832 SUMMARY OF CURRENT RESEARCHES RELATING TO 



column (calculated by Mr. Stephenson) showing the " penetrating 

 power " of objectives from a numerical aperture of • 50 to 1 ' 52. 



" Penetrating power" or "focal depth " is in inverse ratio to the 

 numerical aperture. Thus, if a dry objective of 180° angle, or 1*00 

 N. A., is taken as unity, the penetrating power of one of • 50 N. A. 

 would be 2, and of an oil-immersion of 1 • 50 N. A., • 667. 



This follows from the consideration that the depth of focus (<^) is 

 — other circumstances being equal — inversely proportional to the 

 linear diameter of the delineating pencils at their emergence from the 

 eye-piece. This diameter is = 2/a, /being the focal length of the 

 whole Microscope,* and a the numerical aperture, and the depth of 

 focus is therefore inversely as a, provided the whole aperture of the 

 system is utilized by the image-forming pencils. 



It must be carefully borne in mind, however, that this column of 

 " penetrating power " is by no means on a level, in practical value, 

 with those indicating the " illuminating power " and " resolving 

 power." 



As was shown by Prof. Abbe in the paper translated at p. 680, 

 the total dejjth of vision of the Microscope depends upon two factors : 

 (1) the power of accommodation of the eye, and (2) the depth of focus 

 of the objective. 



The depth of focus again consists of several elements, the medium 

 in which the object is, the magnifying power of the Microscope, &c. 



lih.e penetrating power of the objective ( - ) is one only of those elements, 



so that with exactly the same values of a (i. e. with the same numerical 

 aperture) the depth of focus might considerably vary, if in the one 

 case the object were in air and in the other in balsam, or if the 

 amplification was different in the two cases. 

 By referring to the equation at p. 689, 



T 2 T 



Depth of vision = n ^r=:^X-\- n -- — , 

 ^ •' N^ N a 



it will be better seen how many other elements make up the total 



effect of depth of vision, in addition to -, viz. : — 



a 



n - the refractive index of the medium in which the object is. 



L = the distance of the virtual image from the "eye-point" 



above the eye-piece. 

 N = the linear amplification of the virtual image. 

 A = the range of accommodation of the observer's eye in ordinary 



vision. 

 M = the angle under which the circles of indistinctness may appear 



in the virtual image. 



* The focal length of the whole Microscope is the focal length of that infinitely 

 thin lens, which would give the same amplification of an object if projected to 

 the same distance. If the amplification of the whole Microscope is = N, the 



virtual image being projected at a distance of vision = L, we have — = equiva- 

 lent focal length of the Microscope. 



i 



