pol- ished plane surface in any direction whatever, and let fall at the point of incidence a perpen- dicular to the surface ; then, first, it is univer- sally true that the reflected ray will be situated in the same plane in space in which this perpendicular and the line of the incident ray are situated. Thus we may always determine the plane, vertical to the reflecting surface, in which to look for the reflected ray. The an- gle I O P, fig. 1, included between the perpen- dicular and incident ray, is termed the angle of FIG. 1. incidence ; that between the same perpendicu- lar and the reflected ray, P O R, the angle of reflection. These angles are always equal. Thus, the fundamental and universal law of reflection from plane surfaces is simply this : the paths of the incident and reflected rays al- ways lie in the same plane with the perpendic- ular to the reflecting surface drawn to the point of incidence ; and in that plane the angle of re- flection is always equal to the angle of incidence. This law is strictly verified by experiment and measurement. Necessary consequences of its truth are, that beams or rays parallel before incidence on a plane mirror will remain paral- lel after reflection, and that divergent rays will after reflection continue to diverge, and con- vergent rays to converge, at the same rates as before impinging on the reflecting surface. All the facts relating to images in plane mir- rors follow from the same law. But a very important truth in relation to images, and one too often lost sight of, must be premised. Par- allel rays or beams of light, or a single beam, may show us the existence of the object emit- ting them, but they do not enable us to deter- mine its place or distance. We can do this in regard to an object or image,' or any point in it, only by means of pencils of light, divergent in themselves, proceeding from the points or point to the eye. We necessarily judge of the size of this object chiefly by the angle subtended at the eye by a line joining its extreme points (the visual angle) ; and of its distance by the amount of reconvergent action the eye must exert upon the pencils painting its several points, in order to focus them upon the retina, as well as by the convergency of the axes of the two eyes upon the place of the object, if near. (See STEREOSCOPE, and VISION.) The pencils of light from the various points of an object before a plane mirror, being divergent at the same rate after as before reflection, and the eye of necessity seeing the object in the direction in which the rays of light finally come to it, the determination of the position
