But 

 whence 



244 Prof. Silvanus P. Thompson on 



BM = CM-CB, 

 = CM-A.AC, 

 = CM-A(OM-AM), 

 = CM(l-/0-A.AM; 



01(1 -h) = fl 



q)= $+h<M. . (8)6w. 



D. Lens Formula. 



Case i. Thin Lens ; Plane Wave. 



In the case of a lens, the curvature ^ imprinted on a 

 plane wave by entrance at the first surface may he regarded 

 as an initial curvature of the wave which emerges through the 

 second surface. Emergence into air will, as shown above, 

 alter the curvature by augmenting it in the ratio of 1 to h, 

 and superpose upon it the focal curvature ft 2 due to the 

 second surface. Hence the whole resultant curvature $ 

 imprinted by a thin lens on the plane wave will be 



= £ft + flr 



But 



and 



whence 

 or 



i (l-A), 



. 1-h „ 1-h 



h 



This formula may be compared with that in the current 

 notation, 



HIHI"-' 



/ 



In the case of a lens composed of a medium h 2 , lying 

 between two other media A 2 and h 3 , the formula becomes 



^ = l^\^iOh~h)h+ ^ 2 {h~1 h )l h \ . . (12) 



