flare spots in photography. 209 
ut it will be convenient to give it here as the mathematical 
nethods can be transferred, with little change, to the solution of 
he other problems considered. 
_ Let AKB (Fig. 2) be a thin lens. Let S be a point source of 
Fig. 2. 
ight on the axis of the lens and let 7 be its image. Let the 
radii of the faces Ak, BK be a, b cm. and let the nelineiive index 
vf the lens be yu. The radii are counted positive wien the faces 
we convex, asin Fig. 2. Let the focal length be f em.; we shall 
‘ollow the rule of the practical opticians and count f positive when 
she lens is a converging one. Where convenient, capital letters 
mill be used to denote “ powers” or reciprocals of distances. Thus 
1 
i ee F, 
i 
a F cm. or 100 F dioptres is the “ power” of the lens. 
_ When spherical aberration is negligible, any spherical wave 
front (, which expands from S as centre, becomes, after passing 
shrough the lens, a spherical wave front 2D, contracting to 7’ as 
entre. Hence the time taken by light in passing from S to 7’ is 
she same for every ray—an example of the principle of Least (or 
Stationary) Time. 
Let M be the point in which the plane of the edge of the lens 
ntersects the axis. 
Let SM =u, MT =v and KM=h. 
Phe position of 7 is found by equating the optical length of the 
vath from S to 7’ for the ray which starts along SA to that for 
he ray which starts along SA. If X, Y be points on SK, TK 
uch that SY =SA and 7 Y =TB, the optical length of the path 
rom X to Y is equal to that of the path from A to B. Since the 
speed of light in glass is only uy times its speed in air, the optical 
ength of AB is w~AB. Hence the optical equation is 
RIECAE VEO es TAN Bn ep ope pp anoonenonons 6 (QD) 
i 
fee VOL. XVII. PT. II. 14 
i 
