APERTURE TABLE. 
Numerical 
Apert lire. 
(n sin « = a.) 
Corresponding Angle (2 u) for 
Limit of Resolving Power, in Lines to an Inch. 
Illuminating 
Power. 
(«*■) 
1 Penc- 
tratin, 
Power 
0 
Air 
(ft = 1*00). 
Water 
(n = 1-33). 
Homogeneous 
Immersion 
(« ~ 1-52). 
White Light. 
(A = 0-5269 
Line E.) 
Monochromatic 
(Blue) Light. 
(A = 0-4861 ii . 
Line F.) 
Photography. 
(A = 0-4000 ii . 
Near Line h.) 
1-52 
•• 
180 ° 0 ' 
146,543 
158,845 
193,037 
2-310 
•658 
151 
.. 
166 ° 51 ' 
145,579 
157,800 
191,767 
2-280 
•665 
1-50 
161 ° 23 ' 
144,615 
156,755 
190,497 
2-250 
•667 
1-49 
1 
157 ° 12 ' 
143,651 
155,710 
189,227 
2-220 
■671 
1-48 
153 ° 39 ' 
142,687 
154,665 
1 S 7,957 
2-190 
• 67 € 
1-47 
, . 
150 ° 32 ' 
141,723 
153,620 
186,687 
2-161 
• 68 C 
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 
• 69 C 
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 
i 
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 
•801 
1-22 
133 ° 4 ' 
106 ° 45 ' 
117,620 
127,494 
154,937 
1-488 
• 82 C 
1-20 
128 ° 55 ' 
104 ° 15 ' 
115,692 
125,404 
152,397 
1-440 
• 83 c 
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 
•865 
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 
• 89 i 
110 
111 0 36 ' 
92 ° 43 ' 
106,051 
114,954 
139,698 
1-210 
• 90 ! 
108 
108 ° 36 ' 
90 ° 34 ' 
104,123 
112,864 
137,158 
1-166 
• 92 ( 
106 
105 ° 42 ' 
88 ° 27 ' 
102,195 
110,774 
134,618 
1-124 
• 94 ; 
104 
102 ° 53 ' 
86 ° 21 ' 
100,266 
108,684 
132,078 
1-082 
•965 
102 
100 ° 10 ' 
84 ° 18 ' 
98,338 
106,593 
129,538 
1-040 
• 98 C 
100 
180 ° 0 ' 
97 ° 31 ' 
82 ° 17 ' 
96,410 
104,503 
126,998 
1-000 
1 - 00 ( 
0-98 
157 ° 2 ' 
94 ° 56 ' 
80 ° 17 ' 
94,482 
102,413 
124,458 
•960 
1 • 02 ( 
0-96 
147 ° 29 ' 
92 ° 24 ' 
78 ° 20 ' 
92,554 
100,323 
121,918 
•922 
1-045 
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 
111 ] 
0-88 
123 ° 17 ' 
82 ° 51 ' 
70 ° 44 ' 
84,841 
91,963 
111,758 
• 774 : 
1 • 13 t 
0-86 
118 ° 38 ' 
80 ° 34 ' 
68 ° 54 ' 
82,913 
89,873 
109,218 
•740 
1 • 16 c 
0-84 
114 ° 17 ' 
78 ° 20 ' 
67 ° 6 ' 
80,984 
87,783 
106,678 
•706 
1 • 19 ( 
0-82 
110 ° 10 ' 
76 ° 8 ' 
65 ° 18 ' 
79,056 
85,693 
104,138 
•672 
1 • 22 C 
0-80 
106 ° 16 ' 
73 ° 58 ' 
63 ° 31 ' 
77,128 
83,603 
101,598 
•640 
1-256 
0-78 
102 ° 31 ' 
71 ° 49 ' 
61 ° 45 ' 
75,200 
81,513 
99,058 
•608 
1-285 
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 
1-385 
0-70 
88 ° 51 ' 
63 ° 31 ' 
54 ° 50 ' 
67,487 
73,152 
88,899 
•490 
1-425 
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 
1-565 
0-62 
76 ° 38 ' 
55 ° 34 ’ 
48 ° 9 ' 
59,774 
64,792 
78,739 
•384 
1-611 
0-60 
73 ° 44 ' 
53 ° 38 ' 
46 ° 30 ' 
57,816 
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 
1-855 
0-52 
62 ° 40 ’ 
46 ° 2 ' 
40 ° 0 ’ 
50,133 
54,342 
66,039 
•270 
1-921 
0-50 
60 ° O ' 
44 ° 10 ' 
38 ° 24 ' 
48.205 
52,252 
63 , 49 Sf 
•250 
2 006 
0-45 
53 ° 30 ' 
39 ° 33 ' 
34 ° 27 ' 
43,385 
47,026 
57,149 
•203 
2-225 
0-40 
47 ° 9 ' 
35 ° 0 ' 
30 ° 31 ' 
38,564 
41,801 
50,799 
•160 
2 - 50(1 
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 
3-331 
0-25 
28 ° 58 ' 
21 ° 40 ' 
18 ° 56 ' 
24,103 
26,126 
31,749 
•063 
4 • 00 ( 
0-20 
23 ° 4 ’ 
17 ° 18 ' 
15 ° 7 ' 
19,282 
20,901 
25,400 
•040 
5 - 00 ( 
0 15 
17 ° 14 ' 
12 ° 58 ' 
11 ° 19 ' 
14,462 
15,676 
19,050 
•023 
6-667 
010 
11 ° 29 ' 
8 ° 38 ’ 
7 ° 34 ' 
9,641 
10,450 
12,700 
•010 
lOOOt 
0 05 ! 
5 ° 44 ' 
4 ° 18 ' 
3 ° 46 ' 
4,821 
5,252 
6 , 350 
•003 
20 • 00 < 
