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 n = 1, for water 

 immersio7is n = 1.33, and for homogeneous immersions 71 = 1.52. {For 

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



Objective;. 



25 mm. 

 (Dry.) 



25 mm. 

 (Dry.) 



T2^ 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. 



3 v n 



Natural Sine 



of half the angular 



aperture. 



(sin u). 



40° 



42° 



100° 



75° 



136° 



115 



163° 



96° 1 2' 



no°38' 



Sin ^ = 0.1736 

 2 



Sin*? = o.3420 

 2 



Sin 4f =0.3583 

 2 



Sin 15? = 07660 



Sin Z5 = o 6087 

 2 



,Z5 : 

 2 



Sin -5- = 0.9272 



Sin HS =0.8434 

 2 



Sin -^ =0.9890 

 2 



„• 96° 12' 



Sin^ =07443 



2 



Sin IIO ° 3 8/ =o8223 



cv i34°io' 



Sin -=^ = 0.9210 



2 



Index of 

 Refraction 

 of the medi- 

 um in front 

 of the objec 

 tive. («). 



» = i-33 



n = 1.52 



« = 1.52 



Numerical Aperture 

 (N.A. ) = n sin ft. 



N.A. = 1X01736 = 0.173 



N.A. = 1X0.3420 = 0.342 



N.A. = 1X03583 = 0.358 



N. A. = 1 X o. 7660 = 0.766 



N.A. = 1X06087 = 0608 



N.A. = 1X0.9272=0.927 



N.A. = 1 X0.8434 — o 843 



N.A. = 1 X0.9890 = 0.989 



N.A. = 1.33 X o.7443 =0.99 

 N.A. = 1.52 X0.8223 = 1.25 

 N.A.= 1.52 Xo.g2io= 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 



