Fig. 228.
342. Mirrors.—That reflected light does thus form images of objects you see in the common mirror. The image formed in it of any object comes from the light reflected from that object into the glass. Then in seeing the image light is reflected from it into the eye, there to form a similar image, though of much less size. By using two or more mirrors the reflections of the image can be multiplied, and by some arrangements of them to a very great extent. That the image appears to be at the same distance beyond the surface that the object is before it, is owing to the fact that the reflected rays come from the glass at the same angle that the incident rays strike upon it. This may be shown from Fig. 228 (p. 263). Suppose m m' is a looking-glass, and an arrow, A B, is before it. Rays of light come from it at all points to the glass. We will take only two of these rays at each end of the arrow. The ray A g will be reflected to the eye at the same angle in the ray g o, and the ray A f will be reflected in the ray f E. And the reflected rays will have the same rate of divergence as the incident rays. The same can be shown in regard to rays from B or any other point on the arrow. Now if the lines o g and E f be extended, they will meet at the point a, which is at the same distance behind the mirror as A is before it. The same thing can be shown of the rays from B or any other point. Therefore the image of the arrow will appear to the eye to have the same relative position behind the glass that the arrow itself has before it.
Fig. 229.
343. The Kaleidoscope.—I have already noticed the multiplication of the images of objects by using two or more mirrors. In the kaleidoscope, by a particular arrangement of mirrors, the images are multiplied, and by changes in the position of the objects the relative positions of the images are infinitely varied. Fig. 229 will serve to explain the operation of the instrument. Let A B and B C be two plane mirrors placed at right angles to each other, and a an object before them. Let I be the position of the eye looking at the mirrors. The rays a f and a g will be reflected to I as represented, and the eye will see two images, which appear to be at b and E. But the ray a K will be reflected to c, and then to I, so that a third image will be seen at d. Here is but a single second reflection, or reflection of an image; but by placing the mirrors at an angle of 60°, 45°, and 30° the images may be increased to six, eight, and ten, having a circular arrangement. In the kaleidoscope two mirrors are placed in a tube at an angle of 30°, and variously-colored pieces of glass in the farther end of the instrument, changing their relative position with every movement of it, give an endless variety of images symmetrically arranged.
Fig. 230.
Fig. 231.
344. Curved Mirrors.—These may be concave or convex. The action of a concave mirror upon light may be illustrated by Fig. 230. If parallel rays, as represented, strike upon the mirror they will, in their reflection, be made to converge, or come together, at the focus, a. But suppose the light comes from this focus, the rays of course diverging, or going away from each other; then the rays, as reflected, will be parallel. If the light or object be nearer to the mirror than the focus, and the rays of course be more diverging, then the effect of the mirror will be to lessen the divergence when the rays are reflected. You see that the tendency is to make the rays converge. And hence concave reflectors are much used when it is desired to throw a great amount of light in one direction. The effect of the concave mirror upon the apparent size and position of objects placed before it varies with the relation of their position to the focus. The action of a convex mirror upon light is the opposite of that of the concave. Its tendency is to make the rays diverge. Thus (Fig, 231), if parallel rays strike upon a convex mirror they diverge, as if they came from a focus behind the mirror, as b, as indicated by the dotted lines.