aperture of the stop of a photographic lens 1g) 
of the nodal points. Since G is in the focal plane, all the rays due 
‘to G which emerge from the lens LZ are parallel to N,K. The 
extreme ray is the one which, in its passage through the system, 
passes through the point P on the edge of the stop, P and G both 
lying in the plane of the diagram. But Q, is the image of Je 
formed by the lens L, and thus the extreme ray, on emerging from 
L, must be directed away from the point Q,. Hence, if Q,.CU be 
drawn parallel to GN, it will give the direction of the extreme 
emergent ray. If C is the pomt in which it strikes the matt 
surface of the glass scale ABC, AC will be the radius of the 
bright patch on the scale*. 
Since OQ, is parallel to VG, the triangles CBQ,, GFN, are 
similar, and hence CB/BQ, = GP,/F,N2. 
If d is the diameter of the opening in the focal plane, then 
F,G=id. If BC=4b and BQ,=2, we have b/a=d/f or 
ys eV RS ee Ola MN aE ae RS: (3) 
Hence, if ¢ is the diameter of the bright circular patch on the 
matt surface of the scale, 
6S Oss WG AE GUiy GocsecoccsSonononbee (4) 
and therefore OS OS MIfa - scsosoocosooonsesss00nas (5) 
The distance BQ, =~ is the distance between the matt surface 
of the scale and the plane of the image of the stop formed by the 
lens L. A plate of transparent glass of good quality is fixed 
against the mount of the lens in place of the glass scale (the 
latter may be used if the surface is cleaned) and a little lycopodium 
is placed on the face nearest to L. A microscope on a sliding 
carriage is then arranged so that its axis and the direction of 
motion of the carriage are parallel to the axis of the lens system, 
and the microscope is focussed through the glass plate ABC first 
on the edge of the stop and then on the lycopodium, the adjust- 
ment being effected by sliding the carriage along its track. The 
distance through which the microscope is moved is equal to BQ, 
or w. After each pair of observations the track may be slightly 
moved so as to obtain independent readings for the next pair. 
* It has been assumed that the aperture in the metal plate S (Fig. 2) really 
acts as a stop for rays which converge to F,. In other words, it is assumed that 
the effective diameter of the incident beam is limited by S and not by the mount- 
ings of the lenses. If the aperture in S is so large that the ray which passes 
through P in its course to Fz passes close to the lens mountings, it may happen, 
as Mr T. Smith has pointed out to me, that, unless F',G is small, the ray from G 
which is directed to Qs is caught by the lens mountings and does not penetrate the 
system. In that case the edge of the luminous patch is not at C but at some point 
nearer to A, and thus the diameter of the patch depends not on S but on the 
diameter of one of the lens mountings. If such a system were used for landscape 
photography, there would be a great falling off of illumination towards the edges 
of the plate. This defect is avoided in good photographic lenses by keeping the 
stop of greatest aperture sufticiently small. 
