This gives from (4.14)
Since (ti'ff)1 > 1 and g is positive, the lens is a plano-concave field flattener with its first radius negative.
From (3.221) and (3.20), a single plate in air has a chromatic variation of each aberration directly proportional to the chromatic variation of (n'pi_ — 1), about 10% for crown glass from 1000 nm to 300 nm. Over most of the range it is far less and chromatism can be further reduced by supplying two Gascoigne plates for different wavelength regions.
The finite thickness of the plate adds a plane-parallel 'plate which, in the converging beam, also produces aberrations. As windows, filters, etc., planeparallel plates are common elements in the converging beams of telescopes. The aberrations introduced by such a plate are given in the works of Hopkins and Welford cited in Chap. 3 (refs. [3.3] and [3.6]) and are as follows (see Eqs. (3.254))
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