I I 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 -01 x 60 -6 1 



/= T = ^4- = ^4=4 ....... (XX1) 



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



= 



where / is the focus of one lens and /' 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 



o 



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



Then/=2/'. 



2// _2.f 



" 



_ 



'+/' :;./" 3 



/ = ^ = L 8 = -9; and/=2/' = l-8 . . . . (xxii) 

 i ^i 



r = (^ = 1) /= / 3 - l\ 1-8 = -9 ; similarly r --- '45 . . (vil i 

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



which may be written = 2 -.. 



5 ./ 



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 = the distance between the lenses : 



F _ - , iin 



f+f'-a 



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

 I ' l-y those of the second, A B and A' B' being the respective vortices, 

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

 the combination, are : 



F= f+f-i ........ 



I ' i- nii'iisurod from o)ie of the principal points of the combination. An 

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

 tin field lens of a lluyghenian eyepiece; find their focus. 



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



