CATOP'TRICS. The divisions of the science of optics are laid out and explained in the article OPTICS (q.v.). C. is that subdivision of geometrical optics which treats of the phenomena of light incident upon the surfaces of bodies, and reflected therefrom. All bodies reflect more or less light, even those through which it is most readily trans missible; light falling on such media, for instance, at a certain angle, is totally reflected. Rough surfaces scatter or disperse (see DISPERSION OP Limn) a large portion of what falls on them, through which it is that their peculiarities of figure, color, etc., are seen by eyes in a variety of positions; they are not said to reflect light, but there is no doubt they do, though iu such a way, owing to their inequalities, as never to present the phenomena of reflection. The surfaces with which C., accordingly, deals, are the smooth and polished. It tracks the course of rays and pencils of light after reflection from such surfaces, and determines the positions, and traces the forms, of images of objects as seen in mirrors of different kinds.
A ray of light is the smallest conceivable portion of a stream of light, and is repre sented by the line of its path, which is always a straight line. A pencil of light is an assemblage of rays constituting either a cylindrical or conical stream. A stream of light is called a converging pencil when the rays converge to the vertex of the cone, called a focus; and a diverging pencil, when they diverge from the vertex. The axis of the cone in each case is called the axis of the pencil. When the stream consists of parallel rays, the pencil is called cylindrical, and the axis of the cylinder is the axis of the pen cil. In nature, all pencils of light are primarily diverging—every point of a luminous body throwing off light in a conical stream; converging rays, however, are continually produced in optical instruments, and when light diverges from a very distant body, such as a fixed star, the rays from it falling on any small body, such as a reflector in a tele scope, may, without error, be regarded as forming a cylindrical pencil. When a ray falls upon any surface, the angle which it makes with the normal to the surface at the point of incidence is called the angle of incidence; and that which the reflected ray makes with the normal, is called the angle of reflection.
Two facts of observation form the ground-work of catoptrics. They are expressed in what are called the laws of reflection of light: 1. In the reflection of light, the inci dent ray, the normal to the surface at the point of incidence, and the reflected ray, lie all in one plane. 2. The angle of reflection is equal to the angle of incidence. These laws are simple facts of observation and experiment, and they are easily verified experimentally. Rays of all colors and qualities follow these laws, so that white light, after reflection, remains undecomposed. The laws, too, hold, whatever be the nature, geometrically, of the surface. If the surface be a plane, the normal is the perpendic ular to the plane at the point of incidence; if it be curved, then the normal is the perpendicular to the tangent plane at that point. From these laws and geometrical
considerations may be deduced all the propositions of catoptrics. In the present work, only those can be noticed whose truth can in a manner be exhibited to the eye without any rigid mathematical proof. They are arranged under the heads plane sur faces and curve surfaces.
Plane When a pencil of parallel rays falls upon a plane mirror, the reflected pencil consists of parallel rays. A. glance at the annexed figure (fig. 1), 'j 211 Q IL s P R ,A16,111,.. S A • c Igor c irrA : .---f:" -D a wif b Fig. 1. Fig. 2. Fig. 3.
where PA and QB are two of the incident rays, and are reflected in the directions AR and BS respectively, will make the truth of this pretty clear to the eye. The propo sition, however, may be rigidly demonstrated by aid of Euclid, bpok xi., with which, however, we shall not presume the reader to be acquainted. The reader may satisfy himself of its truth practically by taking a number of rods parallel to one another and inclined to the floor, and then turning them over till they shall again be equally inclined to the floor, when he will again find them all parallel.-2. If a diverging or converg ing pencil is incident on a plane mirror, the focus of the reflected pencil is situated on the opposite side of the mirror to that of the incident pencil, and at an equal distance from it. Suppose the pencil to be diverging from the focus Q (fig. 2), on the mirror of the surface of which CB is a section. Draw QNq perpendicular to CB and make qN= QN, the nq is the focus of the reflected rays. For let QV, QB, QC be any of the incident rays in the plane of the figure; draw the line AM perpendicular to CB, and draw AR, making the angle MAR equal to the angle of incidence, 3IAQ. Then AR is the reflected ray. Join qA. Now it can be proved geometrically, and indeed is appar ent at a glance, that qA. and AR are iu the same straight line; in other words, the reflected ray AR proceeds as if from q. In tile same \VON, it may be shown that the direction of any other reflected ray, as BS, is as if it proceeded from q; in other words, q is the focus of reflected rays; it is, however, only their virtual focus. See art. Focus. If a pencil of rays converged to q, it is evident that they would be reflected to Q as their real focus, so that a separate proof for the case of a converging pencil is unnecessary. The reader who has followed the above will have no difficulty in understanding how the position and form of the image of an object placed before a plane mirror—as in fig. 3, where the object is the arrow A13, in the plane of the paper, to which the plane of the mirror is perpendicular—should be of the same form and magnitude as the object (as ab in the fig.), and at an equal distance from the mirror, on the opposite side of it, but with its different parts inverted with regard to a given direction. The highest a, for iustance, in the image, corresponds with the lowest point, A, in the object. He will also understand how, iu the ordinary use of a looking-glass, the right hand of the image corresponds to the left hand of the object.