[CH. I 



MICROSCOPE AND ACCESSORIES 



19 



that this is the sine of 31 45V whence 2 u or the entire angle (balsam 

 or oil angle) is 63 31'. 



That is, three objectives of equal resolving powers, each with a 

 numerical aperture of 0.80 would have an angular aperture of 106 16' 

 in air, 73° 58' in water and 63 31' in homogeneous immersion liquid. 



For the apparatus and method of determining aperture, see 

 appendix. 



§ 33. Table of a Group of Objectives with the Numerical 

 Aperture (N. A) and the method of obtaining it. Half the aiigular 

 aperture 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, jot 

 water immersions n = 1-33, and for homogeneous immersions n = 1 .52. 

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



Objective. 



Angular 

 Aperture 

 (2«) 



Natural Sine 



of half the angular 



aperture 



(sin 11. ) 



Index of 

 Refraction NUMERICAL APERTURE 

 of the medi- 

 um in front 

 oftheobjec- ( N. A. ) = n sin u 



tive («). ! 



25 mm. 

 (Dry.) 



20° 



Sin - - =0.1736 

 2 



;; = 1 



N.A.= 



I X 0.1736 =0.173 



2s mm. 

 (Dry. ) 



40° 



„. 40 



Sin — = 0.3420 



11 = 1 



N.A.= 



I X0.3420 =0.342 



12 K mm. 

 (Dry. ) 



42° 



Sin — = 0.3584 



n = 1 



N.A.= 



1 X0.35S3 -0.35S 



12 'i mm. 

 (Dry.) 



IOO° 



■ 100 



Sin = 0.7660 



2 



n = 1 



N.A.= 



I X 0.7660 = 0.766 



6 mm. 



(Dry.) 



75° 



Sin— - = 0.6087 



2 



n = 1 



N.A.= 



1 X 0.6087 =0.609 



6 mm. 

 (Dry.) 



136° 



• 136 

 Sin -— = 0.9272 



11 = 1 



N. A.= 



IX0.9272 =0.927 



3 mm. 



(Dry.) 



115° 



Sin — - =0.8434 



n = 1 



N. A.= 



1X0.8434=0.843 



3 mm. 

 ( Dry. ) 



163° 



Sin- -=0.9890 



n = 1 



N. A.= 



1X0.9S90 = 0.989 



2 mm. 



Water. 



Immersion. 



96° I 2' 



96° I 2' 

 Sin — - — =0.7443 



"= i-33 



N. A.= 



1.33X 0.7443 =0.99 



2 mm. 



Homogeneous 



Immersion. 



no°38 / 



iio^S' 

 Sin —=0.8223 



11 = 1.52 



N. A.= 



1.52x0.8223 = 1.25 



2 mm. 



Homogeneous 



Immersion. 



i 3 4°io / 



„. i34°io' 



Sin — =0.9211 



2 



n ~ 1.52 



N. A.= 



1.52x0.9210 = 1.40 



