Note on the Proper Definition of the Amplifying Power of a Lens or Lens-system

E. Abbe
1884 Journal of the Royal Microscopical Society  
THE generally adopted notion of "linear amplification at a certain distance" is in fact a very awkward and irrational way of defining the "amplifying power" of a lens or a lens-system. Unfortunately, there is little hope that a more rational expression will be generally adopted, because it will seem to be '( too abstract," but it may, nevertheless, be useful to consider the following :-In the formula N = -the (( amplification" of one and the same system varies with the length I, or the "
more » ... I, or the " distance of vision," and an arbitrary conventional value of 2 (e. g. 10 in. or 250 mm.) must be introduced, in order to obtain comparable figures. The actual " linear amplification" of a system is, of course, different, in the case of a short-sighted eye, which projects the image at a distance of 100 mm., and a long-sighted one which projects it at 1000 mm. Nevertheless, the " ampZqying power" of every system is always the same for both, because the short-sighted and the longsighted observers obtain the image of the same object under the same visual angle, and consequently the same r e d diameter of the retinal image. That this is SO will be seen from fig. 48 , where the thick lines show the course of the rays for a short-sighted eye, and the thin lines for a longsighted one, the eye in each case being supposed at the posterior principal focus of the system. The semi-visual angle u* under which an object of semidiameter h is seen, is the same for both observers, as the change resulting from the different positions of the object concerns only the degree of divergence of the various pencils from the various points of the object (and the image), and does not alter the refraction of the principal (central) rays from the various points. This consideration leads to an ex ression of the (( power" which Z f is in conformity to the last-mentione t; salient fact. The quotient where u* is the semi-visual angle corresponding to F, the semidiameter of' the object, is a constant quantity for every system, not depending on the particular circumstances of the observing eye ; and this quotient indicates, obviously, the greater or smaller visual t The original papcr is written by Prof. Abbe in English.
doi:10.1111/j.1365-2818.1884.tb01110.x fatcat:eqnf3jhghnfkjjimsumuykw7fi