.38 Professor Airy on the Spherical Aberration 



Now, since it is impossible to form an image which will be perfectly 

 distinct, we must consider what kind of aberration is least disagreeable 

 to the eye. I believe that the confusion occasioned by making the image 

 of every point a circle is less disagreeable than that occasioned by making 

 the image an ellipse, or straight line. Now, this can be effected in two 



wavs : either by making F+ ^ =0, or by making F=o. The former 



equation is not possible. The latter gives 



e = 



^(»-{)*7yi»-i^/-i(^!- 



and the two values of e are possible, if t; be 



2 M- - 1 ,. / 



> —, c • ti or < -7^ -. . 



2(n-l) •^ 2(«- 1) 



2 M" — 1 



As an example, suppose v= — -r/ The radical disappears, and 



there is, then, but one value of e, namely, 



_ w + i / 2W--1 . _ /"\ ^ _ ./ 

 n K2(n-\y 2 7 2 " 



/' n + 1 . 2 ra - 1 



(n-iy 27 2 n-\ 



Finding from this the value of B, it is discovered to be negative, and, 

 therefore, a diaphragm cannot be placed to receive the rays before they 

 are incident on the lens. It may, however, be placed to receive them after 

 their emergence. The value of C is found to be 



o 



F. Also r = —J— F, s = — - F. 



The second surface is, therefore, concave. This construction is represented 

 in Fig. 8. If we had taken v > _ /, we should have found two 

 positions for the diaphragm, both below the lens. 



