48 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
factors: (i) The magnification due to the objective, which produces an 
image of the object and (2) that resulting from the eye-piece, which func- 
tions as a magnifier through which the image is examined by the eye. If 
the eye-piece magnification be too low, the eye is unable to perceive all the 
details, which are then so minute as to be beyond the limit of visibility, 
and the resolving power of the objective is rendered worthless because of 
the insufficient magnification. The imaging or resolving power of the objec- 
tive, on the other hand, depends on its numerical aperture, and a reduction 
in its E. F. (increase in magnifying power) without corresponding increase 
in its numerical aperture does not reveal any new detail in the image. The 
best magnification is obviously the lowest magnification which presents to 
the eye all the details imaged by the objective. This is called the useful 
magnification. Any increase over this magnification is useless, as there are 
no further details in the image to be resolved. With greater magnification 
the image increases in size but becomes fainter and less distinct; the field 
and illumination are reduced and diffraction phenomena disturb the image 
seriously. Mere magnification can not be carried on indefinitely, as with 
increase in magnification the residual traces of aberrations, which can not be 
removed completely, become prominent and destroy the sharpness of out- 
line in the image. Apochromats which are more highly corrected will bear 
higher magnification than achromats. Magnification beyond the useful 
magnification is called empty magnification. With useful magnification an 
objective attains its highest efficiency ; all the details in the image are seen ; 
and the illumination, the size of field, and the depth of sharpness are at a 
maximum. 
