W. LeConte Stevens — Microscope Magnification. 53 



difficulty arises in regard to the value to be assigned f\ since 

 eye-pieces ordinarily have no labels more intelligible than A, 

 B, or C, which numerically mean nothing. If a positive eye- 

 piece be employed, the focal length of its two lenses being 

 equal, the equivalent focal length of the combination is 

 obtained by the usual formula, if that of either of the two 

 lenses, and the interval between their optical centers, be meas- 

 ured. In case the eye-piece be negative, a majority of those 

 in use belonging to this class, the focal length of its eye lens is 

 easily found by allowing for its thickness and measuring down 

 to the diaphragm where the real image is formed. But the 

 size of this image has been decreased, and its position has been 

 changed by the interposition of the field lens. At the risk, 

 therefore, of giving what seems very elementary, it may be 

 well to consider briefly the theory of the negative eye-piece. 



We may assume the proportions usually said to be adopted 

 in the construction of the negative eye-piece, that the focal 

 length of the field lens is three times that of the eye lens, and 

 the interval between these equal to the difference of their 

 focal lengths. The rays, rr, fig. 2, converging from the 

 objective toward the point, Q, have their convergence in- 



creased by the field lens, so as to cross at Q ; . They are made 

 parallel by the eye-lens, and emerge so as to produce a virtual 

 image which to the receiving eye appears in the direction EX. 

 Hence Q' is in the principal focal plane of the eye lens, and Q 

 in one conjugate focal plane of the objective. 



Let EP' ==f= focal length of eye lens. 

 " 3/'=/"= " ' field lens. 



" LP z—p = distance of virtual point of radiance. 

 " LP' = p' = " actual " convergence. 



Then, by the fundamental law of lenses, 

 1 1 _ 1 



P P J 

 Since EL=2/ V , and EP'=/', we have p 1 '=/' '. Hence, 



1 



? 



1 



•P=Tf- 



