CH. VII] FOCUS OF OCULARS 191 



tion of the real image is 1.25-7-0.1 = 12.5 or the real image is i2 l /> 

 times as large as the object (Figs. 26, 109.) 



To find the equivalent focus of this objective knowing its 

 magnification at 250 mm. one has simply to apply the law as shown 

 graphically in Fig. 109, viz; The si/.e of object and image are di- 

 rectly as their distances from the center of the lens : The distance of 

 the object from tlie lens is with the microscope very nearly the 

 principal focal distance and is designed by f. The formula is then 

 written: the object is to the image as the principal focal dis- 

 tance is to the imagedistance (25omm.) or o:i:: f:25o mm. In this 

 case all the factors are known except f. Then 1.25:0. i::f: 

 250 whence f 20. Or as the magnification of the real image is 

 known to be 12.5 the formula may read 12.5:1 ::f:25o whence f= 

 20 as before. By referring to figures 109 it is seen that if the sim- 

 ple lens had a principal focal distance of 20 mm. and the image dis- 

 tance is 250 mm. then the real image is 12.5 times the length of 

 the object, since the distances from the center of the lens to the object 

 (20 mm) and image (250 mm.) are in the proportion of i to 12.5. 



263 Determination of Initial or Independent Magnifica- 

 tion of the Objective. The Initial magnification means simply 

 the magnification of the real image (A'B 1 , Fig. 26, also Fig 109) un- 

 affected by the ocular. It may be determined experimentally exact- 

 ly as described in 262. For example, the image of the object 

 (y-g- mm.) measured by the ocular micrometer, at a distance of 250 

 mm. is 1.25., z'. <?. , it is 12.5 times magnified, hence the initial mag- 

 nification of the 20 trim, objective is 12.5. 



Knowing the equivalent focus of an objective, one can deter- 

 mine its initial magnification by dividing 250 mm. by the equivalent 

 focus in millimeters. Thus the initial magnification of a 5 mm. 

 objective is ^f- = 50; of a 3 mm., -f- 83.3; of a 2 mm., -:]" =125. 



264. Determining the Equivalent Focus of an Ocular. 

 If one knows the initial magnification of the objective ( 263) the 

 approximate equivalent focus of the ocular can be determined as 

 follows : 



The distance between the position of the real image, a position 

 indicated in the ocular by a diaphragm, and the back lens of the 

 objective should be made 250 mm., as described in 262-263, then 

 by the aid of Wollaston's camera lucida the magnification of the 



