Dr Searle, The determination of the effective aperture, etc. 195 
The deternunation of the effective aperture of the stop of a 
photographic lens. By G. F. C. SEARLE, Sc.D., F.R.S., University 
Lecturer in Experimental Physics, Fellow of Peterhouse. 
[Read 23 February 1914.] 
§1. Notation for stops. The stops of a photographic lens are 
usually marked with the symbols //8, f/16, &c. The symbol 7/8 
means that the effective diameter of the stop is one-eighth of the 
focal length of the lens system. This effective diameter is not the 
actual diameter of the hole in the diaphragm which is used to 
regulate the light entermg the camera, but is, in the case of 
cameras adjusted for landscape photography, the diameter of that 
incident beam of rays parallel to the axis, which in its passage 
through the lens system exactly fills the opening in the actual 
diaphragm. The photographic speed of the lens, when used for 
landscape work, is proportional to the square of the diameter of 
the incident beam, and hence it is important to be able to test 
whether the numbers assigned to the various stops by the makers 
are correct. If, for stance, a maker marks a stop f/8 which is 
actually 7/10, the effective area of the stop is only 64/100 of the 
area suggested by the maker’s mark. 
The “f” notation is not, however, the only system in use. The 
stops on some cameras are graduated i in “U.S.” numbers (Uniform 
System, not United States). The stops supplied with Kodak 
cameras are usually marked with the “U.S.” numbers. On this 
system the stop denoted by 7/4 by English makers is taken as the 
unit, and the numbers are so chosen that the “U.S.” number of a 
stop is proportional to the exposure required. The correspondence 
between the systems is as follows: 
“f” system P/E GSO GMO Bs oe 
Uniform System 1 4, 16 64 256 
For intermediate stops, the relation may be expressed alge- 
braically. If the “f/” number is f/n, we have f/n=//(tn x 4), 
and hence the corresponding “U.S.” number is (7/4), Thus, if 
fin corresponds to the “U.S.” number 8, we have (n/4)?= 8, or 
n? = 128, or n=11°31; this stop is often marked with the approxi- 
mate number f/11. 
The number in the symbol f/n expresses the ratio of the 
focal length of the lens to the effective diameter of the stop in the 
case of landscape work. It is therefore convenient to call the 
reciprocal number I/n, as is done by some writers, the “aperture 
ratio” of the stop. 
13—5 
