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6 This formula for the angular third order spherical aberration due to a thin lens for an object at infinity was taken by Bouwers from the classical work "The Principles and Methods of Geometrical Optics" by J. P. C. Southall (Macmillan 1910), page 388. The same formula is given by Czapski-Eppenstein [3.11(b)], who give its origins as far back as Huygens' "Dioptrica" (Ed. 1703), Prop. 27. The general form for a thin lens with an object at any finite distance contains

6 terms: it is derived for longitudinal spherical aberration by A. E. Conrady in "Applied Optics and Optical Design", Part 1 (Oxford 1929 and 1943), page 95. This is the well-known "G-sum" formula. Hopkins [3.3] also derives it, in the wavefront aberration form.

where n' is the index of the meniscus and r1 the radius of its first surface. From (3.190), bearing in mind that the index in the image space is 1 and (3.21), this gives

i)GF,men vt

m ri

1 men ri

As a further legitimate approximation in view of the thin lens assumption and the fact that, in practice fmen ^ ri, he reduces this to

Eq. (2.51) gave the expression for the total power of a system of two thin lenses in air, separated by a distance d. If the lenses are refracting surfaces separated by d in a medium of index n', we have a "thick lens", the case of our concave meniscus in the Bouwers telescope. The focal length is given by

K referring to the power 1/f'. For the concentric meniscus d = r1 — r2 , in which d > 0 and radii r1 and r2 are negative. Now

ri rl

Substituting (3.274) and (3.275) in (3.273), we derive for the focal length of the concentric meniscus

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