( 6 ) 



I. Numerical Aperture Table. 



The " Aperiube" of an optical instrument indiciites its greater or less capacity for receiving rays from the oljject ad 

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

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

 diameter 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 ?t, n being the refractive index of the medium and u iii^ 

 semi-angle of aperture. The value of n sin u for any particular case is the " numerical aperture" of the objectiva 



Diameters of tbe 

 Back Lenses of various 



Dry and Immersion 

 Objectives of the same 



Power (i in.) 

 fromO-50 tol-53N. A. 



Angle of Aperture (= 2 u). 



Numerical 

 Aperture. | 



{n sin it = a.) ' 



nry 



Olyectives. 



(« = !.> 



j Water- ! Bomogeneous- 

 ; Immersion Jiiimersum. 

 \ Objectives.' Objectives. 

 !(n = l-33.) (n = l-o2.) 



Illumi- 

 nating 

 Power, 

 (a-i.) 



Theoretical 



Resolving 



Power, in 



Lines to an Inch, 



(A=0-5269;a 



=;liue E.) 



52 

 50 

 48 

 46 

 44 

 43 

 40 

 38 

 36 

 34 

 33 

 32 

 30 

 28 

 23 

 21 

 22 

 20 

 IS 

 16 

 14 

 12 

 110 



108 

 106 

 104 

 102 

 1-00 

 0-98 

 0-96 

 0-94 

 0-92 

 0-90 

 0-88 

 0-86 

 0-84 

 0-82 

 0-80 

 0-78 

 0-78 

 0-74 

 0-72 

 0-70 

 0-63 

 0-68 

 0-64 

 0-62 

 0-60 

 0-58 

 0-56 

 0-54 

 0-52 

 0-50 



180^ 



157° 



147° 



140° 



133° 



128° 



123° 



11S° 



114° 



110° 



10G° 



102° 



98° 



95° 



92° 



88° 



85° 



82° 



79° 



7t:° 



73° 

 70° 

 68° 

 65° 

 62° 

 60° 



0' 



2' 

 29' 



6' 

 51' 

 19' 

 17' 

 33' 

 17' 

 10' 

 16' 

 31' 

 5o' 

 28' 



6' 

 51' 

 41' 

 36' 

 35' 

 38' 

 44' 

 54' 



6' 

 22' 

 40' 



0' 



1S0° 0' 

 165° 56' 

 155° 38' 

 148° 28' 

 142° 39" 

 137° 36' i 

 133° 4'; 

 128° 55' 

 125° 3' 

 121° 26'. 

 118° 00' 

 114° 41' 

 111° 36'. 

 103° 36'' 

 105° 42'; 

 102° 53' i 

 100° 



97° 



94° 



92° 



10' 

 31', 

 56'! 

 24': 



89° 56' i 

 87° 32': 

 85° 10': 

 82° 51'; 

 80° 34" 

 78° 20 'i 

 76° S': 

 73° 58'! 

 71° 49' 



69=^ 

 67^^ 



42' i 



3G'i 



55° 

 53° 

 51° 

 49° 

 47° 

 46° 

 44° 



10' 

 Z6' 

 57' 

 40' 

 6' 

 33 

 34' 



io^r 0' 



161° 23' 



153° 39' 



147° 42' 



142° 40' 



138° 12' 



134° 



130° 



126° 



123° 



122° 



120° 



117^ 



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° 



63° 



61° 



60° 



58° 



18' 

 31' 

 45' 

 0' 

 16' 



65° 32' I 

 63° 31' I 

 61° 30' , 

 59° 30' i 

 57° 81' I 



34'! 



38' i 

 42' 

 48' 

 54' 

 2' I 

 10' I 



58° 32' 

 54° 50' 

 53° 9' 

 51° 28' 

 49° 48' 

 48° 9' 

 46° 30' 

 44° 51' 

 43° 14' 

 41° 37' 

 40° 0' 

 38° 24' 



310 

 250 

 190 

 132 

 074 

 016 

 '960 

 •904 

 '850 

 •796 

 •770 

 •712 

 •G9't 

 •638 

 •588 

 •538 

 •488 

 •440 

 •392 

 ■346 

 •300 

 •254 

 •210 

 1-166 

 1-124 

 1-082 

 1-U40 

 1-000 

 •960 

 •922 

 •884 

 ■S4G 

 •810 

 •774 

 •740 

 •706 

 •672 

 •640 

 •608 

 •578 

 •548 

 •518 

 •490 

 •462 

 •436 

 •410 

 •384 

 . •360 

 ■336 

 •314 

 •292 

 •270 

 •250 



146,5-28 



141,600 



142,672 



140,744 



138.816 



136,888 



134,960 



133,032 



131,104 



129,176 



128,212 



127,248 



125,320 



1-23,392 



121,464 



119,536 



117,608 



115,680 



113,752 



111,824 



109,896 



107,968 



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 



7.3,264 



71,336 



69,408 



67,480 



65 , 552 



63,6'24 



61,696 



59,768 



57,840 



55,912 



53,984 



52,056 



50,128 



48,200 



KxAMiT.E. ^The apertures of four objectives, two of which are dry, one water-immersion, and one oil-immersion, 



' woiilii be compared on the an-iular aperture view as follows;— 106° (air), 157° (air), 142° (water), 130° (oU). 

 '.'heir actUiU apertures fire, ho. vevcr, as '80 -98 1*26 1'38 or their 



auinerical aperture:^ 



