Elements of natural philosophy (Volume 2-3) . the image. Let 0, be the optical centre of the eye; then denoting the visual angle p 0 q by J., we have, To find thovisual angleunder which animage formed bya lens is seen; A=qp- qp Oq Eq-OE Value of visualangle; and representing the distances Q E by /, Eqhj /,and EO by d, we find, • qp = QFr. Eq-EO=f-d;and hence a- Qp f ? Same in otherterms; and denoting the visual angle P EQ by A, A_A f f-d\ d_ f Ratio of visualwithout the lens, 16 242 NATURAL PHILOSOPHY. Sign of thisratio dependsupon; Eye placed so asto see the imageformed by aconcave lens; Fig.
Elements of natural philosophy (Volume 2-3) . the image. Let 0, be the optical centre of the eye; then denoting the visual angle p 0 q by J., we have, To find thovisual angleunder which animage formed bya lens is seen; A=qp- qp Oq Eq-OE Value of visualangle; and representing the distances Q E by /, Eqhj /,and EO by d, we find, • qp = QFr. Eq-EO=f-d;and hence a- Qp f ? Same in otherterms; and denoting the visual angle P EQ by A, A_A f f-d\ d_ f Ratio of visualwithout the lens, 16 242 NATURAL PHILOSOPHY. Sign of thisratio dependsupon; Eye placed so asto see the imageformed by aconcave lens; Fig. 46. The angles A and A! will have contrary signs when onopposite sides of the axis of the deviating relation expressed by this equation answers to aconcave lens in which f,f will, Equation (27), be posi-tive for a real object. Moreover, d is positive, the eyebeing on the sameside of the lens asthe object; but thatthe image may beseen the eye mustbe on the oppositeside, in which cased will be negative,and the Equationbecomes. Equationcorresponding tothis case; A A 1 + t f (68) Heal imageformed by aconvex lens; whence we conclude that objects will always appear dimin-ished when seen through concave lenses. If the lens beconvex and theobject be situa-ted beyond itsprincipal focusf will be nega-tive, and Equa-tion (68) becomes
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