Elements of natural philosophy (Volume 2-3) . viation when it passes through a mediumbounded by two parallel planes. If, then, in the caseof an oblique pencil the rays diverge sufficiently tocover the entire face of a lens, there may always befound one at least which will enter and leave the lensat points where tangent planes to its surfaces are pa-rallel. This ray being taken as the axis of a very smallpencil proceeding from the assumed radiant, will con-tain the focus of the others, the distance of which fromthe lens, in very moderate obliquities, will be measuredby f\ given in Equation (27)
Elements of natural philosophy (Volume 2-3) . viation when it passes through a mediumbounded by two parallel planes. If, then, in the caseof an oblique pencil the rays diverge sufficiently tocover the entire face of a lens, there may always befound one at least which will enter and leave the lensat points where tangent planes to its surfaces are pa-rallel. This ray being taken as the axis of a very smallpencil proceeding from the assumed radiant, will con-tain the focus of the others, the distance of which fromthe lens, in very moderate obliquities, will be measuredby f\ given in Equation (27). This is obvious fromthe fact that in the immediate vicinity of the tangen-tial points the surfaces, which are spherical, will besymmetrical in resj)ect to the line which joins them. To find where the ray referred to intersects the axis of thelens after deviation at the firstsurface, let M JSfJSf M repre-sent a section of a concavo- Fis:. 38. optical centre of COnvex lens, of which the ra-ft lens or a dius CO of the first surface is surface. Relation fromfigure; r, and C Of of the second is rf;SP and S P the traces oftwo parallel tangent by t the distance 0 0\between the surfaces measur-ed on the axis, and by e the distance OK, from the firstsurface to the intersection of the line joining the tangen-tial points P, P\ with the axis. Then, since the radiiC P and C P\ drawn to the tangential points, must beparallel, the similar triangles OP /rand C P K, willgive the relation, CO _ COCK~~ C K ELEMENTS OF OPTICS. 221 and replacing these quantities by their values, T T Same in other r — e r — t — e from which we find r t r terms ; e = (49) r—r r[ r t t But this value of e is constant, whence we infer thatall rays which emerge from a lens parallel to their di- optical centrerections before entering it, proceed after deviation at thefirst surface in directions having a common point on theaxis. This point is called the optical centre, and maylie between the surfac
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