304 



Mr. 0. W. Griffith on the 



which states that the system is equivalent to a water sphere 

 of radius r x and a divergent Jens of power equal to the 

 second term. The value of this form ol result will be 

 evident when we have computed the effect of spherical 

 aberration. 



(b) Effect of Spherical Aherration. 



Fig. 1 illustrates the refraction of a parallel beam through 

 a sphere. 



Fig. 1. 



The focal length, measured from the centre, is 



OP sin i 



OL: 



And 



Also # = 2(i — i) and smi = fismi'. Substituting for i' and 

 expanding in terms of sin i by the Binomial Theorem, 

 neglecting all terms above the second power, we get 



• n n/ J, ~~l i . 3//- — JU, 2 — 1 



sin 6 = 2 1 4- „ 9 . sin 



P 2/x 2 



in 2 / s 



sin i. 



Putting PM=a, 0P = r, then if/ is the focal length, 



J 2(^-1) 7 





(6) 



The second term on the right-hand side of equation (6) 

 represents the error due to spherical aberration, and its effect 

 is to increase the converging power of the sphere. Applying 

 this to the case of a thin glass flask filled with water, we may 



