In the case of employing a very small stop in the lens, all objects may, as a matter of fact, appear equally defined in the image, but as soon as we use a considerable aperture we see at once how objects lying either before or behind the selected object plane must become indistinct in the image, due to no inherent defect in the lens itself, but because when points in these objects are projected upon the chief plane of the object they are represented as circles, depending upon the diameter of the aperture of the lens, or the entrance pupil, and their distances from it. In general, every point in the object may be considered as sending out a cone of rays having the entrance pupil as a common base, every point in the object space forming a separate apex for each cone. Similarly the exit pupil forms a common base of a cone of rays for each point in the image space behind the lens.

Fig. 52.

If a represents the aperture of the entrance pupil, Fig. 52, and 00 represents the plane for which we have focused and d the distance between them, we can form a true idea of the perspective given by the points p and p' situated before and behind this plane respectively by considering p and p' the apices of cones whose common base is the entrance pupil; these are seen to be a' and a" respectively ; a' and a" are circles of indistinctness n times as large as the circles of indistinctness which will be found on the image plane when a reduction of n times takes place. This consideration leads to an interesting interpretation of the subject of "depth of focus," to which we shall shortly refer.

The correct distance from which an image formed by an ordinary-photographic lens should be viewed is commonly defined to be a distance equal to that of the focal length of the lens. This rule is very approximately correct from the circumstance that the " Entrance" and " Exit " pupils of an ordinary positive lens very nearly coincide with the "principal" or "nodal" planes of the lens. When applied to the Telephotographic lens this condition is found not to hold. If we take a lens of ordinary construction, of given focal length, which reproduces objects in the chief plane reduced in a definite proportion n : /, the object being a distance d from the lens, we find the correct distance x, Fig. 53, from which to view the image, thus : d : x = n :I, or d = (n + I) f, so that x = n+1/nf ; and if n be infinite x =f, which corresponds with the rule to view landscapes from a distance equal to the focal length of the lens above referred to. Now, if we take a Telephotographic lens of the same focal length, here d = f (n + g m); g = I, or is > I ; and the correct viewing distance x = (n + gm/n)f; here, again, if n is infinite x =f.

These results have a very important bearing upon the perspective rendering of the Telephotographic lens.

When m and n are of the same order, which of course occurs in dealing with near and moderately near objects, x is considerably greater for this type of lens than is the case with an ordinary lens of the same focal length, the result being very closely connected with the fact that a greater distance is required between object and lens for the Telephotographic construction.

There are two errors which may be committed in looking at any photograph. It may be viewed from a point too far away, in which case the receding planes are dwarfed, and "distance" is exaggerated; or, on the other hand, if viewed from too near a standpoint, the opposite impression is conveyed, and the true sense of distance diminishes. Of these two errors the former is much more likely to occur, because, as already pointed out in Chapter II (The Formation Of Images By The "Pinhole Camera," And Its Perspective Drawing)., the photographer is apt to approach his subject and include it under a large angle for the purpose of obtaining a sufficiently large image. The Telephotographic lens will enable him to remove the lens to a greater distance from the subject, and not only to include it under a considerably less angle, but to maintain the size of image that he desired with a lens of ordinary construction. To sum up, we find that with the Telephotographic lens we have the opportunity of employing a greater distance between the "Entrance Pupil" of the system and the chief object plane, thus including a less angle than would be possible in the case of an ordinary lens, and thereby obtaining more satisfactory perspective.

Fig.53.

Depth of Focus (Von Rohr's interpretation). - The conception of the " Entrance Pupil" of a lens and its separation from the chief plane of the image enables us to grasp very readily the meaning of this expression, and also the means of attaining it. Strictly speaking, there is no such condition as "depth of focus" in the image given by a photographic lens. We can only produce a perfectly sharp image of one plane of the object; points in the object situated on either side of it must be represented by circles of varying indistinctness. The size of these circles we can control to a considerable extent by aid of the diaphragm, or by reducing the size of the "Entrance Pupil." We have referred to each point of the object as forming a cone of rays having a common basis - namely, the "Entrance Pupil." Each point in the object is represented by a point somewhere in the image space, but only points in one plane of the object can be received as points in one plane of the image, all the apices of the cones which have a common basis in the "Exit Pupil" being now situated in this plane; all other points in the image space, or apices of the cones on the image side, being cut by this plane, form circles of indistinctness more or less extended. To attain so-called "depth of focus," we make use of a convention, and prescribe a limit to the size of these circles of indistinctness. As a matter of fact, this is somewhat difficult to do, or to state in a definite form, because the admissible degree of indistinctness will depend upon the distance from which it is viewed, particularly and more especially if the result is for pictorial effect and not for scientific accuracy. The convention usually adopted is founded on the fact that at the ordinary reading distance we cannot readily distinguish points which are less than one-hundredth of an inch apart, in other words, if a picture is made up of points which do not exceed circles of indistinctness greater than one-hundredth of an inch, it is said to appear "sharp."