26 ELEMENTARY PRINCIPLES <>F MICROSCOPICAL OPTICS 



have to be withdrawn from the object. Similarly, if the observer 

 were short-sighted, the lens must be placed nearer the object to 

 render the rays more divergent. Dr. Abbe points out 1 that the 

 generally adopted notion of a '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. 



In the formula X = - the amplification of one and the same 



system varies with the length of /. or the ' distance of vision,' and 

 an arbitrary conventional value of I (i.e. 10 inches, or 250 mm.) 

 must be introduced in order to obtain comparable figures. The 

 actual ' linear amplification ' of a system is, of course, different in 



FIG. 28. The amplifying power of a lens. 



the case of a short-sighted eye. which projects the image at a dis- 

 tance of 100 mm., and a long-sighted one, which projects it at 

 1000 mm. Nevertheless, the 'amplifying jtotrer' of every system is 

 always the same for both, because the short-sighted and the long-sighted 

 observers obtain the image of the same object under the same visual 

 angle, and consequently the same real diameter of the retinal image. 

 That this is so will be seen from fig. 28, where the thick lines show 

 the course of the rays for a short-sighted eye, and the thin lines for 

 .i long-sighted one, the eye in each case being supposed at the pos- 

 terior principal focus of the system. 



The other generally adopted expression of the power by X = 



, 



t/ 



may be put on a somewhat more rational basis than is generally 

 done by defining 1 he length I (10 inches) not as ' distance of distinct 

 vision.' but rather as ' distance of projection of the image.' As far 

 as 'distinct vision' is assumed for determining the amplification, 

 the valneof X lias no real signification at all in regard to an observer 



1 Joiirn. tt.M.8. vol. iv. scr. ii. p. :!is. 



