20 



MICROSCOPE AND ACCESSORIES. 



[CH. I. 



% 30. Table of a Group of Objectives with the Numerical Aper- 

 ture (N. A.) and the method of obtaining it. Half the angular aper- 

 ture is designated by u and the index of refraction of the medium in front 

 of the objective by n. For dry objectives this is air and 11 = 1, for water 

 immersions n — 1.33, a7idfor homogeneous immersions n = 1.52. {For 

 a table of natural sines, see third page of cover') . 



Objective. 



25 mm. 

 (Dry.) 



25 mm. 

 (Dry.) 



\i%. mm. 

 (Dry.) 



12^ mm. 

 (Dry.) 



6 mm. 



(Dry.) 



6 mm. 

 (Dry.) 



3 mm. 

 (Dry.) 



3 mm. 

 (Dry.) 



2 mm. 



Water. 



Immersion. 



2 mm. 



Homogeneous 



Immersion. 



2 mm. 



Homogeneous 



Immersion. 



u 



a =< — 



.. — ' ^ 



~ u "- 

 3 V N 



40" 



42° 



100° 



75° 



136° 



115 



163 



96° 1 2' 



110° 38' 



Natural Sine 



of half the angular 



aperture. 



(sin u). 



Index of 

 Refraction 

 of the medi- 

 um in front 

 of the objec- 

 tive. (?:). 



Sin?? =0.1736 

 2 



Sin4° = o.342o 



Sin i? =0.3583 

 2 



Sin ^ = 0.7660 

 2 



lZ5 : 

 2 



Siu 1 ^ 



Sin L? = 0.6087 

 2 



: O.9272 



Sin H5 =0.8434 

 2 



Sin 



163, 



: O. 989O 



Sin *il^o 7443 



Sin IIO °3 8 = .8223 



Sin: 



1O.9210 



» = i-33 



n = 1.52 



n = 1.52 



Numerical Aperture 

 (N.A.) = 11 sin u. 



N.A. = 1X0.1736 = 0.173 



N. A. = 1 X o 3420 = 0. 342 



N.A. = 1X0.3583 = 0.358 



N. A. = 1 X o. 7660 = o. 766 



N. A. = 1 X o. 6087 = o. 608 



N.A. = 1X0.9272=0.927 



N.A. = 1 X 0.8434 — 0.S43 



N.A. = 1 X 0.9890 = 0.989 



N.A. = 1.33 X 0.7443 = 0.99 



N.A. = 1.52 X0.8223 = 1.25 



N.A. = 1.52 X0.9210 = 1.40 



§ 31. Significance of Aperture. — As to the real significance of 

 aperture in microscopic objectives, it is now an accepted doctrine that — 

 the corrections in spherical and chromatic aberration being the same — 

 (1) Objectives vary directly as their numerical aperture in their ability 

 to define or make clearly visible minute details (resolving power). For 

 example an objective of 4 mm. equivalent focus and a numerical aper- 

 ture of 0.50 N. A. would define or resolve only half as many lines to 



