224 HANDBOOK OF PHOTOGRAPHY 



light is doubled, and a shutter speed of Ko sec. is used with an aperture stop of //16, 

 what is the required film speed? The magnification and transmission factor may be 

 neglected, and no filter is used. From these conditions we find that (So = 8, F = 1, 

 _/■(,= 8, / = 16, U = Ho) * = Ko, and la/I = 0.5, since the final illumination I is 

 twice the initial illumination 7o. From these values we obtain, from Eq. (30) 



5=8Xlx(fyx(|i)xl=8 (31) 



SO that a film of the same speed is suitable. 



Exposure with Supplementary Lenses. — Sometimes supplementary lenses are used 

 to increase or decrease the equivalent focal length of a lens. Since the addition of the 

 supplementary lens does not change the engravings of the /-numbers, which are a 

 measure of the diameter of the aperture, but does change the focal length of the lens, 

 the supplementary lens changes the effective /-number of the combination so far as 

 this is a measure of the light-collecting power of the lens system. Consequently the 

 exposure is altered from that required when the supplementary lens is not used, at 

 least so far as the engraved /-numbers may be taken as an indication of exposure. 



The manner in which the actual exposure must be modified because of the change in 

 focal length when a supplementary lens is used may be easily determined. Let Eo be 

 the exposure which is required for a given set of light conditions when the focal length 

 of the lens is Lo and the diameter of the aperture is do. Let E be the exposure required 

 when the supplementary lens is used with the regular lens, so that the focal length of 

 the combination is now L. The diameter of the aperture stop, as indicated by the 

 engraved /-numbers remains unchanged and is therefore do. Then the engraved 

 /-number will be 



/o = ^ (32) 



whereas the true /-number of the combination will be 



Thus for a given aperture the /-number is directly proportional to the focal length of 

 the combination lens system. In terms of the exposure required without the supple- 

 mentary lens, the exposure required when the supplementary lens is used will be 



E - E.(jy = iS.(A)' (34) 



Sometimes the magnification which the supplementary lens produces will be given 

 rather than its effect on the focal length. The /-number of the combination of this 

 case will be 



/ = /o(M + 1) (35) 



in terms of the engraved /-numbers and the magnification M, whereas the exposure 

 will be 



E = EoiM + 1)2 (36) 



in terms of the magnification and the exposure without the supplementary lens. 



As an example, suppose we have a lens of 15-em. focal length with a maximum 

 /-number of 4.5. Then the maximum aperture will be do = Lo/fo = 15/4.5 = 3.33 

 cm. If we use a supplementary lens which makes the combined focal length equal to 



