Volume 1

The American encyclopedia and dictionary of ophthalmology / edited by Casey A. Wood, assisted by a large staff of collaborators.

Date:: 1913-1921

Credit: The American encyclopedia and dictionary of ophthalmology / edited by Casey A. Wood, assisted by a large staff of collaborators. Source: Wellcome Collection.

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$Longitudinal aberration of a thin lens, exposed to an object-point situated at infinity, is expressed by Prof. Southall’s equation: E'L' = h20 ^ (n-1) (n+2) 2(n-l) ] iT c n^ - (2n+l) ^ wherein the value within the major brackets is the factor by which h2 ( 1 1 1 h2 h20 the thickness, 77 J = 2 (n - 1) has to be multiplied in order to obtain the longitudinal aberra- tion, E'L', along the axis. In the above equations, he represents the semi-diameter of the lens; 0 == 1/f, the reciprocal of its primary focal length; n, the index of refraction; and c = l/r^ and c' =— 1/ro, the curvatures of the bounding surface of the lens in air. For instance, practical application of the above formulae to a plano- convex lens reveals that the longitudinal aberration is greatest when its plane side is turned towards, and least when its plane side is turned away from, the object-rays. Since it is not practically feas- ible to entirely abolish longitudinal aberration in an infinitely thin lens that is exposed to an object-point situated at infinity. Prof. Southall gives the following equations for the curvatures Cq and Cq' of the surfaces: n (2n + 1) 2n2 - n - 4 “ 2 (n - 1) (n + 2) ^ ^ 2 (n - 1) (n + 2)^’ which meet the requirement of minimum aberration (E^L') as n (4n -1) expressed by the equation: (E'L')o = — —1)2 (n -7 2)^^^’ In order to secure this minimum degree of aberration in a thin lens exposed to an object-point at infinity, the curvature Cq and Cq' must bear the following relation to each other: n (2n -f 1) ^ 2n2 - n - 4 '• Through the above equations, and the choice of an index = 3/2 it can be shown that a bi-convex lens has the least longitudinal aberration when the curvature of its front surface (Cq) is six times as great as the curvature (Co') of its back surface. Within rational limits it is also feasible to vary the relative curvatures of the surfaces with- out altering the focal length; this procedure being called, “bend- ing the rays,” (q. v.). Least circle of aberration, a circle perpendicular to the axis, lo- cated within the amplitude of the longitudinal aberration, whose diameter is determined by intersections of the edge-rays with the$