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glass, CD of the mirror (sections, of course, as usual), QR, QR′ are two rays of an oblique pencil, of which the former is incident on the glass at R, refracted to S, reflected to T, and refracted towards V; the other in like manner. Now let QR, TV meet in s: the refractions at R and T being equal, the effect on the whole is the same as if a reflexion took place at a mirror parallel to CD, placed at s; in like manner QR′, is as it were, reflected at s′. So far all is regular enough, but are s, s′ equidistant from the mirror CD? because if not, the case is not the simple one of a reflexion at s, s′, instead of one at S, S′. Now strictly speaking Ss, S′s′ are not equal, for it will be seen by referring to p. 47, that there is an aberration in these refractions, of the amount of m2−12n·∆·tanθ2, ∆ being the thickness of the glass, and m the ratio of refraction out of glass into air, which being less than unity, the aberration is negative, and as it increases with θ, the angle of incidence, s′ must be nearer the surface than s, and the rays will not diverge from q′, as if reflected at a plane mirror at s, but will form a caustic to which q′T, q″T′ will be tangents. Hence, the image of any object situated obliquely, with respect to the mirror and the eye, will be more or less confused, besides being situated in a different place from that which it would occupy, in the case of a plain metallic speculum without glass.
There is another irregularity attending these looking-glasses, which is easily perceived, when the incidence of the rays is oblique; it is an additional reflexion at the first surface of the glass. Indeed, when the obliquity is great, there may be observed a series of reflexions, at the two surfaces of the glass, each of the alternate ones attended with an emergence of part of the rays, as shown in Fig. 155, where QR represents a pencil of rays, partly reflected, and partly refracted at R; the refracted rays are reflected at S, and in part emerge at T, in part are reflected at T, and at V, and meeting the upper surface again at X are divided, some escaping in the direction Xx, some suffering another reflexion, and so on.
When the image of a candle is seen in a common looking-glass, the following phænomena may be observed, as the obliquity of the incidence is increased: at first one image is seen, then two, then several in a row, apparently decreasing in magnitude and brightness
