( 6 ) 



I. Numerical Aperture Table. 



The " APER-nntE" of an optical instrument indicates its greater or less capacity for receiving rays from the object i 

 transmitting them to tbe image, and the aperture of a Microscope objective is therefore determined by the ral 

 between its focal length and the diameter ot the emergent pencil at the plane of its emergence — that is, the util" 

 di^meter of a single-lens objective or of the back lens of a compound objective. 



This ratio is expressed for all media and in all cases by n sin u, ?i being the refractive Index of the medium and u\ 

 semi-angle of aperture. The value of n sin u for any particular case is the •'numerical aperture " of the objectiv^ 



Diameters of tbe 

 Back Lenses of various 



Dry and Immersion 

 Objectives of the same 



Power (i in.) 

 from 0-50 to 1-52 N. A. 



Angle of Aperture (= 2 w). 



I Numerical 

 Aperture, 

 (n sin u = a.) 





Dry 



Objectives. 



(n = l.) 



Illumi- 



I Water- \ Homogeneous- nating 

 Immersion Jinmi-rsion Power. 

 ! Objectives. Objectives. [ (a^.) 

 .(h = 1-33.) (« = 1-52.) , 



180' 

 157' 

 147' 

 140' 

 133' 

 128' 

 123' 

 118' 

 114° 17' 

 110° 10' 

 106° 16' 

 102° 31' 



98° 56' 



95' 



92' 



C 

 2' 



29' 

 6' 

 51' 

 19' 

 17' 

 38' 



73° 

 70° 

 68° 

 65° 

 6-^° 

 60° 



28' 

 6' 



88° 51' 

 85° 41' 

 82° 36' 

 79° 35' 

 7(;° 38' 



44' 

 54' 



6' 

 22' 

 40' 



0' 



180° 0' 



161° 23' 



153° 39' 



147° 42' 



142° 40' 



138° 12' 



134° 10' 



130° 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° 43' 



90° 33' 



88° 26' 



86° 21' 



84° 18' 



82° 17' 



80° 17' 



78° 20' 



76° 24' 



74° 30' 



72° 36' 



70° 44' 



68° 54' 



67° 6' 



65° 18' 



63° 31' 



61° 45' 



60° 0' 



58° 16' 



56° 32' 



54° 50' 



53° 9' 



51° 



49° 



48° 



46° 



44° 



310 



250 

 190 

 132 

 074 

 016 

 960 

 904 

 850 

 ■796 

 •770 

 ■742 

 ■690 

 •638 

 ■588 

 •538 

 •488 

 •440 



Theoretical 



Resolving 



Power, in 



Lines to an Inch. 



(A.=0'5269fi 



=line E.) 



1^392 



43° 14' 

 41° 37' 

 40° 0' 

 38° 24' 



•346 

 ■300 

 •254 

 •210 

 ■166 

 ■124 

 ■082 

 •040 

 ■000 

 •960 

 ■922 

 •884 

 •846 

 •810 

 •774 

 •740 

 •706 

 •672 

 •640 

 •608 

 •578 

 •548 

 •518 

 •490 

 •462 

 •436 

 •410 

 •384 

 •360 

 ■336 

 •314 

 •292 

 •270 

 •250 



146,528 

 144,600 

 142,672 

 140,744 

 138,816 

 136,888 

 134,960 

 133,032 

 131,104 

 129,176 

 128,212 

 127,248 

 125,320 

 123,392 

 121,464 

 119,536 

 117,608 

 115,680 

 113,752 

 111,824 

 109,896 

 107,9^18 

 106,040 

 104.112 

 102,184 

 100,256 

 98,328 

 96,400 

 94,472 

 92,544 

 90,616 

 88,688 

 86,760 

 84,832 

 82,904 

 80,976 

 79,048 

 77,120 

 75,192 

 73,264 

 71,336 

 69,408 

 67,480 

 65,552 

 63,624 

 61,696 

 59,768 

 57,840 

 55,912 

 53,984 

 52,056 

 50,128 

 48,200 



T.xAiipiF— Ihe apertures of four objectives, two of which are dry, one water-imraersion, and one oil-immersioil,.-,1 



^woliw be compared on tbe an.j.lar aperture view a. follo^s:-l06= (air), isjo (air), 14 2° (water), 130o (o,l) . ■ | 



Their actual apertures are. however, w= -80 -98 1 • 26 1 38 or their ,, 



numerical apertures. 



