1128 



APPENDICES AND TABLES 



Fig. 6. The same, only/=2/'; 



8F= --5 | 2 -052 (xxxix) 



Fig. 5. The first lens inverted, /=/' ; 



8F=--416| 2 = --043 (xxxix) 



Pig. 8. The same, only 2/=/ / ; 

 8F= --62( 

 Fig. 9. The same, only/=2/; 



= --065 

 .r 



. . . (xxxix) 

 -039 (xxxix) 



FIG. 4. 



FIG. 5. 



FIG. 6. 



i i 



I I 



FIG. 7. 



FIG. 8. 



FIG. 9, 



We see, therefore, that with the same focal length F the aberration of 

 fig. 1 is the greatest, and that of fig. 9 the least. We also see in the com- 

 binations that by decreasing up to a certain point the focus of the first 

 lens the aberration is increased, and vice versa. The best form of a 

 combination of plate glass, p, = 1*516, for parallel rays similar in arrange- 



5 f f 



ment to fig. 9 is when /= --. 

 o 



The Aplanatic Meniscus. A spherical refracting surface has two 

 aplanatic foci, such that if converging rays, which have their focus at P', 

 meet a convex spherical refracting surface, whose centre of curvature 

 is r, and if the distance between the points P' and r =ju,r, then those 

 rays will be refracted aplanatically to some other point, say P, which will 

 lie on the same side of the surface as P'. This fact is of great service, 

 because it enables an aplanatic meniscus to be constructed ; thus, if we 

 make r the radius of the curve A, we can make s, the radius of the curve 

 B, a radius from the point P. If, then, P is a radiant, the light travelling 

 from left to right will pass through the curve B without refraction, because 

 P is the centre of the curve B. The light will then pass on unchanged 

 to the curve A, and will by it be refracted aplanatically, as if it had come 

 irom P'. P will be negative and P' positive. 



The formulae for finding r and P' when P is given are : 



and those for finding r and P when P' is given are : 



V 



(xli) 



