Elements of natural philosophy (Volume 2-3) . shall find the longitudinalaberration for a single lens; and that for any numberof lenses placed close together might be found by thesame process. § 57. We perceive that a spherical wave of any con-siderable extent deviated at a spherical surface, will notin general, be concentrated at, nor will it appear to pro- ^rlcaiceed from, the same point; but if we conceive the wave aberration;to be divided into an indefinite number of elementaryzones by planes perpendicular to the axis of the devi-ating surface, each zone will have its particular point ofco
Elements of natural philosophy (Volume 2-3) . shall find the longitudinalaberration for a single lens; and that for any numberof lenses placed close together might be found by thesame process. § 57. We perceive that a spherical wave of any con-siderable extent deviated at a spherical surface, will notin general, be concentrated at, nor will it appear to pro- ^rlcaiceed from, the same point; but if we conceive the wave aberration;to be divided into an indefinite number of elementaryzones by planes perpendicular to the axis of the devi-ating surface, each zone will have its particular point ofconcentration or of diffusion, according as the foci arereal or virtual. Moreover, longitudinal aberration di-minishes the focal distance, that is, in general, // is lessthan f\ and the deviated rays which are in the samef^0,! , J ^ longitudinal plane and on the same side of the axis, will intersect aberration; General effects of 218 NATURAL PHILOSOPHY. each other before they do this latter line. Thus, if F D Fig. 36. Geometricalillustration;. Explanation ofthe figure; Caustic curve; Caustic surface; Section of thedeviated waveby a planethrough the axisof the surface; When the causticwill be real. be the exterior, and FDr its consecutive incident ray,D Fz and D F\ the corresponding deviated rays, theselatter will intersect each other at some point as c\ on thesame side of the axis OF; in like manner, if DFbe the next consecutive deviated ray to D F\ it willintersect this atter in same point as c\ and so forother deviated rays up to that one which coincides with theaxis. The locus of these intersections c\ e, &c, is calleda caustic curve / and if the curve be revolved about theaxis 0 F, it will generate a caustic surface. This surfacewill spring from the focus of the axial rays at F\ as avertex, and open out into a trumpet-shaped tube towardsthe deviating surface. The deviated wave will no longer be spherical, but willbe of such shape that its section d d d o\ by a planethrough t
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