228 HANDBOOK OF PHOTOGRAPHY 



cated /-numbers lose their meaning in relation to the required exposure. The equiva- 

 lent /-number and exposure under such conditions are given by Eqs. (35) and (36), 

 respectively, in terms of magnification obtained. They may also be given in terms of 

 the lens characteristics. 



Let Lo be the principal focal length of the lens, i.e., the focal length for an object 

 at infinity, and let L be the equivalent focal length when the bellows is extended for 

 photographing near-by objects. Also let /o represent the aperture marked on the lens 

 and / represent the actual /-number. Then the actual /-number when the bellows is 

 extended, as for copying, is 



/=/o(^) =/o(M + l) (44) 



whereas the exposure required is 



E = eJ—Y = Eo{M + 1)2 (45) 



where Eo is the exposure required under the same conditions but with the lens at its 

 infinity position. 



For example, suppose we know that an exposure of %5 sec. is required at aperture 

 of //4.5 when a lens of 15-cm. focal length is set at its infinity position. It is required 

 to know the equivalent /-number and exposure when the lens-to-plate distance is 

 increased to 30 cm. From the above equations involving focal lengths, we find the 

 equivalent /-number to be 



/ = 4.5 X 3%5 = //9 (46) 



Methods of Determining Exposure. — There are three possible methods of determin- 

 ing photographic exposure: (1) estimating or guessing at it on the basis of past experi- 

 ence; (2) using exposure tables, calculators, or guides; and (3) using exposure meters. 



Estimating or guessing light values is extremely difficult because of the self-adjust- 

 ing features of the human eye by which the iris automatically adapts the eye to light 

 levels over a wide range. The use of exposure tables, calculators, or guides is of some 

 assistance, but nevertheless experience is required to judge whether the light is intense, 

 bright, or cloudy-bright. Furthermore, the eye cannot see "light" having wave- 

 lengths shorter than 400 mju, and it is the wavelengths below those that the eye cannot 

 see to which the photographic materials are usually most sensitive. Exposure meters 

 are generally preferred to the previous methods outlined. There are three general 

 types of exposure meters: (1) actinometers, based on the use of sensitive paper which 

 darkens upon exposure to light, (2) visual exposure meters which measure reflected 

 light through the medium of the human eye, and (3) photoelectric meters, capable of 

 measuring either direct or reflected light by means of a photoelectric cell and a sensitive 

 electric-current meter. The construction, use, advantages, and disadvantages of 

 these various types of meters will be considered in greater detail in a later section of 

 this chapter. 



Relative Success Obtained with Various Exposure Aids. — The success which may 

 be expected from the use of these various exposure devices depends upon their intelH- 

 gent use and an understanding of their operation and limitations. It is reported ^ that 

 Milbauer has found that the percentage of correct exposure given by these devices is 

 as shown in Table VI. While these exact figures may not be supported by other 

 observers, especially since the manner in which the results were obtained is not 

 specified, it is safe to assume that the figures given by Milbauer are reasonable and at 

 least approximately correct. Presumably these figures apply to amateur photog- 



1 Fot. Ruiidschau, 74 (No. 20), 348 (1937). 



