The Microscope. Its History, Construction, and Application 15th ed. / Being a familiar introduction to the use of the instrument, and the study of microscopical science

by Jabez Hogg

[15] Numerical aperture is generally used in the sense in which it was introduced in 1873 by Professor Abbe, on the basis of his theoretical investigations. Numerical aperture represents the ratio between the radius of the effective aperture (p) of the system on the side where the image is formed—more accurately the radius of the emerging pencils measured in the upper focal plane of the objective—and the equivalent focal length (f) of the latter, i.e.,

Numerical aperture = p/f.

This ratio is equal to the product of the sine of half the angle of aperture u of the incident pencils and the refractive index n of the medium, situated in front of the objective. With dry lenses n has therefore the value 1; with immersion lenses it is equal to the refractive index of the particular immersion fluid:

Numerical aperture = n Sin u.

The numerical aperture of a lens determines all its essential qualities; the brightness of the image increases with a given magnification and, other things being equal, as the square of the aperture; the resolving and defining powers are directly related to it, the focal depth of differentiation of depths varies inversely as the aperture, and so forth. (Abbe, “The Estimation of Aperture,” “Journal of the Royal Microscopical Society,” 1881, p. 389.)

[16] “Journal of the Royal Microscopical Society.”

[17] “Journal Roy. Micros. Soc.,” p. 19, 1878, and p. 20, 1880.

[18] “The Magnifying Power of Short Spaces” has been ably elucidated by John Gorham, Esq., M.R.C.S. “Journal of Microscopical Society,” October, 1854.

[19] The late Mr. Coddington, of Cambridge, who had a high opinion of the value of this lens, had one of these grooved spheres executed by Mr. Carey, who gave it the name of the Coddington Lens, supposing that it was invented by the person who employed him, whereas Mr. Coddington never laid claim to it, and the circumstance of his having one made was not known until nine years after it was described by Sir David Brewster in the “Edinburgh Journal.”

[20] “Journal of the Royal Microscopical Society, 1890,” p. 420.