28 HANDBOOK OF PHOTOGRAPHY 



Choice of Focal Length for Various Purposes. — Under all circumstances a good 

 rule to follow is that the focal length should be as long as possible, if good perspec- 

 tive representation is desired. In particular for portraiture, to form a head 

 image, say, 3 in. high, a magnification of about one-third is required, and therefore if 

 the subject is to be, for example, 9 ft. from the lens, the plate must be 3 ft. from the 

 lens, requiring a focal length of 28 in. As this is very long, it is generally necessary to 

 place the subject at less than 9 ft. from the camera, with consequent slight "dis- 

 tortion" of the perspective. 



However, in spite of everything, small lenses are by far the most popular, mainly 

 from considerations of portability and cheapness and because the depth of focus 

 for a given /-aperture is considerably increased. Optically, also, small lenses are better 

 because the aberrational defects in a particular type of lens shrink with the scale on 

 which the lens is constructed, while the various aberration tolerances remain 

 unchanged. Thus it is often possible to make an //1. 5 lens for 16-mm. motion 

 pictures of a design which could not be made to exceed, say, //2.0 when used with 

 35-mm. films, or perhaps //2. 5 for a miniature camera covering two frames of 35-mm. 

 film. 



Lens Defects. — We have discussed so far the properties of a perfect lens. In 

 practice no lens is perfect and some slight knowledge of the kinds of defects likely to 

 be encountered is useful to the practical photographer. The principal aberrations 

 may be listed as follows : 



1. Spherical aberration. A longitudinal variation of image position for different 

 zones of the lens. 



2. Coma. Variation of image size for different zones of the lens. 



3. Chromatic aberration. Longitudinal variation of image position for different 

 colors. 



4. Chromatic difference of magnification, or transverse chromatic aberration. 

 Variation of image size for different colors. 



5. Distortion. Variation of magnification in different parts of the field. 



6. Astigmatism. A longitudinal separation between the images of radial and 

 tangential lines in the field. 



7. Curvature of field. A curvature of the "field surfaces" obtained by joining 

 up the radial and tangential astigmatic images over the entire field. 



These will be considered separately. 



Spherical Aberration. — In practically every lens of any kind it is found that 

 rays from an object point on the lens axis, entering the lens at different distances out 

 from the center, cross the axis again on the image side at different points. This is 

 clearly a defect, since in a perfect lens all the rays from an axial object point cross 

 the axis again together at the image point. 



The situation for an entirely uncorrected simple convex lens is indicated in Fig. 21. 

 The point P represents the "axial image point," which is the crossing point of raj's 

 passing through the lens near its center. The position of this image point is given 

 hj the formulas on page 15. Now in a simple lens, the other rays which pass through 

 the outer parts of the lens fall short and cross the axis at points M, N, etc. The 

 distance from P to M is called the spherical aberration of the lens for the particular 

 ray concerned, usually the extreme marginal ray at full aperture. Evidently stopping 

 down the diaphragm of such a lens will reduce the spherical aberration drastically. 

 The dotted curve in Fig. 21 is a graph connecting the height of incidence of the ray 

 with the position of its crossing point with the axis. This graph is approximately 

 a parabola for an uncorrected lens because the aberration increases approximately 

 as the square of the height of incidence; thus halving the lens diameter reduces the 

 aberration to one-quarter of its previous amount. 



