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22 A TREATISE ON OPTICS. PART I.
F, their virtual focus behind the mirror. By comparing fig.12. with fig. 11., it is obvious that the ray A M, fig. 12., is farther from M E than in fig. 11., and consequently the reflected ray M B must also be farther from it. Hence, as the same is true of the ray N B, the point F, where these rays meet, must be nearer to D in fig. 12. than in fig. 11.; that is, in the reflexion of diverging rays, the virtual focal distance DF is less than for parallel rays.
For the same reason, if we suppose the point of divergence A to approach the mirror, the virtual focus F will also approach it; and when A arrives at D, F will also arrive at D. In like manner, if A recedes from the mirror, F will recede from it; and when A is infinitely distant, or when the rays become parallel, as in fig. 11., F will be half-way between D and C. In all these cases, the focus is a virtual one behind the mirror.[1]
CHAP. II.
IMAGES FORMED BY MIRRORS.
(23.) THE image of any object is a picture of it formed either in the air, or in the bottom of the eye, or upon a white ground, such as a sheet of paper. Images are generally formed by mirrors or lenses; though they may be formed also by placing a screen, with a small aperture, between the object and the sheet of paper which is to receive the image. In order to understand this, let C D be a screen or window-shut-ter with a small aperture, A, and E F a sheet of white paper placed in a dark room. Then, if an illuminated object, RGB, is placed on the outside of the shutter, we shall observe an inverted image of this object painted on the paper at rg b. In order to understand how this takes place, let us suppose the object R B to have three distinct colors, red at R, green at G, and blue at B; then it is plain that the red light from R will
Fig. 13.
- ↑ For a discussion of the subjects in this chapter, see (in the College Edition) the Appendix of American Editor, Chapter I.