I 1 24 APPENDICES AND TABLES 



The last formula of (xxi) is very convenient for finding the focus of 

 an objective ; w must, of course, be large in proportion to the focus ; 

 o may be a stage micrometer. 



As the posterior focus, /, is in ordinary microscope objectives of 

 1-inch focus and upwards, near the back lens, the distance w may be 

 measured from there. 



Example : The image of '01 inch on a stage micrometer projected by 

 an objective is 2 - 4 inches on a screen, distant 5 feet from the back lens ; 

 required the focus of the objective. 



f _ow_ -01x60 _'6 _1 

 f ~ " -*4 2^4-4 



To find F, the equivalent focus of two lenses in contact : 



F = j^ (xxii) 



where /, is the focus of one lens and f that of the second. 



Example : It is required to make a combination of two plano-convex 

 lenses, the focus of one lens, /, being twice /', that of the other, and whose 



Q 



combined focus F = '6, /u = - ; find their radii (see figs. 4, 6, 8, and 9). 



Then/=2/'. 



F _ 



3 



/ = UL = ? = -9; and/ =2/ = l'8 . . . . (xxii) 

 r = (^ = l) /= /? _ i\ 1-8 = -9 ; similarly r' = -45 . . (vil) 

 The focus for three lenses follows that for two, thus : 



f= *%/,'. *. ( xxii > 



which may be written = 2 -. 



F / 



To find F, the equivalent focus of two lenses, not in contact, generally, 

 F to be measured from the last principal point (E') of the second lens ; 

 Let d = ihe distance between the lenses : 



More accurately, let D E be the principal points of the first lens and 

 D' W those of the second, A B and A 7 B' being the respective vertices, 

 d = the distance from E to D' ; then G and G', the principal points of 

 the combination, are : 



and F=_-^__ (xxvi) 



F is measured from one of the principal points of the combination. An 

 example will be of interest. Let parallel rays fall on the convex face of 

 the field lens of a Huyghenian eyepiece ; find their focus. 



Let /, the focus of the field lens -= 3, and that of the eye lens /' = 1 ; 



