530 Prof. Arthur Schuster on 



in time t/Y, the group-front in a time t/V. The difference 

 in time is t(Y — U)/UV, which, as Y and U do not differ 

 much, we write approximately £(V — U)/V 2 . If t represents 

 the effective thickness of the prism, the distance CK, through 

 which the group is displaced, will be, remembering that /uY 

 is the velocity in air, 



p - Rr _ ^(Y — U) _ fitXdY_ fit\ dY dfi 

 Y~ ~~ ~T dx~ T dfidx 



It has been shown by Rayleighthat the resolving power (R) 



d Lb 



of a prism defined as in (14) is t -^— , so that the displacement 



CK of the group will be 



CK = RX, 



just as in the case of a grating. 



What holds for the group front and rear will also hold for 

 any portion of the group in so far as it is made up of wave- 

 lengths differing only to a small extent from the one under 

 consideration. The analogy between a prism and a grating 

 of the same resolving power is therefore complete. 



16. The consideration of the group-front instead of the 

 wave-front in optical systems 

 leads to known results in a Fig. 5. 



somewhat novel and instruc- 

 tive way. Thus a lens (fig. 5) 

 will convert a plane front HK 

 into a spherical front ACB ; 

 but the group-front will be 

 distorted into a form such as 

 ACB ; where CG / depends on 

 the thickness of the lens. The 



displacement does not alter the focus but it interferes with 

 the definition of the image. The want of definition thus pro- 

 duced is known as chromatic aberration, Chromatic aberra- 

 tion may partially be corrected by joining two lenses of different 

 materials. From our point of view a lens is achromatic when 

 the time taken from the original wave-front to the focus F is 

 the same along all paths for the group-fronts as well as for 

 the wave- fronts ; and it is easily shown that this condition will 

 lead to the well-known relation for achromatism. It" must 

 be understood of course that the group-front differs from the 

 wave-front in the important particular that the phases at 

 different points of the group-front are not the same. In a 



