FIRST ORDINARY MEETING. 15* 



II. 



24. The geometrical method of the preceding sections may also be 

 extended to the case of reflection at one or more spherical surfaces. 

 A few examples "will suffice to illustrate the method. 



Thus for a convex mirror F and F' are coincident ; f is negative 

 and f positive, and formula (1) becomes 



P P 

 Hence the line joining conjugate points on the two axes passes 

 through X (—/,/), as in Fig. 11. 

 For a concave mirror the formula is 



^--< = i, 



P P 

 and X is (/, — /), as in Fig. 12. 



25. In either case we have, from the similar triangles PFX, 

 XF'F (Fig. 11 or 12), 



PF _ F'X 

 TX ~ FF' 

 that is 



dd' =f\ 

 which is Newton's formula. 



If d. and d' be measured respectively from P and P' in accordance 

 with the rule of signs (§ 1), this formula should be written 



dd' = — /2, 

 as appears by deducing it from the relation dd^ =^ff' of § 3. 



26. The relation between the lengths of the object and image is 

 most readily obtained by making the axes cross at 0, the centre of 

 the mirror. 



Thus for a convex mirror we have (Fig. 13) 

 w' _ OP' _ FX _ / 

 ^ ~" "op ~ PF ~ H' 

 In the case either of a convex or a concave mirror it may be 

 remarked that, if account be taken of the signs oi /,/', d, d',th.e 

 relation 



co' f d' 



