If we suppose a real object placed at IM, then OB will represent its magnified image, which will be larger than the object, in proportion to its distance from the mirror. This may be experimentally illustrated by a concave mirror and a candle. Suppose a concave mirror whose focal distance is five inches, and that a candle is placed before it, at a little beyond its focus, (as at IM)—suppose at five and a half inches,—and that a wall or white screen receives the image, at the distance of five feet six inches from the mirror, an image of the candle will be formed on the wall which will be twelve times longer and broader than the candle itself. In this way concave mirrors may be made to magnify the images of objects to an indefinite extent. This experiment is an exact counterpart of what is effected in similar circumstances by a convex lens, as described p. 74; the mirror performing the same thing by reflection, as the lens did by refraction.
From what has been stated in relation to concave mirrors it will be easily understood how they make such powerful burning-glasses. Suppose the focal distance of a concave mirror to be twelve inches, and its diameter or breadth twelve inches. When the sun’s rays fall on such a mirror, they form an image of the sun at the focal point whose diameter is found to be about one-tenth of an inch. All the rays which fall upon the mirror are converged into this small point; and consequently their intensity is in proportion as the square of the surface of the mirror is to the square of the image. The squares of these diameters are as 14,400 to 1; and consequently the density of the sun’s rays, in the focus, is to their density on the surface of the mirror as 14,400 to 1. That is, the heat of the solar rays in the focus of such a mirror will be fourteen thousand four hundred times greater than before—a heat which is capable of producing very powerful effects in melting and setting fire to substances of almost every description.
Were we desirous of forming an image by a concave speculum which shall be exactly equal to the object, the object must be placed exactly in the centre; and, by an experiment of this kind, the centre of the concavity of a mirror may be found.
In the cases now stated, the images of objects are all formed in the front of the mirror, or between it and the object. But there is a case in which the image is formed behind the mirror. This happens when the object is placed between the mirror and the focus of parallel rays, and then the image is larger than the object. In fig. 23, GF is a concave mirror, whose focus of parallel rays is at E. If an object OB be placed a little within this focus, as at A, a large image IM will be seen behind the mirror, somewhat curved and erect, which will be seen by an eye looking directly into the front of the mirror. Here the image appears at a greater distance behind the mirror than the object is before it, and the object appears magnified in proportion to its distance from the focus and the mirror. If the mirror be one inch focal distance, and the object be placed eight-tenths of an inch from its surface, the image would be five times as large as the object in length and breadth, and consequently twenty-five times larger in surface. In this way small objects may be magnified by reflection, as such objects are magnified by refraction, in the case of deep convex lenses. When such mirrors are large, for example six inches diameter, and eight or ten inches focal distance, they exhibit the human face as of an enormous bulk. This is illustrated by the following figure. Let C N, Fig. 24, represent the surface of a concave mirror, and A a human face looking into it, the face will appear magnified as represented by the image behind the mirror D Q. Suppose a ray A C proceeding from the forehead, and another M N from the chin; these rays are reflected to the person’s eye at O, which consequently sees the image in the lines of reflection O D, O Q, and in the angle D O Q, and consequently magnified much beyond the natural size, and at a small distance behind the mirror.
figure 23.
figure 24.
If we suppose the side T U to represent a convex mirror, and the figure D Q a head of an ordinary size, then the figure A will represent the diminished appearance which a person’s face exhibits, when viewed in such a mirror. It will not only appear reduced, but somewhat distorted; because from the form of the mirror, one part of the object is nearer to it than another, and consequently will be reflected under a different angle.