332 



F. J. CHESHIRE ON SIMPLE METHODS OF 



the difference of the magnifications.* Fig. 1 is a diagram which 

 represents the production of an image of an object by an optical 

 system with principal planes P and P^. The object of length o 

 is first supposed to be at (1), giving an image ?', and is then 

 supposed to be moved to (2) to give an image {^ in a plane 

 at a distance 8 from the first image-plane ; f and f^ equal the 

 focal lengths of the system, and w the distance between the prin- 

 cipal focus of the image-space and the first image-plane. Two 

 rays are drawn as usual from a terminal point of the object — 

 one parallel to the axis to the second principal plane P, and 

 then through the second principal focus ; and the other through 

 the first principal focus to the first principal plane P^, and 

 then parallel to the axis. 



When the object is at (1) the magnification — 



f 



and when at (2) the magnification — 



f 



Deducting equation (1) from (2) — 



o> -f- 8 — to 



(2) 



Whence 



Mi-M = 

 S 



/ 



8 



7 



/= 



Mi-M 



(3) 



Using the microscope, then, the magnifying power of the 

 objective is first determined with the draw-tube pushed in. This 

 may be done by placing a sheet of ground glass on the top of the 



* Actually, in Abbe's focometer, it is the distance between two object 

 planes that is measured, but this obviously does not affect the principle 

 involved. 



