APERTURE TABLE, 
Corresponding Angle (2 u) for 
Limit of Resolving Power, in Lines to an Inch. 
Illuminating 
Power. 
( 02 .) 
Pene- 
Numerical 
Aperture. 
(« sin u = a.) 
Air 
(n = 1-00). 
Water 
(n = 1-33). 
Homogeveous 
Immersion 
(7! =1*62). 
White Light . 
(A = 0*5269 g, 
Line E.) 
Monochromatic 
(Blue) Light. 
(A = 0*4861 g. 
Line F.) 
Photography. 
(A =0*4000 g, 
Near Line h.) 
trating, 
Power 
0 
1*52 
180 ° 
G ' 
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 
•694 
1-42 
138 ° 
12 ' 
136,902 
148,395 
180,337 
2-016 
•709 
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 
118 
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 
110 
111 ° 
36 ' 
92 ° 
43 ' 
106,051 
114,954 
139,698 
1*210 
•909 
108 
108 ° 
36 ' 
90 ° 
34 ' 
104,123 
112,864 
137,158 
1166 
•926 
106 
105 ° 
42 ' 
88 ° 
27 ' 
102,195 
i 110,774 
134,618 
1*124 
•943 
104 
102 ° 
53 ' 
86 ° 
21 ' 
100,266 
108,684 
132,078 
1*082 
•962 
102 
100 ° 
10 ' 
84 ° 
18 ' 
98,338 
106,593 
129,538 
1*040 
•980 
100 
180 ° 
O ' 
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 
98,223 
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 
1136 
0-86 
118 ° 
38 ' 
80 ° 
34 ' 
68 ° 
54 ' 
82,913 
89,873 
109,218 
•740 
1*163 
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 ° 
31 ' 
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 
0-66 
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 52 
62 ° 
40 ' 
46 ° 
2 ' 
40 ° 
0 ' 
50,133 
54,342 
66,039 
•270 
1*923 
0 50 
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 ' 
33,744 
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 ' 
I 12 ° 
58 ' 
11 ° 
19 ' 
14,462 
15,676 
19,050 
•023 
6-667 
010 
1 11 ° 
29 ' 
I 8 ° 
38 ' 
7 ° 
34 ' 
9,641 
10,450 
12,700 
•010 
10*000 
0 05 
5 ° 
44 ' 
4 ° 
18 ' 
3 ° 
46 ' 
4,821 
5,252 
6,350 
•003 
20-000 
