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.

In Fig. 4 reference has been made to the lengths of the images a' b'.

a b, a" b" corresponding to a b at different distances of the screen from p, or different camera-extensions as they are termed. These lengths were found to be 1, 2, and 4 respectively. Let us suppose the object to be a square; then the image at a' b' will be one unit square, the image at a b, two units square, and at a" b" four units square.

It is evident that the quantity of light received at ctIt (Fig. 5) is spread over four times the same area at a b, and sixteen times the same area at a" b". The correct relative exposures to give to a photographic plate at these distances from the pinhole p are proportional to the areas in the figure, provided the aperture at p remains the same. We see thus early in our investigations the importance of the "law of inverse squares " in photographic practice : a b is twice the distance of a' b' from the source of light p, and receives one-fourth of the light; a" b" is four times the distance of a' b' from the same source, and therefore receives but one-sixteenth of the light.

Fig.6.

It must be remembered that when we speak of the relative sizes of object and image, or of two images, we always refer to linear measurements. For convenience we shall frequently speak of "magnification " in this treatise, meaning invariably linear magnification. If we refer a" b" to a' b' for example, we say that the magnification of a!' b" is four times ; we also speak of either reduction or magnification (in their ordinary sense) as "magnification." Thus in Fig. 4 the "magnification " of a b at a' b', a b, a" b" is 1/40, 1/20, and 1/10 respectively.

The pinhole camera will assist us materially in a preliminary inquiry into the perspective drawing given by lenses. We shall, however, go into the matter more fully in due course.

Let us suppose we have two objects a b, a' b', (Fig. 6), of the same height at a given distance apart, and that the camera is made to approach a b, until the image a b is conveniently included upon the screen or plate; it will be obvious that a' b' the image of a' b' is also included upon the plate, and is smaller than a b.

If the eye be placed at p, a' b' subtends a greater angle than a b, and hence a' b' appears larger than a b.

In order to see the entire image ab a' b' in true perspective subsequently, it is necessary to consider the image projected forwards through the pinhole towards the object, until, when viewed from p, this image exactly overlaps, or coincides with its further projection on to the object itself, p, or the pinhole, is termed the "Entrance Pupil" (Abbe) of this image-forming appliance.*

Fig.7.

The distance between this "pupil" and the image - when it is made to occupy a position in which its projection towards the object coincides with the object - determines the proper viewing distance for the image or photograph. We may say in passing that this consideration has a very important bearing on the perspective given by the Telephotographic lens.

It is evident from Fig. 6 that it is immaterial how near, or how

* There are two "Pupils" in every lens-system, termed the "Entrance" and " Exit" Pupils of the system, which are the centres of perspective for object and image respectively. In the case of pinhole projection, they coincide in the pinhole itself. (See Chapter VI (The Use And Effects Of The Diaphragm, And The Improved Perspective Rendering By The Telephotographic Lens)., and Notes to same.) distant, the screen or plate is placed to the pinhole p in order to produce theoretically perfect perspective, because a position can always be found in front of the "Entrance Pupil" p, where this image, when projected towards the object, coincides with it exactly. (In the case under consideration the correct viewing distance is identical with the measure of the distance between the pinhole and the screen. It is, however, a less comprehensive method of examining the perspective drawing of photographic instruments in general.)

The theoretically perfect perspective above referred to may, and frequently does, impose conditions that are unsuitable, and often impossible, to observe if we possess normal powers of vision. We cannot, without effort or discomfort, look at an object that is nearer than about 10 inches. The result of this is that we usually view small photographs from too great a distance, and accordingly the image appears crowded into a smaller space than it ought to be.

In Fig. 7 the image a a' b' b appears in true perspective from p ; if, however, P e is not a convenient distance for normal vision, we should in reality view it from the same position q. From this point Q the conditions for true perspective do not obtain, and the projection of the image towards the object does not coincide with it, but falls within it as at c d, c' d', giving an appearance of crowding.

It is evident that if a distance q e is necessary to view the picture (image) in comfort, the only way to maintain correct perspective will be to project aa' b' b towards the object until it would occupy the position at e', where e'p=qe in the top drawing; in other words, the image must be enlarged. It may be stated here that enlargements are usually more satisfactory in perspective than small photographs, because the tendency is to view the latter from a greater distance than the theoretical conditions for true perspective allow. On the other hand, if we look at a photograph at a normal distance of vision, and this happens to be within the correct distance for true perspective, we do not feel that the perspective drawing given by the instrument is as unsatisfactory as in the former case; although if carried to an exaggerated degree, we become sensible that objects in the receding planes of the picture appear to be rendered too nearly upon one plane, or, to use the common phrase, "flat."*

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