\CH. I 



MICROSCOPE AND ACCESSORIES 



19 



that this is the sine of 31 45-i-' whence 2 71 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 obtainiyig it. Half the angular 

 aperture is designated by u and the index of refraction of the medhim in 

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

 water immersions n = 1.33, and for homogejieous immersions n = 1 .§2 . 

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



Objective. 3 1! 





< 



25 mm. 



(Dry.) 



25 mm. 

 (Dry. ) 



12^ mm. 

 (Dry.) 



I2_K mm. 

 (Dry.) 



6 mm. 

 (Dry.) 



6 mm. 

 (Dry. ) 



3 mm. 

 (Dry.) 



3 mm. 

 (Dry.) 



2 mm. 



Water. 



Immersion. 



2 mm. 



Homogeneous 



Immersion. 



20° 



40° 

 42° 



IOO° 



75° 

 136° 

 115 

 163 



no°38 / 



2 mm. 



Homogeneous i34°io / 

 Immersion. 



Natural Sine 



of half the angular 



aperture 



(sin u. ) 



Sin = 0. 1736 



2 ,sJ 



r,- 40 



Sin = 0.3420 



Sin ^- = 0.3584 



„ 100 



Sin = 0.7660 



Sin— =0.6087 



o- : 3 6 



Sm — = 0.9272 



Sin ^=0.8434 

 Sin — = 0.9890 



n . 96°i2 / 



Sm 2- =0.7443 



Sin 



2 



IIO*^' 



2 



i34°io / 



11 = 1.33 



0.8223 « = 1.52 



n = 1.52 



Index of 

 Refraction 

 of the medi- 

 um in front 

 of the objec- 

 tive (n). 



Numerical Aperture 

 (N. A.) =7zsin u 



11 = I 



N.A.= 



1 X0.1736 = 0.173 



fl = I 



N.A.= 



1 X0.3420 = 0.342 



n= i 



N.A.= 



1 X 0.3583 =0.358 



n = 1 



N.A.= 



1 X 0.7660 = 0.766 



n = 1 



N.A.= 



1 X 0.6087 =0.609 



n = 1 



N. A.= 



1X0.9272 =0.927 



n = 1 



N. A.= 



1X0.8434 = 0.843 



n = 1 



N. A.= 



1X0.9890 = 0.989 



N. A.=i.33X 0.7443 = 0.99 



N. A.= 1.52X0.8223 = 1.25 



N. A.= 1. 52X0. 9210 = 1.40 



