EXPOSURE AND EXPOSURE DEVICES 219 



very large exposures — much larger than are encountered in ordinary practice — the 

 density of the silver deposit may no longer increase as the exposure is increased. 



From Eq. (18) we may derive the following practical formula which indicates the 

 light intensity required when various factors are changed. Thus 



is the most general case likely to occur in practice. Equation (20) refers only to the 

 intensity and not the spectral-energy distribution of the illuminant. 



As an example of the application of this equation, suppose, as reference conditions, 

 it is known that, for a light intensity of 100 units (/o = 100), an aperture stop of 

 //8 (/o = 8), and a film speed of Weston 20 {So = 20), the required shutter speed is 

 J^5 sec. (to = Ms) when we are photographing a beach scene with a yellow filter 

 having a factor of 5 {F =5). It is desired to know what light intensity would be 

 required for the same shutter speed (t = 3^5) when the same film is used {S = 20) but 

 when the aperture stop is//4 (/ = 4). For photographs of this type the magnification 

 is so small that it may be neglected and we may consider that M = 0. Furthermore, 

 since the same lens is used in both cases, To — T, and consequently {To/T) becomes 

 unity. Substituting these values into Eq. (20) the required illumination is found to be 



/ = 10o(^)(^)2(29^o) X 5 = 125 (21) 



so that the light required is not changed appreciably from its original value. 



Aperture Stop or f-number. — The aperture stop or /-number is defined as the ratio of 

 the principal focal length of a lens L to the diameter of its exit pupil d, or 



/ = ^ (22) 



For example, if a lens whose principal focal length is 8 in. has an aperture 1 in. in 

 diameter, the /-number is //8. For a given lens the /-number varies as the diameter 

 of the iris diaphragm is changed. This diameter determines the amount of light 

 reaching the film. By varying the /-number, the amount of light and consequently 

 the exposure of the film may be controlled. It is customary to mark the lens system 

 with a series of /-numbers each of which gives twice the exposure of the next highest 

 number. Since the exposure is proportional to the square of the /-number, for the 

 exposures to be doubled the /-numbers must progress in sequence according to •\/2. 



Table II. — Progression of English and Continental Aperture Systems 



Continental System English System 



//1.6 //1.4 



//2.3 f/2.8 - 



//3.2 //4 



//4.5 //5.6 



//6.3 //8 



//9 //ll 



//12.5 //16 



//18 //22 



//25 //32 



//36 //45 



//50 //64 



//72 //90 



There are two methods of marking /-numbers in common use as shown in the 

 Table II. In each case the exposure given by any stop is twice that of the next larger 



