158 HANDBOOK OF PHOTOGRAPHY 



Effect of Voltage on Incandescent Lamps. — The spectral-energy distribution, as well 

 as the intrinsic brightness, of incandescent lamps depends upon the temperature at 

 which they are operated, and this in turn depends upon the filament voltage and 

 current. Therefore, for precise standardized conditions, the filament voltage must be 

 maintained constant. Maintaining constant voltage on the filament of the lamp 

 likewise keeps the absolute magnitude of the emitted radiation constant, another 

 essential requirement for sensitometry. 



As the temperature of the tungsten lamp is raised, a larger portion of the total 

 energj^ is shifted into the blue end of the spectrum so that the lamps tends to approach 

 a more nearly white light source. But, even at the highest temperature at which 

 tungsten lamps can be operated, a filter is required, for incandescent lamps are still 

 entirely too deficient in blue radiation to produce a true white-light source. Further- 

 more, as the temperature of the lamp is raised, the life is considerably decreased and 

 the characteristics change more rapidly with age. A temperature of about 2500°K. 

 is the highest at which incandescent lamps may be operated if they are to give satis- 

 factory characteristics so far as life, reproducibility, and precision are concerned. 



The manner in which the life, radiant energy, and other characteristics of tung- 

 sten-filament lamps vary with the applied voltage has been studied at the National 

 Bureau of Standards.^ Some of the results of this investigation may be used to 

 determine the effect on the light output of small variations in applied voltage. Sup- 

 pose we let F represent the luminous output (lumens) of the lamp at voltage V, and 

 Fo the normal or rated huninoas output of the lamp at its normal or rated voltage, Vo. 

 Then we may use the approximate relation 



^=^o(^) (1) 



(where 5 2 is an exponent which depends upon the size and type of the lamp) to com- 

 pute the allowable variation in voltage for a specified small variation in luminous out- 

 put. In order to make the most use of this equation, it is desirable to specify F and V 

 in terms of the normal valvies Fo and Vo, and the variations from these normal values, 

 b and d, respectively. We may therefore write 



F = Fo(l + b) (2) 



and 



V = Fo(l ± d) (3) 



where b represents the change in luminous output as a result of the voltage variation d. 

 Substituting these last two equations into Eq. (1), we have 



F = Fed ±b) = ^^[^'''0-Tr)T' ^ ^"^^ - "^^^^ ^^^ 



froni which 



(1 + 6) = (1 + df' (5) 



From Eq. (5) the maximum allowable voltage variation, ±d which may be tolerated 

 for a specified fluctuation in luminous output ±6 is then given by 



_]_ 

 + d = (1 + b)Bi - 1 (6) 



In all these equations, the plus signs are to be used if the voltage (and hence the light 

 output) increases, whereas the minus signs are to be used if they decrease. Figure 4 



1 Babrow, L. E., and J. Franklin Meyer, "Characteristic Equations of ^'acuum and Gas-filled 

 Tungsten Lamps," Bur. Standards J. Research, 9,721 (1932). 



