NUMERICAL-APERTURE TABLE.* 



Tlie " Aperture " of an optical instrument Indicates its greater or leas capacity 

 tor receiving rays from the object and transmitting them to the image, and the 

 aperture of a microscope objective is therefore determined by the ratio between its 

 focal length and the diameter of the emergent pencil at the plane of its emergence 

 —that is, the utilized diameter of a single-lens objective or of the back lens of a 

 compound objective. 



This ratio is expressed for all media, in all cases by n sin. »,, n beingi the refrac- 

 tive index of the medium, and « the semi-angle of aperture. The value of h, sin. a 

 for any particular case is the numerical aperture of the objective. 



Numerical 



Aperture. 



<» sin »=«.) 



Angle of Aperture (= 2 «). 



Dry 



Objectives. 



(n. = 1.) 



180 



157 3 



147 29 



140 6 



133 51 



128 19 



123 17 



118 88 



114 17 



110 10 



106 I'o 



102 81 



98 56 



95 28 



92 6 



88 51 



85 41 



82 86 



79 85 



76 38 



73 44 



70 54 



68 6 



65 22 



62 40 



60 



Water- 

 Immersion 

 Objectives, 

 (n = 1 33 ) 



180 

 165 56 



155 88 



148 28 



142 89 



137 36 



133 4 



128 55 



125 8 



121 26 



118 00 



114 44 



111 86 



108 36 



105 42 



102 58 



100 10 



97 31 



94 56 



92 24 



89 56 



87 32 



85 10 



82 51 



80 34 



78 20 



76 8 



73 58 



71 49 



69 42 



67 36 



65 83 



63 31 



61 80 



59 80 



57 81 



55 34 



53 88 



51 43 



49 48 



47 54 



46 3 



44 10 



Homoge- 

 neous 

 Immersion 

 Objectives. 



(n = 1-52.) 



180 



161 38 



153 89 



147 43 



142 40 



138 12 



134 10 



l^.O 26 



126 57 



123 40 



122 6 



120 33 



117 34 



114 44 



111 59 



109 20 



106 45 



104 15 



101 50 



99 29 



97 11 



94 56 



92 48 



90 83 



88 36 



86 31 



84 18 



82 17 



80 17 



78 20 



76 24 



74 30 



73 86 



70 44 



68 54 



67 6 



65 18 



63 31 



61 45 



60 



58 16 



58 83 



54 50 



53 9 



51 38 



49 4^ 



48 9 



46 80 



44 51 



48 14 



41 37 



40 



88 24 



Illumin- 

 ating 

 Power. 



(at'.) 



3-310 



3-350 



2-190 



2133 



3074 



3-016 



1-960 



1-904 



1-850 



1-79G 



1-770 



1-742 



1-690 



1-688 



1-588 



1-538 



1-488 



1-440 



1.392 



1-346 



1-300 



1-254 



1-310 



1-166 



1-134 



1-082 



1-040 



1000 



-960 



•922 



■884 



-846 



•810 



•774 



-740 



-706 



•672 



•640 



■608 



■578 



-548 



-518 



•490 



•462 



•436 



•410 



•384 



•860 



•336 



•314 



•292 



•270 



•250 



Theoretical 

 Resolving 

 Power in 



Lines to an 

 Inch. 



U=0.r)269// 



= line E.) 



146,538 



144,600 



143,673 



140,744 



138,816 



136,888 



134,960 



188,033 



131,104 



139,176 



138,212 



127,248 



125,320 



123,392 



121,464 



119,586 



117,608 



115,680 



118,753 



111,834 



109,896 



107,968 



106,040 



104,113 



102,184 



100,356 



98,338 



96,400 



94,473 



93,544 



90,616 



88,688 



86,760 



84,832 



82,904 



80,976 



79,048 



77,120 



75,193 



73,264 



71,336 



69,408 



67,480 



65,552 



68,624 



61,696 



59,768 



57,840 



55,912 



53,984 



53,056 



50,138 



48,200 



a)' 



■658 



•667 



-676 



•685 



-694 



•704 



•714 



•725 



•785 



•746 



•758 



•758 



•769 



•781 



■794 



-806 



•820 



•833 



•847 



•862 



•877 



-898 



•909 



■926 



•943 



•963 



-980 



1-000 



1-030 



1-043 



1064 



1-087. 



1-111 



1.136 



1168 



1190 



1-320 



1-250 



1-282 



1-316 



1-351 



1-889 



1-429 



1-471 



1-515 



1-562 



1-618 



1-667 



1-724 



1-786 



1-852 



1-923 



3-000 



Example. — The apertures of four objectives, two of which are 

 dry, one water-immersion, a;nd one oil-immersion, would be 

 compared on the angular aperture view as follows : 



io6° (air), 157° (air), 142"^ (water), 130"^ (oil). 



Their actual aper- 

 tures are , how- 

 ever, as -So ■gS i'26 i'38 

 or as their numerical apertures. 



* From Jovrnot of the Royal Microscopical Society. 



MICROMETRIC TABLE. 



7^ = 



: one thousandth of a 

 millimetre. 



»S00o 



iOObO 



10 Off 



1 

 "STTOTT 



1 



850Tr 



1 



"STFOO' 



"g^TiOCT 

 1 



rooo 

 _ 1 __ 



'SiTOO 

 "^0 0^ 



J. 



"To (f (T 



¥6 



1 

 TOO 



800 

 ¥T0 



TOO 



1 

 ■§•0" 



1 

 "55" 



1 



~50~ 



1 

 TS" 



1_ 

 "T5 



1 

 "T¥- 

 J. _ 

 "10 



