16 



HANDBOOK OF PHOTOGRAPHY 



from the image to the second focal point (on the left). The two principal points 

 fall within the lens as usual, and the focal length is now negative. 



The Size of the Image. — The size of an image can be obtained at once if it is 

 remembered that any ray entering toward the first principal point of a lens leaves from 

 the second principal point at the same slope as it enters (Fig. 8). Thus, if an object 

 subtends an angle B at the first principal point of a lens, the image will subtend the 



same angle 6 at the second principal point. 

 Therefore, if p, p' represent the distances of the 

 object and image from the two principal points, 

 respectively, the magnification will be given 

 by 



Fig. 8. — Equal slope property of 

 the principal points. In this dia- 

 gram d\ = Oi. 



image size _ image distance _ p' 

 object size object distance p 



(7) 



If object and image distances are measured from the focal points (x, x'), then the 

 magnification is given by 



x' f 

 m = — :t = - 



(8) 



(A negative magnification merely implies an inverted image.) If an object is very 

 distant and subtends an angle 6 at the lens, its image will lie in the focal plane and will 

 also subtend an angle 6. Thus the linear size of the image in this case will be equal 

 to / tan d. 



Telephoto Lenses. — A telephoto lens is a lens having a long focal length but 

 a short "back focal distance," or distance from the rear lens surface to the focal point. 

 The long focal length ensures a large-scale picture, but, since the image is close to the 

 back of the lens, the over-all camera length is kept short. This result is achieved by 

 using a positive front element and a negative rear element, usually of approximately 

 equal focal length, separated by a finite distance. In such a combination (Fig. 9) the 



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Fig. 9. — The telephoto lens. 



two principal points fall in front of the convex element, giving the desired long focal 

 length and short back focus. The focal length of the system can be altered by chang- 

 ing the separation. In the past, many "telenegative" lenses have been designed for 

 use behind an ordinary photographic lens to convert it into a telephoto lens; it is now 

 customary to use only complete telephoto lenses properly designed for the purpose. 

 The ratio of focal length to back focal distance is called the "telephoto magnification." 

 Longitudinal Magnification. — If an object has a depth q along the lens axis, then 

 its image will have a depth q' along the axis (Fig. 10), where A', B' are, respectively, 

 the images of the object points A, B. Then the ratio q' /q is called the "longitudinal 

 magnification" of the image. It can be shown that, if q and q' are small, the longi- 

 tudinal magnification m' is equal to the square of the ordinary magnification in. Hence 

 in any ordinary camera, where m is generally fairly small, m' is very small, and a 

 considerable range of object distances appear equally in focus on the plate. On the 

 other hand, in photomicrography where the magnification m is high, m' is very high. 



