114 THEORY OF THE MICROSCOPE 



That is to say the resolving power the capacity to recognize as distinct 

 two closely adjacent points is more than twice as great, and the brightness 

 of the image more than 4J times as great when the same lens is -used with 

 oil as when used dry ; while as regards penetrating power a dry lens is more 

 than twice as efficient as an oil lens, so that when thick sections have to be 

 examined a dry objective of low N.A. should be selected. 



And it is clear that the N.A. is of fundamental importance in determining 

 the efficiency of a microscope. 



7. Definition. 



The definition of a lens is its capacity to render the outline of an object 

 or image distinct to the eye, and depends partly upon the sufficiency of the 

 correction for aplanatism, which can be assisted by the use of diaphragms, 

 and partly upon the sufficiency of the correction for chromatic aberration : 

 from which it follows that an achromatic lens has a better definition than a 

 lens not so corrected. 



The definition and resolving power of a lens are in practice tested by means of 

 preparations of diatoms, those generally used for the purpose being Pleurosigma 

 angulatum, Grammatophora subtilissima, Navicula crassinervis, Surdrella gemina, 

 etc. With a good objective a very distinct image with sharply defined outlines will be 

 obtained ; in the case of Pleurosigma angulatum it should be possible to make out, 

 under a magnification of 500-600 diameters, a central venule on to which two 

 systems of oblique lines abut, crossing each other at an acute angle and forming a 

 reticulated system of fine lines. 



It is also well when testing an objective, to examine some small organism such 

 as the Bacillus tuberculosis, in order to ascertain the magnification produced as 

 well as the sharpness of the image. 



8. Chromatic aberration achromatism and apochromatism. 



So far the conditions which must be fulfilled by a lens when homogeneous 

 light is the ilmminant have been considered. But in practice white or non- 

 homogeneous light, i.e. light of different wave lengths, is used. And with 

 white light a series of images will be formed of different colours, in different 

 places, and of different sizes. Further, only one of these images corresponding 

 to one definite wave length will be aplanatic. As will be readily appreciated, 

 the calculations required for the correction of chromatic errors are of necessity 

 extraordinarily complex ; it must therefore suffice here to say that in practice 

 chromatic aberration is corrected by the use of lenses combined in pairs (or 

 triplets), one lens being concave the other convex. The convergent convex 

 lens is made of crown glass, which has a low dispersive power, while the 

 divergent concave lens is made of flint glass, which has a high dispersive 

 power. By making these two lenses of a suitable curvature the chromatic 

 aberration for two colours is corrected, and the lenses are said to be achro- 

 matized for those colours. 



If 57 denote the dispersive power of the glass between the F and C lines of the 

 spectrum, and / denote the focal length of the lens, then, in order to achromatize 

 the blue and red colours F and C, the couplet must be such that T 2 /i ~~^i/2' 



In apochromatic (UTTO, apart from; x/<V a > colour) couplets, fluorite takes the 

 place of crown glass. Fluorite has a similar relative dispersion to flint, so 

 that with these couplets 3 (not 2) different colours can be achromatized. 

 Suppose that in a given apochromatic system the focal lengths for the red, 

 the yellow, and the green rays are the same : then the magnifications will be 

 the same, but the images will not all lie in one plane. Again, suppose a 

 system were so constructed that all the different colours should come to a 



