St. Petersburg: Imperial Academy of Sciences, 1769-1771.
First edition, and a very fine copy, of Euler’s rare work on optics, ‘widely known and important in the physics of the eighteenth century’ and which ‘laid the foundations of the calculation of optical systems’ (DSB). The first volume presents his general theory of optics, including his prediction of the possibility of constructing achromatic lenses. The second and third volumes discuss the construction of the telescope and the microscope. “Next to the lunar theory, the most important subject which exercised the genius of [18th century] mathematicians was the improvement of the achromatic telescope” (Edinburgh Encyclopedia, Vol. 6).
“In the second half of his life, from 1750 on and throughout his sixties, Leonhard Euler worked intensively on problems in geometric optics. His goal was to improve in several ways optical instruments, in particular, telescopes and microscopes. Besides the determination of the enlargement, the light intensity and the field of view, he was primarily interested in the deviations from the point-by-point imaging of objects (caused by the diffraction of light passing through as system of lenses), and also in the even less tractable deviations which arise from the spherical shape of the lenses… As was his custom, he collected his results in a grandly conceived textbook, the Dioptrica (1769-1771). This book deals with the determination of the path of a ray of light through a system of diffracting spherical surfaces, all of which have their centres on a line, the optical axis of the system. In a first approximation, Euler obtains the familiar formulae of elementary optics. In a second approximation he takes into account the spherical and chromatic aberrations” (Habicht).
“Since the time of Huygens and Newton theoretical optics had not progressed any further than applied optics. In particular no one had re-examined Newton’s demonstration of the impossibility of correcting chromatic aberration in lenses. In Proposition III, Experiments 7 and 8 in his Opticks, Newton examined the possibility of suppressing chromatic aberration in telescope objectives by using a lens system consisting of two lenses of different refractive indices. The refrangibility of one substance cancelling the dispersion provoked by the other, one obtained at the end of the objective reconstituted white light, but this would only occur if he employed lenses of infinite focal length – an impossibility. This result caused him to abandon the refracting telescope and to construct a reflecting one.
“Newton’s work had such authority that for more than thirty years no one thought of reviewing his conclusions. Physicists and mathematicians held to the opinion that it was impossible to make an achromatic lens by associating two different substances… [Euler] began at the point where Newton left off, and produced a lens-combination formed of two concave lenses whose intervening space was filled with water. Studying refraction in each medium and for each colour he showed that it was possible to correct colour dispersion and gave the corresponding formulae” (Dumas, Scientific Instruments of the 17th and 18th Century and their Makers, pp. 153-4).
Becker Collection 126; British Optical Association Library and Museum Catalogue I, p. 65; DSB IV, 482; Poggendorff I, 690; W. Habicht (ed.), Opera Omnia III-9 Commentationes Opticae.
Three volumes, large 4to (245 x 197 mm), pp. [iv], 337; [vi], 592 (recte 584, pagination jumps 240-249 but signatures Gg4-Hh1 continuous); [viii], 440, with six folding engraved plates. Contemporary calf with raised bands and gilt spine labels. A fine and clean set.