220 HANDBOOK OF PHOTOGRAPHY 



stop. The /-numbers engraved on a lens usuall,y follow either the English or the 

 Continental /-markings quite consistently, although some deviation from this practice 

 frequently occurs for the largest aperture — ^the smallest /-number. For example, 

 many lenses are marked in the English system but have a maximum aperture of 

 //4.5 rather than //4. 



From Eq. (18) we obtain, for the most general expression for the aperture stop, the 

 expression, 



As an example of the application of this relation, suppose exposure tables show that 

 the proper exposure is Hs sec. {to = ^5) at an aperture stop of //8 (/o = 8) if the 

 film speed has a rating of Weston 16 (^So = 16). If we use a film having a speed of 

 Weston 32 {S = 32), a filter having a factor of 4 {F =4), and choose an exposure 

 time t = }^ sec. for identical conditions of illumination (/o = I), what will be the 

 required aperture stop if the magnification may be neglected (M = 0) ? Substituting 

 values in Eq. (23), we find 



V#-'^ ' 



/ = 8 X 1 X \f^ X ^ X 1 X -r = 12.6 (24) 



72 5 J^ O 4 



If the lens is marked with an aperture of //12.5, this should be used, otherwise an 

 aperture of //ll is likely to be nearest to the correct value. Intermediate /-number 

 apertures can be obtained by setting the index of the iris diaphragm at a position 

 intermediate between two markings. For all practical purposes //12.5 would lie 

 about one-third the distance from// 11 and //1 6 and so on. 



Filter Factor. — The purpose of filters is to absorb light of certain portions of the 

 spectrum, thereby modifying the quality of the light reaching the negative. This 

 modification of the quality of the light may be desired for technical or artistic reasons, 

 but it always acts to reduce the amount of light reaching the film from that which 

 would reach it if the filter were not used. In general, it may be said that the more 

 dense a filter is, the more light it absorbs, and consequentlj^ the longer must be the 

 exposure time — other conditions remaining unchanged — ^to produce a given film 

 density. 



But the color of a filter, or, more correctly, its spectral absorption, is also important 

 in determining the increase in exposure occasioned by the use of the filter. The more 

 light which a filter absorbs to which the film is sensitive, the greater will be the filter 

 factor, and the greater will be the increase in exposure required as a result of using the 

 filter. A filter absorbing blue light may appear yellow or orange to the eye and may 

 seem to be, visually, as dense as a blue filter which has its principal absorption at the 

 red end of the visual spectrum. But it is quite likelj^ that the yellow filter will have 

 the greater filter factor and consequently will require greater increase in exposure 

 than the blue filter. The reason for this is that the film is usually more sensitive to 

 blue than to red light, so that the yellow filter will cut out more effectively the light 

 acting on the film than will the blue filter. It should be remembered that the filter 

 factor is not a constant for a given filter but depends upon the spectral absorption of 

 the filter (which is constant), the spectral sensitivity of the film, and the spectral- 

 energy distribution of the light source used. Consequently the filter factor will change 

 as the filter is used with different films or light sources.' 



From Eq. (18) we can determine what effect the filter has on aperture stop, shutter 

 speed, film sensitivity, or light intensity, etc. From this equation we find that 



1 See chapter on Light Filters for further discussion of this point. 



