APERTURE TABLE, 
Numerical 
Aperture 
(n eln u = a.) 
Corresponding Angle (2 u ) for 
Limit of Resolving Power, in Lines to an Inch 
Illuminating 
Power. 
(a 2 .) 
Pene- 
trating 
Power. 
G) 
Air 
(n = 1*00). 
Water 
(n = 1 - 33 ). 
Homogeneous 
Immersion 
(n = 1 - 52 ). 
White Light. 
(A. = 0*5269 / x , 
Line E.) 
Monochromatic 
(Blue) Light. 
(A = 0*4861 n , 
Line F.) 
Photography. 
(A = 0*4000 fx , 
near Line h.) 
152 
180 ° 0 ' 
146,543 
158,845 
193,037 
2*310 
•658 
1-51 
166 ° 51 ' 
145,579 
157,800 
191,767 
2*280 
•662 
1-50 
161 ° 23 ' 
144,615 
156,755 
190,497 
2*250 
•667 
1*49 
.. 
157 ° 12 ' 
143,651 
155,710 
189,227 
2*220 
*671 
1-48 
153 ° 39 ' 
142,687 
154,665 
187,957 
2*190 
•676 
1-47 
150 ° 32 ' 
141,723 
153,620 
186,687 
2*161 
•680 
1-46 
147 ° 42 ' 
140,759 
152,575 
185,417 
2*132 
•685 
1*45 
145 ° 6 ' 
139,795 
151,530 
184,147 
2*103 
•690 
1-44 
142 ° 39 ' 
138,830 
150,485 
182,877 
2*074 
•694 
1-43 
140 ° 22 ' 
137,866 
149,440 
181,607 
2*045 
•699 
1-42 
138 ° 12 ' 
136,902 
148,395 
180,337 
2*016 
•704 
1*41 
136 ° 8 ' 
135,938 
147,350 
179,067 
1*988 
•709 
1-40 
134 ° 10 ' 
134,974 
146,305 
177,797 
1*960 
•714 
1*39 
132 ° 16 ' 
134,010 
145.260 
176,527 
1*932 
•719 
1*38 
130 ° 26 ' 
133,046 
144,215 
175,257 
1*904 
•725 
1-37 
128 ° 40 ' 
132,082 
143,170 
173,987 
1*877 
•729 
1-36 
126 ° 58 ' 
131,118 
142,125 
172,717 
1*850 
•735 
1-35 
125 ° 18 ' 
130,154 
141,080 
171,447 
1*823 
•741 
1-34 
123 ° 40 ' 
129,189 
140,035 
170,177 
1*796 
•746 
1-33 
180 ° 0 ' 
122 ° 6 ' 
128,225 
138,989 
168,907 
1*769 
•752 
1*32 
165 ° 56 ' 
120 ° 33 ' 
127,261 
137,944 
167,637 
1*742 
*758 
1-30 
155 ° 38 ' 
117 ° 35 ' 
125,333 
135,854 
165,097 
1*690 
•769 
1-28 
148 ° 42 ' 
114 ° 44 ' 
123,405 
133,764 
162,557 
1*638 
•781 
1-26 
142 ° 39 ' 
111 ° 59 ' 
121,477 
131,674 
160,017 
1*588 
•794 
1-24 
137 ° 36 ' 
109 ° 20 ' 
119,548 
129,584 
157,477 
1 538 
•806 
1-22 
133 ° 4 ' 
106 ° 45 ' 
117,620 
127,494 
154,937 
1*488 
•820 
1-20 
128 ° 55 ' 
104 ° 15 ' 
115,692 
125,404 
152,397 
1*440 
•833 
1-18 
125 ° 3 ' 
101 ° 50 ' 
113,764 
123,314 
149,857 
1*392 
•847 
116 
121 ° 26 ' 
99 ° 29 ' 
111,835 
121,224 
147,317 
1*346 
•862 
114 
118 ° 0 ' 
97 ° 11 ' 
109,907 
119,134 
144,777 
1*300 
•877 
1 12 
114 ° 44 ' 
94 ° 55 ' 
107,979 
117,044 
142,237 
1*254 
•893 
1*10 
111 ° 36 ' 
92 ° 43 ' 
106,051 
114,954 
139,698 
1*210 
•909 
1*08 
108 ° 36 ' 
90 ° 34 ' 
104,123 
112,864 
137,158 
1*166 
•926 
1*06 
105 ° 42 ' 
88 ° 27 ' 
102,195 
110,774 
134,618 
1*124 
•943 
1*04 
102 ° 53 ' 
86 ° 21 ' 
100,266 
108,684 
132,078 
1*082 
•962 
1*02 
100 ° 10 ' 
84 ° IS '’ 
98,338 
106,593 
129,538 
1*040 
•980 
1*00 
180 °* 0 ' 
97 ° 31 ' 
82 ° 17 ' 
96,410 
104,503 
126,998 
1*000 
1*000 
0*98 
157 ° 2 ' 
94 ° 56 ' 
80 ° 17 ' 
94,482 
102,413 
124,458 
•960 
1*020 
0*96 
147 ° 29 ' 
92 ° 24 ' 
78 ° 20 ' 
92,554 
100,323 
121,918 
*922 
1*042 
0*94 
140 ° 6 ' 
89 ° 56 ' 
76 ° 24 ' 
90,625 
98,233 
119,378 
•884 
1*064 
0*92 
133 ° 51 ' 
87 ° 32 ' 
74 ° 30 ' 
88,697 
96,143 
116,838 
*846 
1*087 
0*90 
128 ° 19 ' 
85 ° 10 ' 
72 ° 36 ' 
86,769 
94,053 
114,298 
•810 
1*111 
0*88 
123 ° 17 ' 
82 ° 51 ' 
70 ° 44 ' 
84,841 
91,963 
111,758 
*774 
1*136 
0*86 
118 ° 38 ' 
80 ° 34 ' 
68 ° 54 ' 
82,913 
89,873 
109,218 
*740 
1163 
0*84 
114 ° 17 ' 
78 ° 20 ' 
67 ° 6 ' 
80,984 
87,783 
106,678 
*706 
1*190 
0*82 
110 ° 10 ' 
76 ° 8 ' 
65 ° 18 ' 
79,056 
85,693 
104,138 
•672 
1*220 
0*80 
106 ° 16 ' 
73 ° 58 ' 
63 * 81 ' 
77,128 
83,603 
101,598 
•640 
1-250 
0*78 
102 ° 31 ' 
71 ° 49 ' 
61 ° 45 ' 
75,200 
81,513 
99,058 
•608 
1*282 
0*76 
98 ° 56 ' 
69 ° 42 ' 
60 ° 0 ' 
73,272 
79,423 
96,518 
•578 
1*316 
0*74 
95 ° 28 ' 
67 ° 37 ' 
58 ° 16 ' 
71,343 
77,333 
93,979 
*548 
1*351 
0*72 
92 ° 6 ' 
65 ° 32 ' 
56 ° 32 ' 
69,415 
75,242 
91,439 
*518 
1*389 
0*70 
88 ° 51 ' 
63 ° 31 ' 
54 ° 50 ' 
67,487 
73,152 
88,899 
•490 
1*429 
0*68 
85 ° 41 ' 
61 ° 30 ' 
53 ° 9 ' 
65,559 
71,062 
86,359 
•462 
1*471 
0*66 
82 ° 36 ' 
59 ° 30 ' 
51 ° 28 ' 
63,631 
68,972 
83,819 
•436 
1-515 
0*64 
79 ° 36 ' 
57 ° 31 ' 
49 ° 48 ' 
61,702 
66,882 
81,279 
•410 
1*562 
0*62 
76 ° 38 ' 
55 ° 34 ' 
48 ° 9 ' 
59,774 
64,792 
78,739 
•384 
1*613 
0*60 
73 ° 44 ' 
53 ° 38 ' 
46 ° 30 ' 
57,846 
62,702 
76,199 
•360 
1*667 
0*58 
70 ° 54 ' 
51 ° 42 ' 
44 ° 51 ' 
55,918 
60,612 
73,659 
•336 
1*724 
0*56 
68 ° 6 ' 
49 ° 48 ' 
43 ° 14 ' 
53,990 
58,522 
71,119 
•314 
1*786 
0*54 
65 ° 22 ' 
47 ° 54 ' 
41 ° 37 ' 
52,061 
56,432 
68,579 
•292 
1*852 
0*62 
62 ° 40 ' 
46 ° 2 ' 
40 ° 0 ' 
50,133 
54,342 
66,039 
•270 
1*923 
0*60 
60 ° 0 ' 
44 ° 10 ' 
38 ° 24 ' 
48,205 
52,252 
63,499 
•250 
2*000 
0*45 
53 ° 30 ' 
39 ° 33 ' 
34 ° 27 ' 
43,385 
47,026 
57,149 
•203 
2*222 
0*40 
47 ° 9 ' 
35 ° 0 ' 
30 ° 31 ' 
38,564 
41,801 
50,799 
*160 
2*500 
0 35 
40 ° 58 ' 
30 ° 30 ' 
26 ° 38 ' 
33,741 
36,576 
44,449 
•123 
2*857 
0*30 
34 ° 56 ' 
26 ° 4 ' 
22 ° 46 ' 
28,923 
31,351 
38,099 
•090 
3*333 
0*25 
28 ° 58 ' 
21 ° 40 ' 
18 ° 56 ' 
24,103 
26,126 
31,749 
•063 
4*000 
0*20 
23 ° 4 ' ! 
17 ° 18 ' 
15 ° 7 ' 
19,282 
20,901 
25,400 
•040 
5-000 
0*15 
17 ° 14 ' 
12 ° 58 ' 
11 ° 19 ' 
14,462 
15,676 
19,050 
•023 
6*667 
0*10 
11 ° 29 ' 
8 ° 38 ' 
7 ° 34 ' 
9,641 
10,450 
12,700 
•010 
10*000 
0 05 
5 ° 44 ' 
4 ° 18 ' 
3 ° 46 ' 
4,821 
5,225 1 
6 [350 
•003 
20-000 
