This section is from the book "Telephotography: An Elementary Treatise On The Construction And Application Of The Telephotographic Lens", by Thomas Rudolphus Dallmeyer. Also available from Amazon: Telephotography and Telephotographic Lens.
On increasing the separation (3), or making d a definite quantity, the focal length decreases until d=f2, or the whole separation a =f1 when the image is formed in the centre of the negative lens, and the focal length is a minimum, or equal to the focal length of the positive lens f1 If we increase the separation still further, (4), the negative lens forms a virtual image of the real image formed at f1
These results will be readily understood from our examination of the conditions necessary for convergent rays meeting a negative lens to form a real image. (Chapter IV (The Formation Of Images By Negative Lenses)., Fig. 33.)
Negative lens forms virtual image of real image formed by positive lens at f1.
In (1) they converge towards a point beyond the focal point of the negative lens, and therefore emerge divergent, giving a virttual image.
In (2) they converge towards the focal point of the negative lens and therefore emerge parallel; d=o.
In (3) they converge towards a point between the negative lens and its focal point, and therefore continue to converge, and form a real image; d = a positive quantity greater than o and less than f2.
In (4) the positive lens forms a real image on the axis of the lens in front of the negative lens, which forms a virtual image of it.
Diagram (3) of the figure gives us, then, the keynote of the Telephotographic construction: d must be equal to, or greater than o, and equal to, or less than, the focal length of the negative lens, in order that real images may be formed.
In mounting the lenses of the instrument, we must adjust the separation of the two elements (positive and negative lenses) so that first: the minimum separation makes d=o, or parallel incident rays will emerge parallel; and secondly : the maximum separation will allow the negative lens to coincide with the focal point of the positive lens; d=f. (When mounting the lenses we actually allow a greater separation than this, to provide for the temporary increase in the conjugate focal distance of the positive lens when near objects are focused upon.)
In treating the Telephotographic lens as a complete optical system, it is evident that if we make d = o as a starting-point, and know the focal lengths of the component lenses f1 and f2, we know the focal length of the compound lens for any value of d greater than o; for
F=f1f2/d... (3) that is to say, the focal length of the compound lens is always equal to the focal length of its two components multiplied together, and divided by the interval d.
Supposing we mount two lenses of 6 inches positive and 3 inches negative focal length respectively in a tube 3 inches apart (i.e., separated by a distance equal to the difference of their focal lengths), making this their minimum separation (d - o), the compound lens has an infinite focal length.
If we now separate them by any greater interval d, say 3/4of an inch, the focal length f = 3x6 = 24 inches 3/4.
To mount these two lenses 3 inches apart involves in reality a knowledge of the positions of the principal (or nodal) points of each combination, and would be a difficult matter for an amateur to accomplish. The reader will readily see, however, that if we know the focal lengths of the component lenses, and separate them until parallel incident rays emerge parallel, we have discovered the position in which they are 3 inches apart, without the knowledge of the principal points of either combination.
To take d = o as a starting-point constitutes the beauty of the method of treating the instrument as a complete system. We can read off the interval d on the mounting of the instrument and instantly calculate the focal length of the compound lens for that particular intervals.*
As in the case of ordinary positive lenses, we have now to determine the position of the "cardinal points" of the Telephotographic system, in order to find the position and magnitude of the image of any object.
This is somewhat more complicated, but the reader will not find it difficult to commit to memory the few formulae necessarily given.
We may consider both component lenses l1 and l2 as infinitely thin, but as the principal points of the whole system are sometimes widely separated, we cannot consider them as coinciding in one "optical centre."
We may here state that the focal length of the negative lens is
* The Author devised this method in his early work on the subject, "Telephotographic Systems of Moderate Amplification," 1893, p. II, engraving the focal lengths of the compound lens for increments of separation, to avoid the necessity of calculation. He has found, however, that the capabilities of the instrument are more readily understood when it is considered as consisting of two separate parts, as described further on, under b.
Plate IX [E. & H. Spitta, Photos.
" Upper Picture, View of Mattmark Glacier. Photographed with 8.8 Ross Triplet at - , yellow screen, Edward's iso-medium plate. Exposure three seconds. Top of Glacier about 10 miles distant. The portion included in the telephoto view is that immediately under the two asterisks.
"Lower Picture, Telephoto - The top of the Glacier. Dallmeyer 2B patent portrait lens and high power tele-attachment. Camera extension from back of negative attachment 19 inches. Portrait lens was closed to F/22.6. Edward's snap-shot iso-plate with yellow screen. Exposure three seconds. Hour about 9 a.m. Point of View about 10 miles distant.
(Dr. E. Spitta's description.)