A concave mirror causes the pencils of light that impinge upon it to converge. As the law that the angles of incidence and reflection are equal applies to all reflecting surfaces, it will not be difficult to trace upon paper the effect of any mirror upon the direction of any ray of light. In Figs. 312, 313 and 314* the arcs that stand for curved mirrors are struck from the points marked C, and this point is called, in each case, the center of curvature of the mirror.
If a luminous point be placed in the center of curvature of the mirror (c. Fig. 312) the rays emanating from it travel in the direction of the radii of the sphere of which the mirror is a part, and those rays that impinge upon the mirror are reflected back along their original paths to the luminous point, and add their effect to the light emanating in the opposite direction. If, however, the luminous point be removed to a position half-way between the center of curvature and the surface of the mirror, the light reflected forms a bundle of approximately parallel rays, as shown in Fig. 313, excluding the dotted lines, and conversely, if parallel rays impinge upon such a mirror, they are brought to a point of focus half-way between the center of curvature and the mirror.
This point is termed the prin cipal focus P F. In Fig. 314 we see at once that a lumin ous point placed farther from the mirror than its cen ter of curvature, has its light that impinges upon the mirror brought to an approximate focus at a point between the principal focus and the center of the curvature A. Conversely, a luminous point placed at A would have its light concentrated at B, these two points, or any two points similarly related to each other, being termed conjugate foci. The dotted lines in Fig. serve to show that if the curve of the mirrors were continued the concentration at the principal focus is not even approximate. This lack of focussing power is termed spherical aberration by reflection to dis tinguish it from the spherical aberration by refraction, which occurs in the case of lenses.
Parabolic mirrors are concave mirrors, whose surface is generated by the revolution of the arc of a parabola, A B about its axis A A. (Fig. 315.) In spherical mirrors the rays parallel to the axis con verge only approximately to the principal focus. Para bolic reflectors are free from this defect. It is a prop erty of a parabola that the right line F B, drawn from the focus F to any point B of the curve, and the line B C parallel to the axis of A A', make equal angles with the tangent D D' at this point. Hence all rays parallel
to the axis after reflection meet in the focus of the mirror F, and conversely when a source of light is placed in the focus the rays incident on the mirror are reflected exactly parallel to the axis. The light thus reflected tends to maintain its intensity even at a great distance.* The use of mirrors of different kinds for plibtographic purposes is large. In the early days of the Daguerreotype a camera was constructed having a concave mirror instead of a lens. Owing to many drawbacks, however, this method was not found to be an advantage over the lens. In stellar photography, however, the mirror possesses several advantages over the lens. It can be made larger at less expense, gives a much brighter image, and is entirely free from chromatic aberration. Heliostats are adjustable mirrors, which receive their movements from clockwork in such a manner that the solar rays reflected remain motionless in a given direction.
Convex mirrors do not possess real images ; they are, therefore, of comparatively no use in photography.
Single Refraction and ray of light proceeds in a straight line so long as the medium through which it is traveling is of uniform density. If, however, it passes obliquely from one medium to another of a denser kind, it is refracted towards a line drawn perpendicularly to the surface of this medium at the point of incidence ; conversely on passing obliquely from a denser into a rarer medium it is refracted from the line. If the ray passes perpendicularly from one surface to another it continues its course in a straight line. Refraction is more clearly shown in Fig. 316. The incident ray R C is refracted in the direction C R' by passing obliquely from air into water. The path of the light in the denser medium forms a smaller angle with the per pendicular A B than it does in the rarer medium. The line D E is the sine of the angle of in cidence, and the line G F the sine of the angle of refraction. Analysis has shown that the direc tion of refraction depends on the relative velocity of light in the two media. The laws of single refraction are :—(1) Whatever the obliquity of the incident ray the ratio which the sine of the in cident angle bears to the sine of the angle of refraction is constant for the same two media, but varies with different media. (2) The incident and the refracted ray are in the same plane, which is perpendicular to the surface separating the two media.