214 HANDBOOK OF PHOTOGRAPHY 



This equation gives in the most general form the connecting Hnk relating the intensity 

 of the image and that of the original subject, so far as the lens system is concerned, 

 provided that the object and image are not far removed from the optical axis of the 

 lens. For objects considerably off the optical axis, and especially when the view angle 

 is large, the intensity of the image at a corner of the plate may vary considerably from 

 that given by Eq. (7). 



By definition the /-number of a lens is the ratio of the focal length to the diameter 

 of the aperture. Thus we may substitute / for L/d in the above equations, where / 

 represents the /-number of the lens for a specified diameter of aperture d. When this 

 substitution is made, we obtain 



/' = ^^^ (8) 



P{M + 1)' ^ 



which is, perhaps, in its simplest and most practical form. This equation states that 

 the intensity of the image is proportional to the intensity of the original object, 

 proportional to the transmission of the lens system, inversely proportional to the 

 square of the /-number, and inversely proportional to the square of the linear mag- 

 nification plus one. 



Image Brightness as Function of Filter. — A filter is frequently emploj'^ed in pho- 

 tography to increase contrast, to produce desirable pictorial effects, or to distinguish 

 between tone rendition of various colors. The property inherent in all filters is 

 absorption of a portion of the spectrum to which the photographic emulsion is sen- 

 sitive, and it thereby decreases the effective intensity of illumination on the pho- 

 tographic material. Because of this reduction of luminous intensity, the exposure 

 must be increased. The filter factor, for a particular filter, light source, and pho- 

 tographic emulsion, is a measure of the required increase in exposure and is also a 

 measure of the extent to which it reduces the quantity of light reaching the photo- 

 graphic material. 



If the filter factor is F, the intensity of the light passing through it^ is inversely 

 proportional to the filter factor or to 1/F. We may consider the effect of the filter, 

 as well as that of the lens system, in determining the intensity of the image for the 

 filter and lens system 



/' = H^ (a\ 



Exposure Time and Film Speed. — The sensitivity or speed of a photographic 

 material is an important factor in determining the exposure required to produce a 

 given photographic effect. Various methods of determining and specifying the speed 

 of photographic materials are in use and are described in the chapter on Photographic 

 Sensitometr3^ It is sufficient to say that in all the common methods of specifying 

 film speed, the larger numerical units indicate the faster or more sensitive emulsions, 

 i.e., those requiring the least exposure to produce an image of given density. This 

 may be seen by comparing the speed numbers in the various systems with the relative 

 exposure as given in column 1 of the table of film speeds. Appendix B. 



The various film-speed systems are not based on the same fundamental use of the 

 D-logio E cun^e, and the film-speed numbers do not progress uniformly in the various 

 systems; in some cases the speed numbers progress proportionately to the relative 

 speed, in others they do not. It is possible, however, to devise a relationship between 



' In speaking of the transmission of light through a filter it must be remembered that a true filter 

 does not provide equal absorption for all wavelengths to which the photographic material is sensitive. 

 Strictly speaking, it is therefore improper to deal with the intensity of light passing through the filter 

 without considering the spectral distribution of the light and the spectral transmission of the filter. 

 These factors are implicitly taken into account, however, in the determination of the filter factor. 



