226 Focometry of Lenses and Lens- Combinations. [Feb. 10, 



the approximate positions or distance apart of the two principal 

 points, but in which both the true focal length and the width between 

 the principal points are determined by direct measurements of 

 lengths. 



The principle of the method is as follows : Beyond the principal 

 focal points on each side of the lens, at distances equal to the true 

 focal length, are two points which are conjugate to one another 

 and symmetrically situated at twice the true focal length from the 

 two principal points. These may be called the symmetric points : 

 and the planes drawn through them orthogonally to the principal 

 axis may be called the symmetric planes. They are planes of unit 

 magnification, and possess the known geometric property that the 

 ordinate in one of these planes of the point of intersection of any 

 incident ray is equal in magnitude, but opposite in sign, to the ordin- 

 ate in the other plane of the point of intersection of the emergent 

 ray. Let AB be the lens or combination of lenses, F,F 2 the principal 

 foci, H^fclj the principal points, SjSj the symmetric points. Then 

 the true focal length is F 2 H 2 = FjH, = F^ = F 2 S 2 . 



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Suppose a parallel beam to be sent from left to right through AB ; 

 an image will be formed at Fj. Let the light then be sent from right 

 to left forming an image at F 2 . Suitable transparent micrometers 

 are placed to receive these images and to ascertain their precise 

 position in space. A graduated bench is provided upon which the 

 lens and the micrometers are placed so as to read off the distances 

 between these points. A gearing is provided, namely, a right- and 

 left-handed screw, by means of which, when the two micrometeru 

 have been placed at F T and F 2 and clamped to the screw, they can be 

 moved by the experimenter at exactly equal rates outwards, so that 

 when one arrives at S t the other arrives at S 3 . This is known by 

 observing in one micrometer the exact image of the other of equal 

 size. The distance through which the micrometers have each been 

 displaced is equal to the true focal length ; and the distance H , H., 

 between the two principal points is found by reckoning backwards 

 from Fj and F 2 distances equal to the focal length so found. The 

 positions of the two principal points can then be marked upon the 

 outside of the tube of the objective. 



These principles are embodied in an instrument described in the 



