( 6 ) 



I. Numerical Aperture Table. 



The " Apeetuee" of an optical instrument indicates its greater or less capacity for 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 and in all cases by n sin u, n being the refractive index of the medium and u the 

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



Diameters of tlie 

 B.ick Lell^e^ of various 



Dr\- and Immi'i-sioii 

 Obji'Ctiv's 01 thi' same 



Power (I in.) 

 tVo.ii 0-5;i to 1-52 N A. 



N'u.merical 

 Aperture. 



(n siu u = a.) 



•52 

 •60 

 •48 

 •46 

 •44 

 •42 

 •40 

 •38 

 •36 

 •34 

 •33 

 •32 

 •30 

 •28 

 •26 

 •24 

 •22 

 •20 

 •18 

 •16 

 •14 

 •12 

 •10 

 •08 

 ■06 

 •04 

 •02 

 •00 

 •98 

 •96 

 •94 

 •93 

 •90 

 •88 

 •86 

 •84 

 •82 

 •80 

 •78 

 •76 

 •74 

 •72 

 •70 

 •68 

 •66 

 •64 

 •62 

 •60 

 •58 

 •56 

 •54 

 •52 

 •50 



Angle of Aperture (= 2 u). 



Dr,/ 

 ObjiCtives. 



Water- j Bomogemnti 

 Im,'inersi(in\ Immtrsion 

 Obj(-ctives. Objectives. 

 \(n = 1-33.) (n= 1-52.) 



180° 0' 



157° 2' 



147° 29' 



140° 6' 



133° 51' 



128° 19' 



123° 17' 



118° 38' 



114° 17' 



110° 10' 

 106<: 

 102^ 

 98^ 



16' 

 31' 



56' 



95° 28' 



92° 6' 



88° 51' 



85° 41' 



82° 36' 



79° 35' 



76° 

 73° 



38' 

 44' 



70° 54' 



68° 6' 



65° 22' 



62° 40' 



60° 0' 



180° 0' 



165° 56' 



155° 38' 



148° 28' 



142° 39' 



137° 36' 



133° 4' 



128° 55' 



125° 3' 



121° 26' 



118° 00' 



114° 44' 



111° 36' 



108° 86' 



105° 42' 



102° 53' 



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° 32' 



63° 31' 



61° 30' 



59° 30' 



57° 31' 



55° 34' 



53° 38' 



51° 42' 



49° 48' 



47° 54' 



46° 2' 



44° 10' 



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° 28' 



49° 48' 



48° 9' 



46° 30' 



44° 51' 



43° 14' 



41° 37' 



40° 0' 



38° 24' 



Illumi- 

 nating 

 Power. 

 (a2.) 



310 



250 



190 



132 



074 



016 



960 



904 



850 



796 



770 



742 



690 



638 



588 



538 



488 



440 



392 



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 



Theoretical 



Resolving 



Pov^er, in 



Lines to an Inch 



(A=0*5269(K. 



=line E.) 



Example. — ^The apertures of four objectives, two of which are dry, one water-immersion, and one oU-immersion, 

 would be compared on the angular aperture view as follows; — 106° (air), 157° (air), 142° (water), 130° (oil). 



Their actual apertures are, however, as -80 '98 1'2S 1'38 or their 



numerical apertures. 



