154 MICKOSCOPIC VISION. 



solving power of a microscope objective depends on its 

 capability of picking up certain pencils that have been 

 scattered by diffraction. We have seen that diffracted 

 beams diverge in air according to the Frauenhofer law 



sin u=^j and in any medium as n sin u=-^. We are now 

 o o 



in a position to make a great generalization, viz., that the 



expression "Numerical Aperture " or n sin u is the correct 



measure of the aperture of a microscope objective. First, 



s 

 because it is equal to the ratio ~~ or semi-aperture to focus. 



Secondly, because the radiation of light in a plane angle in 

 any medium is measured by n sin u. Thirdly, because 



8 = — % which means that the extreme resolving limit 



n sm 10 



of an objective is in the ratio of half the wave length to 

 n sin u. 



By comparing this state of knowledge with that which 

 existed before the publication of Dr. Fripp's translation of 

 Prof. Abbe's papers by the Bristol Natural History Society, 

 we are able to precisely estimate the great benefit Prof. 

 Abbe has conferred on the microscopical world. Angles 

 had been correctly measured, and air, water, and balsam 

 angles had been correctly compared before Prof. Abbe had 

 published anything on the subject ; but the correct and 

 full ideas of aperture in contradistinction to mere angle, 

 and all the important corollaries that flow from those views, 

 are entirely due to Prof. Abbe. 



We must, however, return to the diffraction theory 

 because it was not free from error when it was first 

 enunciated, and it was no doubt often wrongly inter- 

 preted. 



Prof. Abbe stated that the image in the microscope had a 



