_ flare spots in photography. 207 
image will not generally be of the same size as the primary image 
and may even be erect when the latter is inverted. 
Thus when 7, coincides with 7, a faint secondary image of the 
objects to be photographed will be impressed upon the plate in 
addition to the primary image. Chapman Jones (Science and 
Practice of Photography, p. 248) states that he “has seen a 
portrait spoiled by an inverted image of the shirt front appearing 
over the model’s head.” 
The position and magnitude of any secondary image can be 
determined when we know the positions of the corresponding 
cardinal points, viz. the principal (or unit) points and the principal 
foci. To each pair of surfaces which act as reflectors there corre- 
sponds a set of cardinal points. When the lens system is of 
considerable length, the cardinal points corresponding to any pair 
of surfaces may occupy all sorts of positions. 
In the case of the secondary image described by Chapman 
Jones, the system behaved as one of negative focal length with its 
cardinal points so placed that it formed a real erect image of a 
distant object. A system of two thin convex lenses separated by 
a distance greater than the sum of their focal lengths behaves in 
the same manner with respect to a primary image. The system 
has a negative focal length and forms a real erect image of a 
distant object. 
§3. Flare spots in photography. ‘The rays which have been 
twice reflected may give rise to trouble in another way. The 
primary image of the stop R (Fig. 1) will be so far from the plate 
that its effects may be disregarded ; the image will generally be 
virtual. But when the camera is directed towards any landscape 
or other scene, an infinite number of rays passes in all directions 
(within limits) through every point of the opening of the stop, 
and thus this opening will behave as if it were a self-luminous 
disk which, however, only emits light towards one side. One or 
more of the secondary images of this equivalent disk, formed by 
rays which have suffered the first reflexion at some surface 
between the stop and the plate and a second reflexion at any 
other surface of the lens system, may be accurately or nearly 
focussed on the plate and so give rise to a well defined bright 
spot in the centre of the plate. This spot is known as a “flare 
spot.” 
For a given background, the flare spot image of the stop 
aperture will be of the same intensity whatever the size of the 
stop, at least in those cases where the second reflexion takes place 
at a surface behind the stop. But the intensity of the primary 
image of the background will be proportional to the area of the 
stop. Hence, although the flare spot image of the stop may be 
