CH. /.] MICROSCOPE AND ACCESSORIES. 21 



the millimeter or inch as a similar objective of 1.00 N. A. So also an 

 objective of 2 mm. focus and 1.40 N. A. would resolve only twice as 

 many lines to the millimeter as a 4 mm. objective of 0.70 N. A. Thus 

 it is seen that defining power is not a result of magnification but of 

 aperture, otherwise the 2 mm. objective would resolve far more than 

 twice as many lines as the 4 mm. objective. 



(2) The illuminating power of an objective of a given focus is found 

 to vary directly as the square of the numerical aperture (N. A. ) 2 . Thus 

 if two 4 mm. objectives of N. A. 0.20 and N. A. 0.40 were compared 

 as to their illuminating power it would be found from the above that 

 they would vary as 0.20 2 : o.40 2 = 0.0400 : o. 1600 or 1 : 4. That is the 

 objective of 0.20 N. A. would have but J^th the illuminating power of 

 the one of 0.40 N. A. 



In considering illuminating power the equivalent focal length must 

 also be considered. If the N. A. were the same in a 3 mm. and a 6 

 mm. objective their illuminating power would vary directly with the 

 square of the foci. Thus the illuminating power of the 6 and the 3 

 mm. objectives would be as 6 2 : 3 2 or 36 to 9 or 4 : 1, that is 4 times as 

 great in the 6 mm. as in the 3 mm. objective. As the magnification of 

 an objective varies indirectly as the equivalent focus, it follows also 

 that the illuminating power will vary indirectly as the square of the 

 magnification of the objective. The magnification of the 6 mm. is 42 

 and of the 3 mm. 84, whence the illuminating power of the two objec- 

 tives are as 42 s : 84* or 1764 : 7056 or 1 : 4. As the ratio is inverse in 

 this case the result is the same as before, that is 4 times as great for the 

 6 mm. as for the 3 mm. objective. 



(3) The penetrating power, that is the power to see more than one 



plane, is found to vary as the reciprocal of the numerical aperture — — — - 



so that in an objective of a given focus the greater the aperture the less 

 the penetrating power. 



In comparing the penetrating power of objectives of different foci, 

 the numerical aperture being the same, it is found that the penetrating 

 power increases directly as the square of the focus. For example, two 

 objectives of the same N. A., one of 4 mm. and the other of 2 mm. 

 focus, the penetrating power would be as 4 s : 2 2 or 16 : 4 or 4 : 1. That 

 is, the numerical aperture remaining the same, the greater the equiva- 

 lent focus the greater the penetration. 



To briefly summarize : The numerical aperture is concerned with 

 resolution and the resolving power varies directly as the numerical 

 aperture, thus if the N. A. is doubled, twice as many lines to the mil- 

 limeter or inch can be resolved. 



