aperture of the stop of a photographic lens 205 
Since X, is the image of XY, and QO, is the image of O, formed in 
each case by the complete lens system, we have, by Newton’s 
_ formula, 
PLX,. FX, =) 0.F). OF, = f°, 
Lie. O,F, pee FLX, +0,F,? 
| and hence eo (1 sk —) = eS) eerie (12) 
| ls Ig NE 
and thus ihe = = ae BW er sina eee ee (13) 
- Hence the intensity of illumination of the image diminishes as the 
object approaches the focus /, from infinity. If we measure the 
distance between QO, and /’, we can find the value of L/Z,, for any 
given value of #,X,. In the second method (§ 5) the distance, z, 
of O, or Q, from the plane of the end of the lens mount was deter- 
mined. The focus F, can be identified by placing a pin so that its tip 
coincides with the image of a very distant object, or by making the 
tip coincide with its own image when a plane murror is placed on 
the other side of the lens system. A/ter the pin has been placed 
at F,,a plate of glass or metal of known thickness is placed against 
the mount and the distance of the pin from this plate is measured. 
In this way the distance of /, from the plane of the end of the 
mount is found. Adding this to the distance 2, we obtain O, F;,. 
The effect of the finite distance of the object in diminishing the 
illumination of the image may be met either by increasing the 
time of exposure or by using a larger stop. 
If, for a given stop, the time of exposure, for an object surface 
of standard intrinsic brightness, is t,, when the object is at infinity, 
and is ¢ when the object is at a finite distance, then 
eee Sy 
2) 
eae 2 Seed TP LOS 
If the camera is used for copying and the linear dimensions of 
the copy are to be m times those of the original, we must have 
F,X,=f/m. We then obtain, if 0, F, = 6f, 
_ @ = a ‘) Some) ee (15) 
ao 
If the lenses are not very thick and are not-widely separated, 
O,F, will not differ much from 7, and thus 8 will be nearly unity. 
In this case we obtain approximately 
t=(1+m/t,. 
If we wish to keep the exposure unaltered, we must increase 
the stop aperture when the object is at a finite distance. If the 
stop marked //n,, is suitable when the standard surface is at an 
