482 Dr. C. V. Drysdale on the 



where U, is the convergence on meeting the second surface 

 and t is the thickness. 



This equation can, however, be written 



Nomenclature for Thick Lenses and Lens Systems. — We 

 can greatly reduce the labour and simplify the working of 

 problems relating to lens systems by adopting a suitable 

 nomenclature and notation. This was done by Gauss *, who 

 introduced the idea of " absolute " and " reduced " distances 

 and thicknesses. Following this we may introduce the term 

 i( reduced convergence " of a pencil as the product of its 

 actual or " absolute " convergence and the refractive index 

 of the material; while the "reduced thickness," as with 

 Gauss, is defined as the negative of the " absolute thickness " 

 divided by the refractive index of the medium. 



Denoting these quantities by accented letters, we have 



V'=fiU, Y'=ftY, ?=--; 



and the equations for the surface and interspace are 

 tV-U'. 1 = (^ 1 - /t _ 1 )R„=F , 



and ti i _ 1 _ V, 



Ul "777 i ~W+T 



It is worthy of note that each of the reduced quantities 

 has a simple physical meaning. For in the first equation, 

 if the surface is plane 



Vi'-UL^O, or V/^U^. 



Consequently the reduced convergence of a pencil does not 

 change in passing through a plane surface separating any 

 two media. But if the second medium is air yLt 1 = l and 

 V = Ul_ r Hence the reduced convergence of a wave-front 

 in any medium is the convergence it would have if it emerged 

 from that medium into air through a plane surface. The 

 term "equivalent" instead of reduced convergence may 

 therefore be employed if preferred, but is preferably kept 

 for the equivalent convergence of the combination. Similarly 



t l '= is the "apparent thickness"" of a parallel plate of 



the medium when viewed in air. 



* Pendlebury, ' Lenses and Systems of Lenses.' 



