240 Prof. Silvanus P. Thompson on 



As a result the wave is imprinted with the curved surface 

 S B S, the centre of which is at F, toward which point the 



Fig. 5. 



wave convei'ges. The sagitta A B measures the focal curva- 

 ture thus impressed on the wave. Now 



AB=AM-BM 



=AM-LAM, 



° r ^=^(1-7*) (4) 



It will be noted that if the curvature of the surface is positive 

 (i. e. bulging toward the source of light), the impressed focal 

 curvature is also positive. For the case of any two media 

 having respective velocity-constants h x and h 2 , the formula 



becomes 



&=& 



1 h -k 

 h 



(5) 



Case (i.) b. Entrant Wave; Concave Surface. 

 Consider the plane wave which would have reached the 



Fig. 6. 



vertical line though A had its path lain wholly in air ; the 

 central portion does reach A, but the marginal portions are 



