. A text book of physics, for the use of students of science and engineering . FIG. 540.—Refraction at aplanatic surface. XLVI LENSES 591 But BOOC _BCO = _ECD, and <lOBC=<iOCA; sin ECD Wl=lx- sin OCA It follows that for an incident ray AC, the refracted ray is CD ; andall other rays that leave A and emerge from the sphere, in a mannersimilar to CD, will travel after refraction as though they came from the sphere is an aplanatic surface with respect to two_conjugatefeoints such as A and B. This fact is used in oil immersion micro-jscopes (p. 611). Refraction at two spherical surfac
. A text book of physics, for the use of students of science and engineering . FIG. 540.—Refraction at aplanatic surface. XLVI LENSES 591 But BOOC _BCO = _ECD, and <lOBC=<iOCA; sin ECD Wl=lx- sin OCA It follows that for an incident ray AC, the refracted ray is CD ; andall other rays that leave A and emerge from the sphere, in a mannersimilar to CD, will travel after refraction as though they came from the sphere is an aplanatic surface with respect to two_conjugatefeoints such as A and B. This fact is used in oil immersion micro-jscopes (p. 611). Refraction at two spherical surfaces.—Lenses.—The result onp 589 may be used to find the lens formula by applying it to the tworefracting surfaces in turn. In Fig. 541 the radii rx and r2 are taken. v Fio. 541.—Refraction by a lens. L both positive to avoid confusion of signs, but the result is quitej general. A is the object, and refraction at the first surface of radius r,• would produce an image at A1; according to the relation \j±zl (1) u rx A is now the object with respect to the second surface r2, whichby refraction gives rise to the final image A2. For this we have 1 , - v v r2remembering that the index of refraction for a ray passing from glasstoairisl//x; # 1 ^>_ ^-1 (2) 592 LIGHT chap. Adding equations (1) and (2) for the two surfaces, we get ;Ji)(i-i) • (3) If the object A be at infinity, the rays from it are parallel, andl/u = 0, but in this case the image is at the principal focus, sothat v =f. H— r<_1)(H) <4) Further, if this value is substituted for (/*-l)( ) in the lens equation (3), we get 1 2 l-1-1- 0) V u f 16 cm. A24-cm.
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