168 



HANDBOOK OF PHOTOGRAPHY 



T = 

 O = 



u 



h 

 It 



D = logio = logio Y = logio Y ^ -logic T 



(11) 

 (12) 

 (13) 



To a first approximation, D is proportional to the amount of silver deposited per unit 

 area. 



Similar equations may be derived to apply to printing papers as well as to nega- 

 tives. If /o is the luminous flux reflected by the white paper having no exposure and 

 Ir is the light flux reflected from the paper having a deposit of silver whose density is 

 D, then 



D = logio I V- 



m 



(14) 



There is nothing in the preceding equations which leads one to suspect that the 

 application of these formulas would not give definite and precisely reproducible results. 



Fig. 6. 



Polar diagram illustrating the scattering of light in passing through a photographic 



film. 



That such is not the case depends upon the fact that in passing through the developed 

 silver image of a negative, the light beam is scattered, as shown in Fig. 6, so that the 

 determination of density and transmitted light flux depends upon the manner in which 

 the transmitted light flux is measured. 



Scattering of Light by Negative. — To study in greater detail the significance of the 

 scattering of light, suppose /o in Fig. 7 represents a narrow pencil or beam of light inci- 

 dent upon the photographic negative to be measured for density. In passing through 

 the negative, part of the beam is transmitted directly through the film A ; part of the 

 light is also scattered or diffused as it passes through the film, and emerges at some 

 angle from normal. If we investigate the intensity of the transmitted rays as a func- 

 tion of the angle or direction from the point where the normal rays emerge, we find 

 that we can construct a polar diagram as shown in Fig. 7. The lengths of the vectors 

 represent the intensities of the light in that direction. Obviouslj^, a three-dimensional 

 vector plot is obtained, although, for simplicity, only a two-dimensional drawing is 

 shown in the plane of the paper. The outline or envelope of these vectors shows the 

 manner in which the emergent light is distributed as a result of partial diffusion of the 

 normal ray Iq. 



By means of this diagram it may be seen that the value of the transmitted light 

 will depend upon the manner in which it is measured, and consequently several values 

 of density can be obtained. 



