THE OPTICS OF PHOTOGRAPHIC LENSES 



17 



and only a very thin section of the object appears sharply in focus at a time. In this 

 connection, it should be noted that for a fixed lens, if the object is moved to the right, 

 the image moves to the right also. 



A 



A B 



K-Ct-H 



A' B' 



-Photography 

 object. 



obhque 



Fig. 10. — Diagram illustrating longitudinal magnification. 



Image of a Sloping Object. — It can be shown that a perfect lens will produce an 

 undistorted image of a plane object set perpendicular to the axis, in a plane also per- 

 pendicular to the axis. If the object is plane but is inclined to the axis, then a perfect 

 lens will produce an image on a plane which is also inclined to the axis, but the image 

 will not be perfectly sharp all over. Thus when photographing a sloping object, it is 

 necessary to stop down the lens if a sharp 

 picture is desired. A good rule for the 

 correct arrangement of object, lens, and 

 plate is to ensure that object and image 

 planes meet on the median plane of the 

 lens (Fig. 11). The image will, of course, 

 be badly distorted, but the distortion can 

 be rectified by projection printing from a 

 tilted negative, using a tilted easel to hold 

 the bromide paper. 



Measurement of Focal Length of a 

 Camera Lens. — The simplest method is to 

 stand the camera flat upon a table covered 

 with a sheet of paper and to turn it until 



the image of a distant object falls just at one edge of the picture. A pencil line x 

 (Fig. 12) is then made along one side of the base of the camera, and the camera is 

 rotated on the table until the same distant object just falls at the opposite edge of the 

 picture. Another pencil line y is then drawn along the side of the camera base, and 

 the two lines are produced until they intersect at P. The angle 6 between them repre- 

 sents the angular field of the camera corresponding to 

 the particular linear size of the picture used. Hence, 

 by drawing a line across the previous two lines, of 

 length equal to the linear picture dimension D, the 

 focal length / can be at once read off. 



The focal length can also be measured by a "nodal 

 slide" method. In this, the lens is mounted hori- 

 zontally on a simple slide over a vertical axis of rota- 

 tion. The image of a distant object is carefully 

 observed while the lens is turned through a few 

 degrees about the vertical axis, and the lens is then moved back and forth on its 

 slide until no sideways motion of the image is seen during this small rotation. In this 

 case the vertical axis passes through the second principal point of the lens, and the 

 direct distance from the vertical axis to the image gives the focal length (Fig. 13). 

 This follows from the equal-slope property of rays entering toward the first principal 

 point of a lens and leaving from the second. 



Limitation of the Beam of Light. — In every lens system, there is some material 

 stop or diaphragm which actually limits the size of the beam of light passing through 



Fig. 12. — Determination of the 

 focal length of a lens. 



