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as their distance increases. At a certain point the distances between these images attain their maximum, diminish, and vanish, so that the images are all in a line with the eye, and there appears only one. Past this point the attendant images emerge on the opposite side of the principal one, and become more and more distinctly separated, till on the candle being placed in the plane of the glass, they disappear altogether.
The aberration in the refraction appears to be the cause of the latter phænomena: its effect is the same as if the different pencils which convey to the eye the appearances of the different images, were reflected by plane mirrors, at different distances.
The Concave Mirror.
150. This usually consists of a plano-convex lens of glass, silvered on the convex side, as represented in Fig. 156, where BAb is, in fact, the mirror, the glass lens serving only to give it the required form. The first effect of this glass, is evidently to throw an object at Q to q, making Aq=m·AQ (that is, to increase its apparent distance from the mirror about one half): then in order to find the place of the image of q, given by the metallic mirror, we have the equation
1∆+1∆′=2r, or ∆′=∆r2∆−r.
But this is modified again by the glass which alters ∆′ to ∆′m, so that upon the whole, if we put δ for the original distance of the object from the mirror, (neglecting the thickness of the lens,) that of the ultimate image is
1m·mδr2mδ−r, or δr2mδ−r.
When the reflexion takes place obliquely, there is of course a good deal of irregularity, but we cannot enter into the discussion of it at present.
The Multiplying Glass.
151. This is a plano-convex lens, of which the convex side is ground into several plane faces, so as to form a collection of prisms. Fig. 157 will serve to illustrate this, though not exactly in the same
