Geometrical Optics. 245 



Case ii. Thick Lens ; Plane Wave. 



If the lens has thickness d, the rule for expansion of cur- 

 vature at end of § 4 above at once gives 



*-A + X«i^5. < 13) 



or 



' ! ft V-=± 



, n±&i l (i-h)d 2 / h 



-{ 



(14) 



Case iii. -4wy Lens ; ^ny Wave. 

 The principle of superposition at ouce gives the universal 

 formula for all lenses bounded by identical media on the two 

 sides : — 



^ = ^+^ ; (15) 



or, in words, the resultant curvature is the algebraic sum of 

 the initial curvature and the impressed curvature. This may 

 again be compared with the formula in current notation : 



V f u 



The difference in sign attributed to the term — arises from 

 conventions adopted in the two systems. 



E. Two Thin Lenses at distance apart. 



The principle of expansion of curvature at once gives us as 

 the equivalent focal power, 



*=*+*I+^3' (16) 



where $ x and <^ 2 are the focal powers of the first and second 

 lenses, and d the distance between them. $f will be in 

 dioptries if ^ and $ 2 are in dioptries and d in metric units. 

 If the two thin lenses are close together, the resultant power 

 is simply the algebraic sum of the powers of the separate 

 lenses. One simply adds the dioptries of the separate lenses 

 to find the resultant dioptries. 



6. Reflexion Formula. 



Mirrors. 



Case i. Plane Mirror ; Curved Wave. 



The mirror (fig. 9) has surface SMS. The incident wave 

 would have had front S A S at a certain instant had its path lain 



