flare spots in photography: PALL 
‘The symmetry of (9) shows that if 7, is the secondary image of S, 
‘then S is the secondary image of 7. If w=1°5 we have f, = 
: If we measure both f and f,, we can find «~—1 from the 
equation 
| ee ON 2F 1 
be a aap = yp ere ee (12). 
: The method can be applied at once to rays which have suffered 
A, 6 ... reflexions. If F,, be the power for rays which have been 
| ected 2n times, 
(Ziasp ll) josh 
jp Al P. 
Dy, = 
$8. Images by once reflected rays. Two images of S will be 
formed by rays which suffer a single reflexion. One image will 
be formed by reflexion at the surface AK. With this we are not 
here concerned except when that surface is concave; in that case, 
if S be placed at the centre of curvature of AK it will coincide 
with its own image. 
A second image, S, (Fig. 2), will be formed by rays which have 
suffered one reflexion at BK and two refractions at AK. Let 
S,M = u, and let uw, be positive when the image, Sj, is real. 
If X, he on 8,& and if SX, =S8,A, the optical equation is 
AK + KX, = AB. 
Multiplying this equation by 2/h? and using the results of § 6, we 
have 
(L/w + 1/a)+ (1/um + 1/a) = 24 (1/a + 1/6), 
or 1/u + 1/u, = 2(w—1)(1/a + 1/b) + 2/b = 2/f + 2/6. 
If S be adjusted so that the image S, coincides with S, and if 
p denote the common value of wu and wu, in this case, 
iP = lifes (ies lye Myr to TD ecoccogeas (13). 
Similarly, if an object at a distance g from M on the other side of 
the lens coincides with its image formed by rays reflected once at 
AK and refracted twice at BK, 
a lips Wy iso Wlisaco suadecobobosaceen (14). 
Adding (13) and (14), we have 
Up + 1/q=2/f+ A/a + 1/b) = {2 + 1/(u— 1}. Uf 
Thus, if p, g and f are known, we can find »— 1 from the equation 
Iie F 
—-l= Se ‘ 
aio PhO lr 
The value of ~—1 found by (15) from f, » and qg can be compared 
