PHOTOGRAPHIC LIGHT SOURCES 



269 



Density Dependent upon Light Intensity. — Suppose we have an optical bench upon 

 which is mounted, at one end, a photographic plate behind a shutter which is arranged 

 to let light through to the plate for a given amount of time, e.g., t sec, but shuts off all 

 light from reaching the film except when it is open. Let a convenient light source, 

 such as an incandescent lamp, be arranged before the shutter in such a way that the 

 distance between the film and the light source may be varied at will. It is assumed 

 that the light source is maintained constant in intensity and spectral-energy distribu- 

 tion. ^ This may be accomplished by operating the lamp at sufficiently low tem- 

 peratures (not more than 2400°K.) and by maintaining the temperature of the lamp 

 constant. The most convenient way of maintaining constancy of the luminous 

 output is to maintain the voltage across its terminals constant. 



Under the conditions assumed, exposure of the photographic plate will only take 

 place during the time the shutter is open, and during this time the illumination on the 

 plate will depend upon the intrinsic brightness of the lamp with its associated filter as 

 well as the distance between the lamp and the photographic plate. If the lamp is 

 rated at k candle power and the distance between the lamp and photographic plate is 

 D, then the Light intensity on the photographic 

 plate will be 



£)2 



(1) 



If t is the time during which the shutter is open, 

 the exposure of the plate may then be defined as 



kt_ 



Z)2 



E = It ^ ^^ 



(2) 



By keeping k and t constant, the exposure given 

 to the photographic plate may now be made to 

 depend only upon the intensity of light falling 

 upon the photographic plate /. 



E = It 

 Log,oE = Log,ol+Log,ot 

 For t = constant 

 Log,oE- A + LogioL 



^ Log,ol 

 Fig. 8. — Characteristic of typical 

 negative materials, showing the man- 

 If we give different sections of the photo- ner in which the density depends upon 

 graphic plate different exposures by varying the the intensity of illumination for con- 

 distance D for each successive exposure and stant exposure time (constant shutter 



. speeds). 

 then determine the density of the silver deposit 



after the film is properly processed, we may determine the manner in which 

 the density depends upon the intensity of the light source to which it was 

 exposed. If such a series of exposures is made, the densities are measured and plotted 

 against intensity /, the results will give the typical characteristic curve shown in 

 Fig. 8. From this curve it will be seen that: (1) for extremely low values of illumina- 

 tion, only a small silver deposit occurs corresponding to the fog density of the material; 

 (2) for increasing values of illumination, additional deposits of silver occur; (3) for a 

 considerable range, the density is proportional to the logarithm of the illumination; (4) 

 this proportionality fails but reaches a maximum density after which (5) the density 

 decreases for extremely large values of light intensity. In practice, this last region, 

 corresponding to extremely large values of exposure, is of no practical use; the most 

 important part of this characteristic is the linear region for which the density is pro- 

 portional to the logarithm of the light intensity, so long as the shutter speed is main- 

 tained invariable. 



Effect of Sensitivity of Photographic Material. — The sensitivity of a photographic 

 plate may be, and is, expressed in a rather wide variety of ways.^ Because of the 



1 For simplicity and consistency with sensitometric practice, let it be assumed that the spectral 

 radiation of the lamp is modified by means of filters so that it closely approximates that of mean 

 noon sunlight. 



^ See p. 190, Chapter on Photographic Sensitometry. 



