48 Lord Rayleigh's Investigations in Optics. 



to zero. Tiie roots are reciprocals, and are given by 



r V 2 + V~l • • • • K±£) 



If the actual value of s : r be nearer unity than the values de- 

 termined by (42), the aberration may be destroyed by selecting 

 for v! one of the roots of (40). 



If, for example, /j, = 1'62, and the refracting angle be 60°, 

 //= 2*392, 



s =1-43 or (1-43)" 1 . 



Unless, therefore, the curvatures are opposite and pretty nearly 

 equal, no adjustment of the focus of the collimator can destroy 

 the aberration. 



In any optical instrument whatever, the aberration in the 

 primary plane may be eliminated by sloping one of the lenses 

 to a suitable angle ; but, as was shown in the preceding sec- 

 tion, we have also in many cases to contend with the aberra- 

 tion of the rays in the secondary plane. The latter aberration 

 is more difficult to calculate than the former. Among lenses, 

 the only case that I have investigated is that of a plano-convex 

 lens on the curved side of which parallel light falls. It ap- 

 pears that the aberration of the rays in the secondary plane 

 vanishes when the following relation obtains between the 

 refractive index and the obliquity : 



rirf^ 8 ^- 1 (43) 



The obliquity is zero when /jl=1'62 — the same value of ft 

 that gives no aberration in the primary plane for rays of small 

 obliquity. Neither kind of aberration is important for a glass 

 lens of this sort moderately sloped. If /jl=1'5, (43) gives 

 <£ = 73°. If fM exceed 1*62, (43) cannot be satisfied. 



Another case of considerable interest can be investigated 

 more easily. It is that of a prism with flat sides, through 

 which convergent or divergent light passes. The prism is 

 supposed to be adjusted until the symmetrical (horizontal) 

 plane contains the radiant point ; but it need not be in the 

 position of minimum deviation. The problem depends upon 

 the same principles as are applied by Professor Stokes* to in- 

 vestigate the curvature of the image of a straight line when 

 seen through a prism. If 6 denote the altitude of a ray before 

 it falls upon the prism, 6' the altitude of the ray within the 

 prism, the horizontal projection of the ray follows a course 



* Royal-Society Proceedings, April 30, 1874. 



