THE OPTICS OF PHOTOGRAPHIC LENSES 15 



power becomes zero and the focal length is infinite. This case represents the common 

 telescope, or the so-called afocal system. 



Distances of Object and Image. 



1. From the Principal Points. — If p, p' are the distances of object and image, 

 respectively, from the first and second principal points of a lens and if / is the focal 

 length, then 



2. From the Focal Points. — If x, x' are the distances of object and image, respec- 

 tively, from the first and second focal points of a lens, then 



xx' = -p (6) 



In both these equations, distances measured to the left of their respective focal or 

 principal points must be regarded as negative and distances to the right as positive. 

 Calculation of the Focusing Scale for a Camera. — If the focal length of a camera 

 lens is /, we may use the formula xx' = —f^ to calculate the positions of the divisions 

 on a focusing scale. For if x is the distance from the object to the first focal point of 



the lens, the distance of the object from the lens is (/ — x), and x' = is the distance 



to be marked off from the » mark on the focusing scale. Remember that the sign 

 of X will be negative if the object is to the left of the lens, with the light going from 

 left to right. This procedure applies only in the case of cameras in which the entire 

 lens is moved back and forth to focus it. In some recent cameras only the front 

 element of the lens is adjusted for focusing, and in these cases the correct focusing 

 scale must be determined by computation or by direct trial and error. On account 

 of the variation in the aberrations caused by this method of focusing, the trial-and- 

 error method of constructing a focusing scale is probably the most satisfactory. The 

 advantages of moving only the front lens are (1) greater rigidity is possible in the 

 camera if no sliding front has to be provided and, (2) a very small longitudinal move- 

 ment of the front lens often produces a very large movement of the final image on the 

 plate. 



The Thin Lens. — If a lens is extremely thin, its two principal points fall together 

 within the lens, and we can then measure all our distances from the thin lens instead 

 of from one or other of the principal points. This is often a great assistance in making 

 approximate lens calculations or measurements. 



Concave Lenses. — Concave lenses fit into the scheme outlined above for convex 

 lenses, provided we remember that the focal points are interchanged in position (Fig. 



Fig. 7. — Focal and principal points of a concave lens. 



7) as compared with a convex lens. This affects the use of the formula xx' = —f, 

 connecting the distances of object and image from their respective focal points. To 

 use this equation with a concave lens, if the light travels from left to right, x must mean 

 the distance from the object to the first focal point (on the right) and x' is the distance 



