Geometrical Optics. 



241 



retarded, and only reach the vertical line T B T drawn through 

 B, a point such that B M = h . AM. The impressed curve is 

 TAT with centre F. That is to say, the concave (or nega- 

 tive) surface imprints a negative focal curvature on the wave, 

 its sagitta being A B. 



AB=AM-BM 

 = AM- h. AM, 

 $?=M(l-h) (4) bis 



The formula, therefore, is the same for entrant plane waves 

 whether the surface be convex or concave, the sign of $ 

 following the sign of 01. 



Case (ii.)a. Emergent Wave; Surface Convex toward light 

 (i. e. concave toward air into which wave emerges) . 



The plane wave would have had its front at S A S (fig. 7) 

 Fig. 7. 



at a certain instant had its path lain wholly in the retarding 

 medium ; but the central portion being accelerated by its 

 emergence at M into air reaches B, where B M is to A M as 

 1 to h. Hence the curve 8BS, whose curvature is measured 

 by the sagitta A B, is the impressed focal curvature. It will 

 be noted that this is of opposite sign to that of the surface of 

 emergence. Hence the sagitta AB must be taken with 

 minus sign. 



- AB = BM - AM 



= J-AM-AM 



+ AB = AM 



^= ^ 



(>-S 



(6) 



