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 

 immersions n = 1.33, and for homogeneous immersions n = 1.32. (For 

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



V 



u 



5 3 - 



Natural Sine 

 Objective;. 9 fc s j of half the angular 

 I be cx,^ , aperture. 



;=< (shi«). 



25 mm. 

 (Dry.) 



25 mm. 



(Dry.) 



12)4 mm. 

 (Dry.) 



I2>£ 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. 



20" 

 40° 

 42° 

 IOO° 



75° 



136° 

 115 

 163° 



Q6°I2' 



no°3S / 



1 34 10' 



20 



Sin — =0.1736 

 2 



Sin =" = 0.3420 



Sin 4? =0.3583 

 2 



Sin _? = o 7660 



75 

 2 



Sin=_ = o 



Sin^ = o6oS7 

 2 



9272 



Sin H 5 - = 0.8434 

 2 



Sin ±^? = 0.9890 

 2 



163 

 2 



Sin *!i_- : ,07443 

 2 



Sin II ^38_=o 8223 



Sin 



134 io'_ 



:0.92I0 



Index of 



Refraction ! NUMERICAL APERTURE 

 of the medi- 

 um in front 



oftheobjec- (N. A. ) = 11 sill U. 



tive. (n). 



11 = 1 N.A. = 1X0.1736 = 0.173 



n = i N.A. = 1X03420 = 0.342 



» = i N.A. = 1X0.3583 = 0.358 



«=i N.A. = 1X0.7660 = 0.766 



n = 1 



N.A. = 1X0.6087 = 0608 



n = i N.A. = 1X0.9272=0.927 



n = 1 



11 = 1 



N.A. = 1X0.8434 = 0843 



N.A. = 1 X0.9S90 = 0.989 



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



n = 1.52 



« = 1.52 



N.A. = 1.52 X0.8223 = 1.25 



N.A. = 1.52 Xo.92io= 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 



