FIRST ORDINARY MEETING. 15 
1 
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 /’ positive, and formula (1) becomes 
t ai shige 
saa 
iy 
Hence the line joining ie points on the two axes passes 
through X (—f, f), as in Fig. 11. 
For a concave mirror the formula is 
WHILE cesofh 
(Maes) Tex's 
and X is (f/f, —/), as in Fig. 12. 
25. In either case we have, from the similar triangles PFX, 
ene (Big. 11 or 12), 
Led el 339-5 
Eke DAne 
that is 
da’ =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' = — f”, 
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 O, the centre of 
the mirror. 
Thus for a convex mirror we have (Fig. 13) 
neg OE ine HEX 
a OP a PH ae 
In the case either of a convex or a concave mirror it may be 
remarked that, if account be taken of the signs of ff’, d, d’, the 
relation 
