108 



THEORY OF THE MICROSCOPE. 



their path between the diaphragm and the original source of light, 

 as is exhibited by the lines in the Fig. 



The relations are altered when the aperture of the incident cone 

 is limited by the mirror. The insertion of a convex lens produces 

 in this case a stronger convergence of the rays, as shown in Fig. 

 46, and therefore, under certain circumstances, 

 a greater angle of aperture. It is always 

 possible to place the lens so that the effective 

 cone of light, whose apex lies in p, has for its 

 base the whole upper surface of the lens. The 

 lens produces, therefore, the same result as a 

 diaphragm situated in the same plane, which 

 receives light from a relatively unlimited mirror 

 surface, and, like the latter, furnishes more light 

 in inverse ratio to its distance from the object- 

 plane. The increase, however, in both cases 

 reaches its limit as soon as the marginal rays> 

 produced backwards, meet the periphery of the 

 mirror. 



This consideration also applies to the case 

 where the original source of light is limited, 

 while the reflecting surface is unlimited. It is 

 only necessary to substitute the former word 

 for the latter, in order to make the preceding sentences literally 

 correct for this supposition also. They may, mutatis mutandis, be 

 extended to the very common case where the source of light as 

 well as the mirror surface are limited, or where the illumination is 

 not uniformly bright. The greatest possible brightness which can 

 be attained by means of illuminating devices cannot under any 

 circumstances exceed that which a sufficiently large mirror with 

 a relatively unlimited source of light would alone afford. 



It follows that if the illuminating apparatus is furnished with a 

 diaphragm which neutralizes the inequality of the conditions for 

 the differently-coloured rays (in the sense that all the rays, without 

 exception, if produced backwards, would reach the source of light), 

 no difference can possibly exist between achromatic and non- 

 achromatic systems of lenses. If the source of light were of so 

 small an extent that the blue marginal rays, for instance, could 

 not meet it, together with the red rays, or conversely ; if, moreover, 

 it were not possible to regulate the illumination so that the 



FIG. 46. 



