( « ) 



I. Numorical Aperture Tabic. 



Tlic " AiK.iriKK " ..[ all i.pll.'jil iiistrumont lii.llcaloa il« gioator or has Ciipacily lur vpcr-ivlr,g riys from the obU 

 traiisiiilttInK tliom li> tlio Image, niid tlie apertnro cf a Microscope olj.ctlvc 1b tlicrcroic detonniiUHl by tli 

 betw.'.'ii ils foinl Iciiptli and tli" dlamoter of tliP omerg-nt p-ncll at the pUiio of iU emergence— that is, the 1 

 Uiami'ler of a sinfjle-leiis ohjeillve or of llio hack hiis of a compouiul obJiTtivc. 



This ratio is express.-.! for all media aii.l in all cases hy n sin m, n being Iho refractive In.l.^x of the modiiim an.! 

 seml-nngle of aperture. The value of n siu u for any particular caeo Is tho " numerical ainrture " of the obj 



niainelevs of the 

 B.itk L< I)^cs of various i 



Dry and Immersion 

 Objectives of the Bamo 



I'o«cr a in.) 

 from 0-60 to 1-62 N A. 



Numerical] 

 Aporture- i 

 (»i sin u = a.) , 



Angle of Aperture (= 2 u). 



•52 



•50 



•48 



•46 



■44 



•42 



•40 



1^38 



1^36 



1-34 



Dry 



Obj.<;tivcs. 



(« = 1.) 



Iiluml- 



I Water- IJTomogeneout- iiatlng 

 j Immeriion' Immersion ■ Power. 

 i Objectives.' Objectives. | (o».) 

 !(n = l-33.) (n = 1-52.) I 



Theoretiral 

 I Uesolvlng 

 ' I'ower, in 

 Lines to an Inch 

 I (A=0-5269f* 

 ' =liue K.) 



180° 0' 

 157° 2' 

 147° 29' 

 140° 6' 

 133° 51' 

 128° 19' 

 123° 17' 

 118° 38' 

 114° 17' 

 110° 10' 

 106° 16' 

 102° 31' 

 98° 56' 



95° 

 92° 



28' 

 6' 



88° 51' 



85° 41' 



82° 36' 



79° 35' 



76° 

 73° 

 70° 

 68° 

 65° 

 62° 

 60° 



38' 

 44' 

 54' 



6' 

 22' 

 40' 



0' 



I1S0° 0': 

 '165° 50' 

 jl55° 38' j 

 148° 28' ! 

 142° 39' 1 

 137° 36' I 

 133° 4'i 

 128° 55' 

 125° 3'' 

 121° 26' 

 118° 00' 

 114° 44' 

 111° 36' 

 108° 30' 

 105° 42' i 

 102° 53' j 

 100° 10' 

 97° 31'! 

 94° 56' 

 92° 24' 

 89° 56' 

 87° 32' 

 85° 

 82° 

 80° 

 78° 

 76° 

 73° 

 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' 



10' 

 51' 

 34' 

 20' 

 8' 

 58' 



180° 

 101° 



ir).r 



147° 



142° 



138° 



134° 



130° 



126° 



12.3° 



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' 

 26' 



0' 

 23' 

 39' 

 42' 

 40' 

 12' 

 10' 

 26' 

 57' 

 40' 



6' 

 33 

 34' 



•310 

 ■250 

 •190 

 •132 

 ■074 

 016 

 960 

 ■904 



•••iSS 

 •.538 

 •488 

 ■440 

 ■392 

 •346 

 ■300 

 254 

 210 

 106 



! 1^124 



•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 



r850i 



790 

 770 



742 I 

 690 1 



r63S 



146,528 

 144,600 

 142,072 

 140,744 

 138.810 

 1.S0,.^'88 

 134,960 

 133.0.32 

 131,104 

 129,176 

 128,212 

 127,248 

 125,. '520 

 123,392 

 121,464 

 119,536 

 117,608 

 115,680 

 113,752 

 111,824 

 109,890 

 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 

 73,264 

 71,336 

 69,408 

 67,480 

 65,552 

 63,624 

 61,696 

 59,768 

 57,840 

 55,912 

 53,984 

 52,0.56 

 50,128 

 48,200 



r 



tr/i- 

 I'o 



c 



:.— The apertures of four objectives, two of which are dry, one water-immersion, and one oil-imiaerti 

 d be compared on the angular aperture view as follows: — 106° (air), 151° (air), 142° (water), 130° (oil), 

 ual apertures are, however, as '80 '98 1-2S 1^38 ortl' 



KXAMPLK 



would 

 Their actu 



numerical apertures. 



