. Physiological optics : being an essay contributed to the American encyclopedia of ophthalmology . following conclusions:— (a) The difference between the focal distances is equal to the radiusof curvature. (b) The distance of the center of curvature from the posteriorfocus is equal to the anterior distance and the distance of the centerfrom the anterior focus is equal to the posterior focal distance. (c) The ratio between the focal distances is equal to the ratiobetween the indices of the corresponding media. 4. To construct the image of a point removed from the principalaxis, we can geometri
. Physiological optics : being an essay contributed to the American encyclopedia of ophthalmology . following conclusions:— (a) The difference between the focal distances is equal to the radiusof curvature. (b) The distance of the center of curvature from the posteriorfocus is equal to the anterior distance and the distance of the centerfrom the anterior focus is equal to the posterior focal distance. (c) The ratio between the focal distances is equal to the ratiobetween the indices of the corresponding media. 4. To construct the image of a point removed from the principalaxis, we can geometrically proceed as shown in Fig. 3. (a) A ray, MB, parallel to the axis NC: it is refracted through theposterior focal point FP. (b) A ray, MC, proceeding toward the center of curvature or opti-cal center C: it is not displaced upon refraction but passes straightthrough. 12 , — •-•- PHYSIOLOGICAL OPTICS (c) A ray, MFA, passing through the anterior focus: it is parallel,after refraction, to the axis. From the similarity of the triangles MNFA and FJRX we havethe ratio NF, MN MN FAX RX M1N1. Fig. 3.—The Geometrical Construction of the Image of an Object as Produced by a Single Eefraeting Surface. lx 0 or — = — and from the similarity of the triangles DYFP and FpM^FA I FP 0 the ratio — = —. Hence we deduce the general formula12 I IA^FaFp and by substitution therein of the values lx = fx — FA and 12 — f2 —FP, we obtain the equation FA FP fi Other expressions for the magnification and size of the object orimage when the size of one of these is known may be deduced fromthe similarity of triangles in Figure 3. Two magnification ratios,other than those just developed, are 0 f, + r (1) M = - = , I f2 —r i. e., whatever may be the distance of the object, its size and that ofthe image are in the same ratio as their respective distances from thecenter of curvature, and 13 PHYSIOLOGICAL OPTICS 0 j^n.,(2) M = — = . I fall! 5. It will subsequently be shown that the co
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