214 DETERMINATION OF EQUIVALENT FOCUS. {APPENDIX. 



It will be seen by glancing at the above table that whenever the liquid in the 

 tester is of lower index than glass, that the concavity with the liquid acts as a 

 concave lens, or in other words like an amplifier {\ 152), and the field is smaller 

 than when tio tester is used. It will also be seen that as the liquid in the con- 

 cavity approaches the glass in refractive index that the field approaches the size 

 when no tester is present. It is also plainly shown by the table that the greater 

 the difference in refractive index of the substance in the concavity and the glass, 

 the more must the tube of the microscope be raised to restore the focus. 



If a substance of greater refraction than glass were used in the tester the field 

 would be larger, i. e , the magnification less, and one would have to turn the tube 

 down instead of up to restore the focus. The tester used in these experiments 

 was made by the Gundlach Optical Company of Rochester. 



EQUIVALENT FOCUS OF OBJECTIVES AND OCULARS. 



\ 356. To work out in proper mathematical form or to ascertain experimentally 

 the equivalent foci of these complex parts with real accuracy would require an 

 amount of knowledge and of apparatus possessed only by an optician or a physicist. 

 The work may be done, however, with sufficient accuracy to supply most of the 

 needs of the working microscopist. The optical law on which the following is 

 based is: — " The size of object and image varies directly as their distance from 

 the center of the lens.'" 



By referring to Figs. 14, 16, 21, it will be seen that this law holds good. When 

 one considers compound lens-systems the problem becomes involved, as the centre 

 of the lens systems is not easily ascertainable hence it is not attempted, and only 

 an approximately accurate result is sought. 



$ 357. Determination of Equivalent Focus of Objectives. — Look into the upper 

 end of the objective and locate the position of the back lens. Indicate the level 

 in someway on the outside of the objective. This is not the center of the object- 

 ive but serves as an arbitrary approximation. Screw the objective into the tube 

 of the microscope. Remove the field lens from a micrometer ocular, thus making 

 a positive ocular of it (Fig. 21). Pull out the draw-tube until the distance between 

 the ocular micrometer and the back lens is 250 millimeters. Use a stage microm- 

 eter as object and focus carefully. Make the lines of the two micrometers 

 parallel (Fig. 101). Note the number of spaces on the ocular micrometer required 

 to measure one or more spaces on the stage micrometer. Suppose the two microm- 

 eters are ruled in j^ mm. and that it required 10 spaces on the ocular micrometer 

 to enclose 2 spaces on the stage micrometer, evidently then 5 spaces would cover 

 one. The image, A'B 1 Fig. 21 in this case is five times as long as the object, A,B. — 

 Now if the size of object and image are directly as their distance from the lens it 

 follows that as the size of object is known ( T 2 ff mm.), that of the intake directly 

 measured ({§ mm.), the distance from the lens to the image also determined in the 

 beginning, there remains to be found the distance between the objective and the 

 object, which will represent approximately the equivalent focus. The general 

 formula is, Object, O : Image, I : : equivalent focus, F : 250. Supplying the 

 known values, = T 2 o, I = x§ then T 2 ,y m : 1 mm : : F : 250 whence F = 50mm. That 

 is, the equivalent focus is approximately 50 millimeters. 



§ 358. Determination of Initial or Independent Magnification of the Objective. 

 The initial magnification means simply the magnification of the real image (A 1 B 1 , 

 Fig. 21) unaffected by the ocular. It may be determined experimentally exactly 



