Part I. By two Positive lens-systems.

Part II. By a Positive system and a Negative system combined - or the Telephotographic Lens.


Every positive lens, as we have seen, is capable of forming a real image. It is evident that this real image may be enlarged by a second positive lens, which in its turn forms a second image of the first one, produced by the first lens.

Fig. 37.

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This process is termed enlargement by "secondary magnification." The lens l1: (Fig. 37) forms an inverted image L, of an object at o ; if we place a second lens l2 behind this real image I1 (although formed in air) at any distance greater than the measurement of its focal point f2 from the lens, a real image of I2 must again be formed. If the distance between the second lens l3 and I1 is greater than the focal length of l2, and less than twice its focal length (the position for unit magnification, or the symmetric plane) a magnified and erect image must be formed as at I2 and can be received upon a screen or photographic plate.

In cases where it is only necessary to magnify a small amount of the image I1 as occurs in photographing the sun, or portions of it, and where the length and bulk of the instrument is of little moment, this method of magnification has been adopted, although it has recently been abandoned for the "negative" enlarging system. (See Plates VII. and VIII.)

Photographers who know the meaning of "curvature of field" in a lens will see that the curvature of the image I1 given by the first lens L1 will be increased by the second positive lens l2, as the curvature is wrongly disposed for reproduction on a plane surface at I2.

For general use, however, bulk is the great drawback to this system. The first lens necessitates the usual camera extension, equal to or greater than its focal length, and the second lens must increase this by more than four times its focal length, before any magnification can begin.

If we were not in possession of the method of enlarging by the negative system, secondary magnification might still be practised in certain cases, because of the advantage gained by the fact that the enlargement given by the second positive lens is of an image formed in air. This image has no granular structure, such as takes place in the photographic film on the plate, hence the enlargement would have that "pluck" and definition which are noticeably wanting in enlargements made from the photographic primary image.

This leads up to saying here that the whole raison d'etre for any optical enlarging system is due to the fact that the grain of the photographic image puts a limit, and a very small one too, upon the number of times it can be enlarged with the requisite degree of definition for analysis.

It may be argued that we can see fine definition in the enlargement of a lantern-slide, for example, thrown upon a large screen. So we can as an illusion, when viewing it from a distance, but as we approach the

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Plate VII

"Photograph of the great Sun Spot of September 1898. Taken with the Thompson photographic refractor, 26 in. in diameter, aperture employed 15 in., focal length 27 ft. 6 in. Image of the Sun in primary focus 2 1/2 in. in diameter. Enlarged in telescope by a Dallmeyer telephoto lens to 29 in. Taken September 11, 1898."

(Notes from the Royal Observatory, Greenwich.) screen, all definition is gone! The chief aim and use of optical enlarging systems for taking photographs is to attain as fine definition in the enlarged image as we should in the small image produced by the "positive" portion of the system; in fact, not a comparative degree of definition or sharpness, but an absolute degree.

Part II

The Telephotographic lens may be conceived to act in either of two ways - (a) as a complete positive system of variable focal length, and therefore capable of producing images of different size of a given object at any definite distance from it; (b) as consisting of two separate parts, a positive lens of definite focal length, whose function is to form a real image of definite size at a definite distance from the object, combined with a negative lens of definite focal length, whose function is to magnify the image given by the positive lens in variable degree.

Both conceptions of its action will be dealt with, as they will assist the reader in completely mastering its use in practice. The former will be found the more elegant perhaps in theory, but the author has found that the latter is more easily grasped by the photographer who is fairly intimate with the working of ordinary positive systems.

Let us take two lenses of the same kind of glass, one a planoconvex and the other a concavo-plane, the curved surface being of the same radius in each case, and place them in contact, as in the figure. As the radii are the same, the focal length of each lens is also the same; but as one is positive and the other is negative, the combination acts as a plain disc of glass with parallel sides.

We have seen that we may consider the disc as a lens of infinite focal length, and hence we know that the combination of the two lenses a and b (Fig. 38) forms a compound lens of infinite focal length.

These two lenses, in this condition, form the simplest conception of the Telephotographic lens that we can imagine, with the components here arranged so as to give the greatest possible focal length.


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Let us examine this arrangement, so that we may define it in general terms for any other combination of positive and negative lenses used in the Telephotographic construction.