Elements of natural philosophy (Volume 2-3) . from a point concias far behind the reflector as the real radiant is infront; but if they converge before deviation, they willbe brought to a focus as far in front as the virtual racli-ant is behind the reflector. usioiL 216 NATURAL PIIILOSOPIIT. SPHERICAL ABERRATION, CAUSTICS, AND ASTIGMATISM. Sphericalaberration; Incident pencilnot small; Illustration; Longitudinal aberration; Lateralaberration; § 56. Thus far the discussion has been conducted uj)onthe supposition that the pencil is veryNsmall, and that 2, theversed-sine of the angle d, included
Elements of natural philosophy (Volume 2-3) . from a point concias far behind the reflector as the real radiant is infront; but if they converge before deviation, they willbe brought to a focus as far in front as the virtual racli-ant is behind the reflector. usioiL 216 NATURAL PIIILOSOPIIT. SPHERICAL ABERRATION, CAUSTICS, AND ASTIGMATISM. Sphericalaberration; Incident pencilnot small; Illustration; Longitudinal aberration; Lateralaberration; § 56. Thus far the discussion has been conducted uj)onthe supposition that the pencil is veryNsmall, and that 2, theversed-sine of the angle d, included between the axis andthe radius drawn to the point of incidence of the extremerays of the pencil, is so small, that all the products ofwhich it is a factor may be neglected. If, however, z beretained, and Equation (18) be solved with reference tof\ the value of this latter quantity wnll be expressedin terms of m, f, r and 2, and may be written /, = &*; (47) and if the semi-arc of the deviating surface, denoted by0, and of which Fi£. z is the versed-sine, be made tovary from zeroto any magni-tude sufficient toembrace the ex-terior rays of anydefinite pencil, it is obvious that fz\ must have an infinite number ofvalues, and that each value will give the focus for thoserays only which make up the surface of a cone and areincident at equal distances from the vertex. This wan-dering of the deviated rays from a single focus is calledaberration, and when caused by a spherical deviatingsurface, as it is in the case under consideration and inpractice generally, it is called sj)lierical aberration. Whenestimated in the direction of the axis, it is called longitu-dinal, and at right angles to the axis, lateral aberration. If we represent the second member of Equation (19)by J/, that Equation may be written / = M (19/ ELEMENTS OF OPTICS. 917 and subtracting this from Equation (47), we find Measure of longitudinaland lateral f /* = 3£ 3£ (48) aberration, and their laws ofvariation;
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