42 Modern Microscopy. 



the angle formed by the extreme rays that could be re- 

 ceived by the object-glass, issuing from the object as an 

 expression of its power of resolution, or ability to delineate 

 delicate structure. Theoretically it is impossible for a dry 

 objective to receive light at a greater angle than 180, and 

 this notation answered its purpose so far as it went, but 

 when immersion objectives were introduced this no longer 

 held good. It was found that by interposing a medium, 

 either water or oil, between the front lens of the objective 

 and the covering glass on which the object is mounted, so 

 that continuity is established between them the objective, 

 of course, being specially corrected for use in this way 

 that a larger number of rays were utilized than when work- 

 ing a lens dry. It is a well-known rule that rays passing 

 from a rarer to a denser medium are refracted towards the 

 perpendicular. Consequently, if an immersion lens be 

 used it is able to transmit a larger number of rays from 

 the object to the image than a dry lens could possibly do. 

 The media used viz., cedar- wood oil or water have re- 

 fractive indices of 1'52 and T33 respectively, the former 

 being the same as crown glass, while air is 1*0; therefore, 

 by employing an oil immersion lens, greater effect is 

 obtained than with a water immersion. So great is the 

 advantage gained by this immersion system, that a dry lens 

 having an air angle of 180 would be equalled by a water 

 immersion lens having a water angle of 96, and this latter 

 equalled by an oil immersion lens having an oil angle of 

 82, and each of these. immersion lenses can theoretically be 

 carried to oil and water angles respectively of 180. This 

 expression of angle would, therefore, be misleading and 

 uncertain, and it would be necessary to have three separate 

 expressions of angle for the different systems. To meet 

 this Professor Abbe devised the notation termed ' numerical 

 aperture,' represented by the formula n sin u, where u 

 equals the sine of half the angle of aperture, and n the 

 index of refraction of the medium by which the objective 

 front is surrounded. 



