USEFUL TO THE MICKOSCOPIST II2./ 



fore a = - 3 (xxxi) ; ' = - (xxxv) ; a> + a/ = 2 a> = - ; 



9fk 



/= 2 F (xxii) ; therefore 2 a> = ^ ^ ; 



XT? 20 F V 5 y 2 



%4W = ~6'F ' ' 



This is half the aberration of an equi-convex lens (fig. 1) of the same 

 focal length as the combination where 



v-. ........ 



If the front lens of the combination be turned round so that its convex 

 surface faces the incident light the aberration is 



or half what it was before (fig. 5). 



This is nearly a third of the aberration of a plano-convex in the best 

 position (fig. 2), which is 



*- - 



The following figures pictorially illustrate spherical aberration in 

 single lenses and in various combinations of two plano-convex lenses, all 

 having the same focus F, the same aperture, and the same refractive 

 index f . The dot nearer the lens is the focal point for the marginal, and 

 that farther away the focal point for the central rays; the distance 

 between the dots is the spherical aberration 8 F. 



PIG. 1. FIG. 2. 



Fig. 1. An equi-convex, r = F ; 



SF= -1-61 2 = -'113 ....... (xi) 



x 1 



F 



Fig. 2. A plano-convex, r = -> 



8F= -1-16= --121 ....... (viii) 



17 



- 



a 



n 17 



Fig. 3. A crossed convex, r = _i- F ; s= --F ...... (xvii) 



8F= -1-07^= -'111 



X 1 



Fig. 7. A combination of two pianos with their convex faces in con- 

 tact, the focus / of the first lens being equal to /, that of the second. 



The focus of the combination F = ^ .......... ( xxii ) 



SF= -'833 2/! = --087 ...... (xxxix) 



Fig. 4. The same, only 2/=/ ; 



fe- -*168 , ..... (xxxix) 

 F 



