368. Optical Illusions by a Plane Mirror.—The illusion called Pepper's Ghost is typical of many illusions produced by reflection. It may be illustrated by taking a piece of plate glass, M-N, a tumbler of water, W, and a lighted candle, C, placed in a box, B, having one side open and arranged as shown in perspective in Fig. 357, and in section in Fig. 358. If the effect is produced in a darkened room, the observer at E sees a virtual image of the lighted candle as if it were in the glass of water, the water being seen by transmitted light through the plate glass, the latter forming a virtual image of the candle by reflection. Some of the illusions produced by this means are: (a) the figure suspended in mid air; (b) the bust of a person without a trunk; (c) the stage ghost; (d) the disappearing bouquet.
Fig. 359.—Action of a concave mirror on parallel rays of light.
Fig. 360.—Real image formed by a concave mirror.
369. Concave Mirrors.—Another useful piece of physical apparatus is the concave spherical mirror. It is frequently made from plano-convex lenses by silvering the convex surface of the lens, thus making a concave reflecting surface from the inner surface of the silvered part; they are also made by polishing the inner surfaces of metallic spherical shells. The concave mirror is represented in section in Fig. 359 by the curve MN; C is the center of curvature or the center of the surface of which this mirror MN is a part; the line VC through the center V of the mirror is called the principal axis; while any other line passing through C is called a secondary axis. The point midway between the vertex V and center of curvature C is called the principal focus, F. It is the point through which parallel incident rays pass after reflection. The angle MCN which the curve of the mirror subtends at the center is called the aperture of the mirror. We learned in Art. 361, the angle of reflection of a ray of light is always equal to the angle of incidence no matter what the nature of the reflecting surface may be. If the reflecting surface is a regular concave surface, like the inner surface of a sphere, the rays of light coming from a point source may after reflection come to a focus, forming a real image. The two extreme points of an object should be selected for locating its image; Fig. 360 shows the construction. The real images formed by concave mirrors are always inverted. The principal focus of a concave mirror may be observed by holding the mirror in a beam of sunlight entering a darkened room. The sun's rays after reflection converge to form a small, round, intense spot of light, which is a real image of the sun, located at the principal focus of the mirror. The distance of the principal focus from the mirror is the least distance that a real image can be formed in front of a concave mirror.
370. Virtual Images by Concave Mirrors.—When light comes from a small point situated between a concave mirror and its principal focus, the reflected rays are divergent and hence no real image of the object can be found in front of the mirror. But if the rays are extended behind the mirror they will meet in a point called the virtual focus. This is the point from which they appear to come. Any image of an object situated between the principal focus and a concave mirror is therefore a virtual image, erect and larger than the object. (See Fig. 361.)
Fig. 361.—Virtual image formed by a concave mirror.
371. Construction of Real Images.—There are five positions at which an object may be situated in front of a concave mirror, namely: (1) beyond C; (2) at C; (3) between C and F; (4) at F and (5) between F and V. There are two ways by means of which the image formed at each of these positions may be located, namely; (1) experimentally, by allowing the rays of light from a luminous body to focus on a screen and (2) diagrammatically. By the latter method the two rays of light are considered the course of each of which may easily be determined; first, the ray which strikes the mirror parallel to its principal axis and which after reflection passes through the principal focus; second, the ray which passing through the center of curvature strikes the mirror at right angles and therefore after reflection must pass directly back along its incident path. Where these two reflected rays intersect is located the real image of the object. Whenever these two rays of light do actually intersect, as in Fig. 360, a real image (ab) is formed of the object AB.