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English: In Opticks, Book 1, Part 1, Proposition 7 Newton considers attempts to improve the clarity of images of refracting telescopes. Although he proves that the major factor is chromatic aberration, he gives a formula to substantially reduce the spherical aberration for a compound lens, which comprises 2 identical glass lenses, with spherical surfaces, glued together with water between them. The formula was misprinted in the original edition, is blatantly erroneous, and was never corrected in subsequent editions. No details of its derivation have been found and, even when corrected, it cannot be justified from the optics of the lens. ‘The Mathematical Papers of Isaac Newton’, by D. T. Whiteside, Cambridge University Press, 1967-1981, Vol. III, page 554, shows the intended formula. Whiteside claims he is the first to comment on the misprint, showing ‘the lack of scholarly criticism of Newton’s geometrical optics’. However, in ‘Demonstration of Newton’s Theorem for the Correction of Spherical Errors in Object Glasses of Telescopes’, Transactions of the Irish Academy, pp 171-175 (1790-1792). Matthew Young points out the error and proposes how the corrected formula may have been derived. The following, which is based on Young’s muddled argument, is an exercise in finding a possible derivation of Newton’s formula.

See also: ‘Opticks’, by Sir Isaac Newton, Dover Publications, Inc, 1952.

https://www.jstor.org/stable/30078672 - Matthew Young’s Paper

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