HPT"" T TTYT T/"\nr/"\ C* T\ A T\l I\/ 
 
 TELEPHOTO GRAPH Y 
 
 THOMAS R.DALLMEYER. 
 
LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
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TELEPHOTOGRAPHY 
 
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TELEPHOTOGRAPHY 
 
 AN ELEMENTARY TREATISE 
 
 ON THE 
 
 CONSTRUCTION AND APPLICATION 
 
 OF 
 
 THE TELEPHOTOGRAPHIC LENS 
 
 BY 
 
 THOMAS R. DALLMEYER, F.R.A.S, 
 
 VICE-PRESIDENT OF THE ROYAL PHOTOGRAPHIC SOCIETY 
 
 WITH TWENTY-SIX PLATES AND SIXTY-SIX DIAGRAMS 
 
 LONDON 
 WILLIAM HEINEMANN 
 
 1899 
 
~This Edition enjoys Copyright in all 
 Countries Signatory to the Berne 
 Treaty, and is not to be imported 
 into the UnitedStatesof America. 
 
 All rights including translation reserved 
 
HetrtcateU 
 TO 
 
 THE MEMORY OF 
 MY FATHER 
 
 JOHN HENRY DALLMEYER 
 
 B. 18300. 1883 
 
 FAMED FOR HIS WORK 
 
 HIMSELF BELOVED 
 
CONTENTS 
 
 CHAP. PAGE 
 
 FRONTISPIECE 
 
 PREFACE AND HISTORICAL NOTES . xi 
 
 I. PROPERTIES OF LIGHT . . . . . . . . .. . i 
 
 II. THE FORMATION OF IMAGES BY THE "PINHOLE CAMERA," AND ITS PER- 
 SPECTIVE DRAWING 5 
 
 III. THE FORMATION OF IMAGES BY POSITIVE LENSES 17 
 
 IV. THE FORMATION OF IMAGES BY NEGATIVE LENSES 41 
 
 V. THE FORMATION OF ENLARGED IMAGES : 
 
 PART I. BY Two POSITIVE LENS-SYSTEMS 51 
 
 PART II. BY A POSITIVE SYSTEM AND A NEGATIVE SYSTEM COMBINED, 
 
 OR THE TELEPHOTOGRAPHIC LENS .... 53 
 VI. THE USE AND EFFECTS OF THE DIAPHRAGM, AND THE IMPROVED PER- 
 SPECTIVE RENDERING BY THE TELEPHOTOGRAPHIC LENS ... 80 
 
 VII PRACTICAL APPLICATIONS OF THE TELEPHOTOGRAPHIC LENS. . . . 114 
 
 VIII WORKING DATA 137 
 
 ABRIDGED FORMULAE FOR REFERENCE 142 
 
 BIBLIOGRAPHY .147 
 
PREFACE AND HISTORICAL NOTES 
 
 THIS treatise is addressed to those who practise photography either for 
 pictorial or scientific ends. 
 
 The late Michael Faraday once remarked : " Lectures which really 
 teach will never be popular ; lectures which are popular will never 
 teach." All writers must experience the same inherent difficulty of 
 treating scientific matter in any but an academic style. The author 
 has endeavoured to present the subject of Telephotography in a 
 manner which presupposes only the very slightest acquaintance with 
 the science of Optics, explaining fully only those few properties or 
 functions of lenses, which are necessary to enable the photographer to 
 understand the action of the Telephotographic lens, and to comprehend 
 the wide possibilities of its applications. 
 
 The aim of the present work, in short, has been to call attention to 
 the scale in which objects are reproduced in the image by ordinary 
 photographic lenses, and to show how this image may be subjected to 
 direct enlargement or magnification before it is received on the photo- 
 graphic plate. 
 
 This method was adopted by the author in his original contribu- 
 tions to the subject. It is perhaps less classical than treating the 
 instrument as a complete optical system, but has a more practical 
 bearing upon its use ; and as might be expected, is more readily 
 grasped by those who are acquainted with the action of ordinary 
 photographic lenses : both methods are, however, included. It is 
 
PREFACE AND HISTORICAL NOTES 
 
 hoped that frequent diagrammatic representation and occasional 
 repetition may be of assistance to the reader. The application of the 
 few formulae given in the work only involve a knowledge of 
 arithmetic.* 
 
 The literal meaning of the term "Telephotography" does not 
 convey the full significance of the applications of the Telephotographic 
 lens. The value of the instrument is as great, if not greater, in photo- 
 graphing near as well as distant objects. It will be found to possess 
 invaluable properties wherever lenses of great focal length are required 
 to produce large images on the one hand, and for rendering improved 
 perspective drawing in any given scale of near objects on the other. 
 This latter effect is brought about by the fact that a greater distance 
 intervenes between a Telephotographic lens and a comparatively near 
 object (as in portraiture) than that required when using a lens of 
 ordinary construction of the same focal length. This property is of 
 great value to the artist when the object he desires to photograph 
 has any "depth of field" enabling him to avoid the apparent ex- 
 aggerated perspective so frequently met with in ordinary photo- 
 graphs. 
 
 The principle upon which the Telephotographic lens is constructed 
 has been applied to the astronomical telescope for nearly seventy years. 
 So long ago as 1834, Peter Barlow, in a communication to the Royal 
 Society, dwelt on the advantages that might accrue from employing 
 his negative lens " in day telescopes " as well as in astronomical 
 telescopes ; "for by giving an adjustment to the lengthening lens, the 
 power may be changed in any proportion, without even removing the 
 eye or losing sight of the object. I have no doubt these and other 
 applications of the lengthening lens will be made." In these last few 
 words Barlow foreshadowed the construction of the Telephotographic 
 lens. 
 
 * The notes to Chapters II., III., IV., V., and VI. may be omitted on first reading. 
 
 xii 
 
Dr. Von Rohr, a contemporary of the present writer, has been at 
 great pains to trace the application of Barlow's lens in the construction 
 of photographic instruments; and it appears that in 1851 Porro, an 
 Italian engineer, utilised a " Barlow" lens for photographing an eclipse 
 of the sun which took place on July 18 in that year. Since that date, 
 the employment of a negative lens in astro-physical work has been 
 adopted in a few isolated instances, notably by Dr. H. Schroeder, and 
 these instruments are reported to have been directed to very distant 
 terrestrial objects for the purpose of photographing them. Ordinary 
 astronomical and terrestrial telescopes of various kinds have been 
 utilised for the same purpose from time to time, and in the year 1873 
 the late Mr. J. Traill Taylor, Editor of the British Journal of 
 Photography, called attention to the use of the Galilean Telescope, or 
 ordinary opera-glass, for the purpose of producing a large direct 
 image. This application of the Galilean telescope is identical with the 
 employment of the " Barlow " lens for direct enlargement of the image, 
 and as the instrument was not designed or corrected for photographic 
 purposes, the reference to the opera-glass, although occurring in photo- 
 graphic literature, was unnoticed elsewhere. 
 
 In February 1890, Steinheil constructed a special photographic 
 instrument upon this principle for the German " Reichs-marineamt," 
 but the fact was not published. 
 
 In the autumn of 1891, A. Duboscq, Dr. A. Meithe and the author 
 almost simultaneously applied for patents concerning Telephotographic 
 instruments ; Duboscq in France on August 7, Dr. Miethe in Germany 
 on October 18, and the author in England on October 2. Duboscq's 
 work was not known till a reference was made to it by A. Sorets in 
 
 1893- 
 
 A controversy between the author and Dr. Miethe as to priority 
 took place in the British Journal of Photography^ in which the author 
 acknowledged Miethe's independence. At this date there had been no 
 
 Xlll 
 
PREFACE AND HISTORICAL NOTES 
 
 previous publication of instruments designed for the use of photo- 
 graphers. 
 
 The author was the first to exhibit instruments so designed at the 
 Camera Club, London, and to explain the theory of construction and 
 working. This is acknowledged by Dr. Von Rohr (of the firm of 
 Zeiss), who points out the widespread effect of this exposition. 
 
 The inherent defect of distortion of the image in the first Tele- 
 photographic constructions led the author to introduce the plan of 
 converting ordinary non-distorting photographic lenses into Telephoto- 
 graphic systems, without interfering with their ordinary use, and this 
 form of combination is the one which is now chiefly adopted by his 
 contemporaries. Full reference is made to particular constructions. 
 
 The author desires to record the fact that his attention was first 
 directed to the subject of Telephotography by his friend Dr. P. H. 
 Emerson, who urged upon him the necessity of a photographic instru- 
 ment to enable the naturalist to record incidents that were then only 
 possible by telescopic observation. Emerson's original work in 
 advancing the pictorial side of photography is now history, and it was 
 his indication of certain drawbacks in photographic methods, as a 
 means of pictorial representation, particularly the inadequate rendering 
 of objects as seen by the normal eye, that led the author to endeavour 
 to overcome them by improved optical means. 
 
 M. Boissonnas, of Geneva, the Earl of Crawford, and Mr. Hodinott, 
 of the Camera Club, London, were the first to test and prove the value 
 of the instrument in distant mountain scenery, and Dr. Emerson (in 
 1892) and later Mr. J. S. Bergheim to exhibit results showing improved 
 perspective in portraiture. The author's thanks are due to these gentle- 
 men and many others for their kindness in offering examples to illustrate 
 this little work. Mr. R. B. Lodge and Messrs. Kearton have exemplified 
 its value to the naturalist, Mr. E. Marriage and Mr. Cruickshank to 
 the architect, while Dr. Victor Corbould and the late Dr. Fallows have 
 
 xiv 
 
demonstrated its utility in surgical and medical records ; some of their 
 splendid work would have been here reproduced, except for reasons 
 that will be obvious when it is remembered that this treatise is 
 intended for perusal by the lay public. A few studies of the eye are 
 therefore substituted. The Astronomer- Royal kindly lends two very 
 interesting examples of solar photography, while Naval and Military 
 records and possibilities are illustrated through the courtesy of repre- 
 sentatives of the Japanese and Italian Governments. 
 
 It may be mentioned that with the exception of one or two articles 
 on the practical applications of the lens by Mr. Lodge, Mr. Marriage 
 and Dr. Spitta, the subject has not been treated by any other English 
 writer. 
 
 The author's papers are scattered some being out of print. He 
 therefore hopes that this treatise may find acceptance, and a place in 
 the literature of photographic optics. 
 
 ROYAL SOCIETIES CLUB, 
 
 ST. JAMES'S STREET, W. 
 September 1899. 
 
TELEPHOTOGRAPHY 
 
 CHAPTER I 
 
 PROPERTIES OF LIGHT 
 
 Light consists of vibrations of a highly elastic solid medium termed 
 ether, which pervades all space. These vibrations are conveyed to the 
 brain by means of our eyes, and produce the sensation of sight. 
 
 All visible objects surrounding us are sources of light. These 
 sources are either self-luminous bodies, such as the sun, fixed stars, 
 electric light, and bodies in a state of combustion ; or illuminated 
 bodies, as the moon, planets, or any body that can be seen by light 
 borrowed from a self-luminous body. 
 
 For our present purpose, it is not necessary to distinguish these 
 two classes of objects ; every point in every object is a source of 
 light. 
 
 Medium. Any space through which light can pass is called a 
 medium; a vacuum, air, gases, water, glass, &c., are media. Bodies 
 through which light can pass are termed transparent, while those 
 through which it cannot pass are termed opaque. 
 
 Light travels in straight lines with iiniform velocity in any homo- 
 geneous medium. In the practice of photography, particularly in 
 Telephotography, we are occasionally reminded of the converse of this 
 law. In observing a distant object across an open landscape, or a ship 
 
TELEPHOTOGRAPHY 
 
 at sea, the object under observation sometimes appears to be disturbed 
 and unsteady, owing to a kind of "boiling" appearance of the atmo- 
 sphere, which is not homogeneous for the time being. When the 
 atmosphere is in this condition, it is hopeless to expect to obtain well- 
 defined photographic images. The observations of astronomers in this 
 country are frequently disturbed by the lack of homogeneity in the 
 atmosphere, even on apparently the clearest nights. 
 
 Light consists of separable and independent Parts. If we place an 
 opaque object in the light proceeding from a luminous body, a portion 
 of the light is intercepted, but the rest of the light proceeds to 
 illuminate surfaces upon which it falls, neither adding to nor 
 diminishing the illumination. Again, light from two independent 
 sources may travel along the same path without interference. Hence 
 light is capable of quantitative measurement ; that is to say, we can 
 compare the intensity of two given sources of light, or in general 
 measure the intensity of light in terms of some fixed standard. In 
 photographic practice, we measure the intensity of light by an 
 instrument known as an "actinometer," the action of which is based 
 upon the period of time taken by the light to discolour a photo- 
 graphically active material to a given shade ; the greater the intensity 
 of the light (photographically), the shorter the period of time taken to 
 discolour the sensitive material. 
 
 Absorption and Transmission of Light. When light travels through 
 any homogeneous medium, part is absorbed and only part transmitted. 
 We shall neglect absorption entirely and presume that all media are 
 perfectly transparent. 
 
 Reflexion of Light on passing from one Medium to another. When 
 light passes from one homogeneous medium to another, part is reflected 
 at the surface of the second medium, and part transmitted. In the 
 construction of photographic instruments, we consider the whole of the 
 light to be transmitted. In our study of the theory of the Telephoto- 
 graphic lens, we shall not then take these factors into consideration ; 
 but, in practice, it must be borne in mind that the absorption of light 
 by thick lenses, and the loss of light by reflexions are not in reality 
 
PROPERTIES OF LIGHT 
 
 quite negligible quantities. Greater optical perfection in an instrument 
 is frequently attained, however, by both these means as exemplified in 
 some of the most recent advances in photographic lens construction. 
 
 A Ray of Light. For theoretical considerations, it is often 
 convenient to consider a portion of light travelling along some 
 particular line in a medium, quite apart from the remainder. We may 
 think of it as an indefinitely attenuated slender cone, or, as older writers 
 put it, the least portion of light we can conceive to exist independently. 
 We term such a portion of light a Ray of Light. 
 
 A Pencil of Ray s\s a collection of rays which never deviate far from 
 some central fixed ray, which is called the axis of the pencil. If the 
 
 FiC.I. 
 
 pencil proceeds towards a point, it is termed a convergent pencil ; if, on 
 the other hand, it proceeds from a point, it is termed a divergent pencil. 
 
 Focus. If a pencil of rays meets in a point, that point is called the 
 focus. A focus is not a measurement, but a position. 
 
 Parallel Rays. The form of a pencil of rays is considered as that 
 of a right cone. The limiting form of a cone when the vertical angle 
 is indefinitely small is a cylinder. Such a cylindrical pencil of rays is 
 termed parallel. 
 
 The intensity of light at different distances from a htminous point is 
 inversely as the square of the distance. 
 
 As we know that light travels in straight lines in all directions, it is 
 easy to find the alteration in the intensity of the illumination* of a 
 surface by changing its distance from the source of light. 
 
 * It is thought unnecessary to introduce " units " into this popular explanation. 
 
 3 
 
TELEPHOTOGRAPHY 
 
 If L be a luminous point, and we imagine concentric spheres with 
 radii R R', &c., described about it, the total quantity of light received 
 by the surface of the sphere of radius R L is the same as that which 
 would reach the surface of the sphere of radius R' L. Now, as the 
 surfaces of the spheres are in direct ratio of the square of their radii; 
 the quantity of light which falls on a given extent of surface must be 
 inversely in the same ratio. 
 
 In the same manner, if we place a small plane surface at A at a 
 given distance from L, the whole quantity of light received at A would 
 be distributed over B, c, and D placed at distances 2, 3, and 4 times 
 the distance of A from the light. The areas of B, c, and D are 4, 9, and 
 1 6 times as great as A, or the intensity of the light on the unit of sur- 
 face is inversely as the square of the distance from the source of 
 illumination. This law is termed the " law of inverse squares," and it 
 has a very important bearing upon our present subject. 
 
 The illumination of the areas we have just discussed is taken as 
 perpendicular to the incident light. 
 
 The illumination of an area inclined to the incident light is found by 
 multiplying the former by the cosine of the angle of incidence. This 
 law, together with the law of inverse squares, enables us to measure the 
 falling off of the illumination from the centre towards the edge of a 
 photographic plate, but need not be dwelt upon here. 
 
CHAPTER II 
 
 THE FORMATION OF IMAGES BY THE " PINHOLE CAMERA," 
 AND ITS PERSPECTIVE DRAWING 
 
 THE simplest of all devices for forming an image is what is termed a 
 41 Pinhole Camera." 
 
 If we make a minute hole in a thin sheet of card or metal, and 
 place this at one end of a [rectangular] light-tight chamber or camera, 
 and place a screen or sensitive photographic plate at the opposite end, 
 
 Rc. 2. 
 
 it is easy to see that any luminous or illuminated object lying in front 
 of this camera will form an image upon the screen. 
 
 Every luminous point that contributes to make up the entire object 
 emits, as we have seen, luminous rays in all directions, but only one 
 very small pencil of light can pass from each separate point through 
 the tiny hole. Each minute pencil passes through this pinhole in 
 straight lines, and passes on until it is intercepted by the screen, where 
 
 5 
 
TELEPHOTOGRAPHY 
 
 it is received as a tiny dot of light, determining its image. Thus the 
 entire object forms a complete image upon the screen or sensitive 
 plate, as illustrated in the figure. (See note at the end of chapter.) 
 
 Successful photographs have been obtained by this means in cases 
 where extremely fine definition is not of prime importance, nor the 
 requisite time of exposure (a few minutes in good light) likely to 
 emphasise any defect in definition by movement of the object. 
 
 The enthusiastic photographer, having inadvertently left his lens 
 
 FlC. 3. 
 
 at home, has before to-day fixed his visiting card over the flange in his 
 camera, pierced a hole in the pasteboard with a pin, and by this means 
 secured a photograph that otherwise might never have been his, or 
 fallen to his lot again. 
 
 The " Pinhole Camera" gives us a clear insight into the formation 
 of images of different sizes, and will help us to understand similar 
 effects when we come to examine the capabilities of lenses in this 
 respect. 
 
 First let us direct the camera towards an object situated at a given 
 distance from the pinhole, the distance between the pinhole and the 
 screen being also known. 
 
 6 
 
FORMATION OF IMAGES 
 
 Let us suppose the object AB (Fig. 3) to be 10 ft. distant from the 
 pinhole P, and that p is 6 inches from the camera screen s ; it is evident 
 that the length of the image a b formed upon the screen bears the same 
 proportion to the length of the object A B as the distance P s (6 inches) 
 is to P o (10 ft.), or the image is one-twentieth of the size of the object.* 
 
 Now let us bring the camera nearer to the object, as shown in the 
 same figure, until o P is only 5 ft., but o s remaining 6 inches. The 
 image now formed upon the screen is affected in a similar manner to 
 our impression of the appearance of the object. As we approach an 
 object it appears to be larger, or the object is said to be viewed under 
 a greater angle, and it now subtends a greater angle at the pinhole 
 
 FIG. 4. 
 
 than it did in its first position. The rays passing from A and B through 
 the pinhole cross at a greater angle. These and all rays forming 
 the image are intercepted by the screen, and the length of the image is 
 again determined by the relation of the distances PO (5 ft.) and PS 
 (6 inches), A B and a b being in the same proportion, or as 10 : i. 
 
 Thus we see that when the camera is one half the distance from the 
 object, the image is double the size (linear) ; and in general the nearer 
 we approach the object, the greater becomes the size of the image. 
 By similar reasoning the converse may be taken for granted. 
 
 Let us now consider the case of the object and pinhole of the 
 camera at a fixed distance apart, but with the screen of the camera 
 made to occupy different positions. 
 
 * A P o and a P s are similar triangles, and if we know the relation existing between the 
 measurement of any two similar sides, o p : P s : : 20 : i, we know that any other pair of 
 similar sides o A, as, bear the same relation to one another. Thus in the similar 
 triangles A p B, a P b, A B : a b : : 20 : i. 
 
 7 
 
TELEPHOTOGRAPHY 
 
 Let the object A B (Fig. 4) be again 10 ft. distant from r, and the 
 screen s 6 inches from p, intercepting the rays of light from the object 
 A B which pass through P, receiving the image at a b. In this position 
 we have seen that the respective lengths of A B and a b are as 20 : i , or 
 as their distances from p. 
 
 Let us now move the screen nearer to P, as at p s', say 3 inches only 
 from the pinhole. We observe that the luminous rays from A B are 
 intercepted sooner, and form an image at a' b'. The relative lengths of 
 AB and a' b' are now as 10 ft. to 3 inches, or as 40 : i. Similarly, it is 
 easy to see that if the screen be removed to s", at a distance of 1 2 inches 
 from P, the image will now be intercepted at a" b", and that the relative 
 
 FIG. 5. 
 
 
 
 
 
 lengths of A B and a!' b" are now only as 10 : i ; and, in general, that 
 the greater the distance between pinhole and screen, the larger will the 
 image become. 
 
 It will be seen later that when we employ an ordinary photographic 
 lens, the only way to increase the size of the image upon the screen is 
 by approaching the object, as we did with the pinhole camera in Fig. 3 ; 
 but when we employ a Telephotographic lens, we can place the screen 
 in any position we like, as in Fig. 4, and obtain different sizes of images 
 from a fixed standpoint. So that the pinhole camera with the screen 
 in a fixed position roughly defines the limited use of an ordinary 
 photographic lens as regards its power of producing images of different 
 size of a given object ; whereas the pinhole camera with a movable 
 screen indicates the far wider possiblities of the Telephotographic 
 lens in this respect. 
 
 In Fig. 4 reference has been made to the lengths of the images a' b', 
 
 8 
 
FORMATION OF IMAGES 
 
 a 6, 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 i, 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 a' b' (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 
 
 FlG.6. 
 
 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. 
 
 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 measure- 
 ments. 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 "magnifica- 
 tion " of A B at a' b', a b, a" b" is tV, w, and ~^ 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 
 
 9 
 
TELEPHOTOGRAPHY 
 
 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 a b a' b' in true perspective subse- 
 quently, it is necessary to consider the image projected forwards through 
 the pinhole towards the object, until, when viewed from P, this image 
 
 FIG. 7. 
 
 =>Q 
 
 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.* 
 
 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., and Notes to same.) 
 
 10 
 
FORMATION OF IMAGES 
 
 distant, the screen or plate is placed to the pinhole p in order to pro- 
 duce theoretically perfect perspective, because a position can always be 
 foimd 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 a a' b 1 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 
 
 ii 
 
TELEPHOTOGRAPHY 
 
 planes of the picture appear to be rendered too nearly upon one plane, 
 or, to use the common phrase, <l flat." * 
 
 In ordinary photographic practice, the camera is usually brought 
 very near to the chief object of interest, so as to give it prominence by 
 obtaining a sufficiently large image. When this takes place, the 
 receding planes of the picture are dwarfed, while the perspective is 
 unsatisfactory ; for we do not so view it that its projection from the 
 point of sight coincides with the objects in space. By the use of the 
 pinhole camera it can readily be seen how this may be overcome. 
 
 In Fig. 8, where p is at a given distance from the object AB in 
 order that a b may be the required size upon the screen s s, at a fixed 
 
 A' A 
 
 Fie. 8. 
 
 distance from P, the objects A B, A' B' are rendered in a certain proportion 
 a b : a' b' ; a' b' being considerably smaller than a b. p E is here the 
 correct but inconvenient viewing distance. 
 
 If we now remove the camera to a greater distance from A B, the 
 image diminishes in size, and becomes too small for our purpose. But 
 if the screen s s be removed from P, so that the image is received upon 
 s' s' in the same size as in the former case, we shall find the image a! b' 
 of A' B' is now greater than before, or that the proportion a b : a' b' is 
 different in this case. In general, the perspective will be much more 
 satisfactory if the nearest object of interest is not too close to the 
 camera. As already stated, the conditions in the upper drawing in 
 Fig. 8 are very approximately those of an ordinary "positive" lens; 
 
 * The reader is referred to Dr. P. H. Emerson's " Naturalistic Photography " (Third 
 Edition, Messrs. Dawbarn Ward) for a fuller study of the perspective rendering of lenses. 
 
 12 
 
FORMATION OF IMAGES 
 
 whereas in the lower drawing we exhibit the possibilities of the Tele- 
 photographic lens. 
 
 It is generally held that we ought to view a photograph from a 
 distance equal to the focal length of the lens with which it was taken. 
 This is very approximately true for all lenses irrespective of their 
 construction, when the object is so distant that all rays meeting the 
 lens may be considered parallel ; but only under these conditions. 
 
 To see the image in true perspective under all conditions we must 
 view it projected towards the object from the "Entrance Pupil" (of 
 the particular optical system with which it was produced), at the 
 position where its projection towards the object will exactly coincide with 
 the object. 
 
 There is, then, a definite and correct distance at which every 
 photograph should be viewed, but if we ask ourselves how often we 
 conform to the correct conditions, we shall have to confess that it 
 is very seldom indeed. It is for this reason that many artists are so- 
 severe upon the rendering of perspective by photographic instruments. 
 It is not difficult to see how this comes about. If we look at a 
 painting, a black and white drawing, or a photograph taken by 
 ordinary means, whatever its size may be, we involuntarily take up a 
 position at a distance equal to two, three, or possibly more times the 
 length of its longest side. This standpoint suits the artist's perspective, 
 and it looks right, because he has considered all this in creating his 
 impression ; but the poor photograph is terribly handicapped, because 
 we oiight to inspect it from a distance equal approximately to the focal 
 length of the lens with which it was produced (generally about the 
 longest side of the print) and when we do not, it looks wrong ! 
 
 The Telephotographic lens, as will be shown anon, acts as a lens of 
 very considerable focal length, and with its aid photographs are 
 produced that ought to be viewed from a distance equal to three or 
 four times the longer side of the print. We thus conform to our 
 conditions of finding the correct position for true perspective involun- 
 tarily, and are not troubled with that apparently false rendering of 
 perspective given by ordinary lenses. 
 
 13 
 
TELEPHOTOGRAPHY 
 
 NOTE. 
 
 By ordinary reasoning, it might be presumed that the smaller the 
 "pinhole" the finer the definition. This, however, is not the case, 
 as light in passing through the small hole is v ' diffracted." This 
 "diffraction" interferes with the definition of the image, and for a 
 given distance between screen and pinhole the size of the hole may 
 be either too large or too small to give the best result. 
 
 Diffraction is due to the retardation of rays proceeding from 
 the margin of the pinhole as compared with rays proceeding from 
 the centre ; to obtain the maximum concentration of light at the 
 
 focus, the retardation should be half a wave length -.* Lord Rayleigh 
 
 has shown at any rate that the limit of retardation may be taken as -. 
 
 4 
 
 Taking - as the retardation, r as the radius of the pinhole, and d 
 its distance from the plate P, it is easily seen that 
 
 I 1 . A \ -7 TO 
 
 = (d + - Y d' ; 
 
 2 
 
 = cT" + d A + _" - d' 2 
 4 
 
 = d \ (as - is very small) ; 
 4 
 
 r 
 or d = 
 
 Example. Let the centre of the plate be 10 inches from the hole, 
 and taking the light near the o line of the spectrum as the most 
 
 * Captain Abney on " Pinholes," Camera Club Journal, May 1890. 
 
 14 
 
FORMATION OF IMAGES 
 
 photographically active, A=. 000017; the radius of the hole should 
 be: 
 
 r = J. 000017 x 10 
 
 = N/. OOOI7 
 
 = .013 inch ; 
 
 or -026, or T jV inch, is the best diameter for the hole. 
 
 By applying this formula to needles of known diameter (Helic 
 needles of Messrs. Milward & Son, Redditch) the following results may 
 be useful : 
 
 N umber. 
 
 Diameter. 
 
 Approx. Diam'r. 
 
 Distance for plate. 
 
 I 
 
 .046 
 
 i 
 7 
 
 31" 
 
 2 
 
 .042 
 
 i 
 
 "2T 
 
 26 
 
 3 
 
 .038 
 
 1 
 TB" 
 
 21 
 
 4 
 
 .036 
 
 1 
 
 2F 
 
 19 
 
 5 
 
 .032 
 
 3T 
 
 15 
 
 6 
 
 .029 
 
 i 
 -g-g 
 
 12 
 
 7 
 
 .026 
 
 Tff 
 
 10 
 
 8 
 
 .023 
 
 1 
 TT 
 
 9 
 
 9 
 
 .02 
 
 1 
 ?TT 
 
 6 
 
 10 
 
 .018 
 
 1 
 7T 
 
 5 
 
 ii 
 
 .Ol6 
 
 1 
 T2 
 
 4 
 
 12 
 
 .014 
 
 1 
 
 TT 
 
 3 
 
 We shall presently see that diffraction may also have a disturbing 
 effect upon the definition given by photographic lenses, when the 
 opening of the diaphragm bears too small a relation to its focal 
 length. 
 
 It may be convenient now to point out that the "pinhole" camera 
 affords a ready means of ascertaining with some accuracy the focal 
 length of positive lenses or lens-systems. A suitable definite distance 
 between the pinhole and screen being accurately set, a negative is 
 taken of some distant object, the image of which is preferably longitu- 
 
 15 
 
TELEPHOTOGRAPHY 
 
 dinally and centrally placed, and of considerable contrast in subject. If 
 this image be very carefully measured in length, its measurement forms 
 a gauge for the determination of the focal length of lenses, by 
 
 comparison with the 
 
 formed by them, a matter of simple 
 
 FIG. 10. 
 
 proportion e.g., if the object, A B formed an image, a' b', with a pinhole 
 at the distance d', then two lenses, forming images a b, a" b", would have 
 focal lengths corresponding to the proportion between a' b' and a b, a!' b" 
 respectively, or their absolute focal lengths would be d and d". 
 
 16 
 
PLATE I 
 
 Taken with an ordinary lo-in. cabinet lens at a distance of 10 ft. ; compare with 
 Plate II. and note the exaggerated size of the hand, flower, and foreground, and the 
 dwarfing of the background. (By the Author.) 
 
PLATE II 
 
 Taken with an 8" c. de v. lens combined with a 4-in. negative lens at a distance of 
 24 ft. The camera extension was set to render the face in the same scale as Plate I. ; 
 the relative planes of the picture have their proper values in respect of drawing. 
 
 (By the Author.) 
 
CHAPTER III 
 
 THE FORMATION OF IMAGES BY POSITIVE LENSES 
 
 THE laws of reflection and refraction of light at plane and spherical 
 surfaces are contained in every elementary treatise on " Optics."' The 
 reader will do wisely to master them, although an intimate knowledge 
 of the subject is not necessary in order to understand how images are 
 formed by lenses and combinations of lenses. 
 
 For our present purpose, it will only be necessary to understand 
 how pencils of light are affected in their passage through a lens, and to 
 define certain characteristics, or elements as they are termed, of the 
 lens itself. 
 
 When a ray of light passes from one transparent homogeneous 
 medium into another (either denser or rarer), it continues its course in 
 a straight line when it meets the surface of the medium perpendicularly 
 (or at " right angles," as it is termed), as A, B, c, D. (Fig. 1 1.) If the 
 ray encounters the second medium in a slanting (oblique) direction, or 
 at any other angle than a right angle, taking a direction A' B', it alters 
 its direction in passing through the second medium, and is bent, or 
 " refracted," as at B' c', continuing its altered course in a straight line 
 within the second medium. On passing from a second into a third 
 medium, the same process continues as at c 1 D', and so on. (See 
 Notes.) 
 
 The altered direction of the ray will depend upon the character of 
 the medium which it meets in its original course. If the second 
 
 * Cole's " Photographic Optics " (Sampson Low & Co.). 
 
 17 B 
 
TELEPHOTOGRAPHY 
 
 medium is denser (or more refractive) than the first, the ray is bent 
 towards the perpendicular p p drawn through the point where it meets 
 the second surface as at B' c'. If, on the other hand, the ray is pursuing 
 its course in a straight line in a denser medium B' c' than that which 
 it next encounters, it is bent away from the perpendicular p' p' drawn 
 through this point as at C'D'. If one medium be denser (or have a 
 higher refractive index, as it is termed) than another, the more will it 
 bend or refract a ray meeting it at a given obliquity. 
 
 In Fig. ii we have illustrated the passage of a ray of light through 
 
 
 a plane plate of glass with parallel faces, and it will be observed that 
 after passing through the glass it emerges in a direction parallel to its 
 original direction. If A'B' had not encountered a medium of different 
 density, it would have pursued the course A' B' c" D". The effect of the 
 slab of glass with parallel sides has been to divert the ray of light from 
 its course, but not to alter its direction. If the glass is very thick, as 
 in the figure, the ray is considerably diverted ; if it be very thin, it is 
 easy to see that its course is very little affected, but in neither case is 
 the direction altered. We shall see presently that certain rays pass 
 
 18 
 
FORMATION OF IMAGES 
 
 through a lens in precisely the same manner, and shall make use of 
 these rays in our investigations on account of the simplicity of the 
 conditions. It must be noted that the ray originates in one medium 
 (air), and after refraction by the denser medium (glass) emerges again 
 into the same medium (air). This is necessary for the condition ; for 
 if the last medium were different from the first, the condition of 
 parallelism would not hold good. In photography the first and final 
 media (air) are almost invariably the same ; an exception would occur 
 if we placed the outside surface of the lens under water to photograph 
 fish, &c. 
 
 A lens is a portion of a refracting medium bounded by two spherical 
 
 Fic.12. 
 
 surfaces of revolution which have a common axis, called the axis of the 
 lens. 
 
 With o as a centre and radius o R describe the curve of the spheri- 
 cal surface of revolution R A' R ; similarly with o' as centre and radius 
 o' R' describe the curve of the spherical surface of revolution R' A R'. The 
 portion L represents the section of a lens, o and o' are the two centres 
 of curvature of the surfaces ; o o', the line joining them, is the axis of 
 the lens ; o R, o' R' the radii ; A, A', the points where the surfaces cut 
 the axis, are called the poles, and the distance between these bounding 
 surfaces, or poles, A A', the thickness of the lens. The surfaces of revolu- 
 tion are either spherical or plane a plane surface being, of course, a 
 particular case of a spherical surface where the radius is infinitely 
 great. 
 
 19 
 
Lenses are classified according to their forms. A lens bounded 
 (i) by two convex surfaces is called a double-convex lens ; (2) by a 
 convex surface and a plane surface, a convexo-plane, or plano-convex lens, 
 according to the surface presented to the light ; (3) by a convex surface 
 and a concave surface, a convexo-concave or concavo-convex lens, accord- 
 ing to the surface presented to the light. A lens of this last form is 
 also termed a meniscus. 
 
 (4) Similarly, a lens bounded by two concave surfaces is called a 
 double-concave lens ; (5) by a plane surface and a concave surface, a 
 plano-concave, or concavo-plane lens, according to the surface presented 
 to the light ; (6) by a concave surface and a convex surface, a concavo- 
 
 Fic.13. 
 
 CONVEX OR POSITIVE LENSES CONCAVE OR NEGATIVE LENSES 
 
 convex or convexo-concave lens, according to the surface presented to the 
 light. This form of lens is also called a meniscus. 
 
 The first three forms of lenses are thicker in the centre than the 
 edge and are called convex or positive lenses, and are capable of form- 
 ing real images. The last three forms of lenses are thinner in the 
 centre than the edge, and are called concave or negative lenses ; they 
 cannot form real images when used alone, but form imaginary or virtual 
 images. We may add here, for a special reason that will afterwards be 
 made clear, that we may conceive a " lens " having two plane surfaces ; 
 this lens can be imagined to form an image at infinity. 
 
 Let us now proceed to determine the elements of a lens necessary for 
 assigning the position and magnitude of the image of any object. They 
 are termed the " four cardinal points " of a lens : * the two " principal " 
 
 * See paper on " The Measurement of Lenses," by Prof. S. P. Thompson, Society of 
 Arts Journal, Nov. 1891. 
 
 20 
 
FORMATION OF IMAGES 
 
 points these may usually be taken to coincide in one " optical centre " 
 for our present purpose and the two " focal " points. 
 
 I. To determine the position of the "optical centre," and the two 
 "principal points" of a lens. Draw any two parallel radii o R, o' R' (of 
 the spherical surfaces) and join R R', meeting the axis of the lens in c. 
 The point c is called the centre, or optical centre, of the lens. 
 
 Any ray of light which, in its passage through the substance of the 
 lens passes through c, will emerge parallel to its original direction, 
 because the lens will act upon such a ray as a plate of glass with 
 parallel faces. In Fig. 14 (3) we have the same figuring as in Fig. n 
 
 FiG.14. 
 
 A - Cp.Fic.ll. 
 
 the direction of A' B' alters in passing through the thickness of the 
 plate, or in passing through the centre of the substance of the lens, but 
 the ray emerges parallel to its original direction. 
 
 In Fig. 14 (2) if we produce A' B' to meet the axis in N lf and D' c' to 
 meet the axis in N 2 , these two new points, N X and N 2 , are called the 
 "principal" or " nodal" points of the lens. 
 
 They have the property, which is evident from the figure, that any 
 ray of light proceeding from any direction towards one of these points 
 passes out of the lens as though it had passed through the other. (See 
 Notes to Chapter II.) 
 
 We ascertained from Fig. 1 1 that if the parallel plate is very thin 
 the displacement of the ray passing through it will be very small. The 
 same reasoning will apply to a very thin lens. If we neglect the thick- 
 
 21 
 
TELEPHOTOGRAPHY 
 
 ness of the plate the ray A' B' will continue in a straight line, and no 
 displacement will occur. Similarly, in Fig. 14 (2) and (3), the thinner 
 the lens becomes, the less will the ray be displaced in passing through 
 it, and the nearer will N t become to N 3 , until, if we consider the lens of 
 negligible thickness, N X and N 3 will coincide (in the centre c), and any 
 ray proceeding from any direction towards the centre c will pass 
 through it in a straight line. 
 
 We see then that in thick lenses there are in reality two principal 
 points (see Notes) ; but for the purposes of our discussion it will be less 
 effort to the reader to consider lenses as very thin, and that these two 
 principal points coincide in one principal point or centre. 
 
 Fic.15. 
 
 Rays of light proceeding from any direction towards the centre of the 
 lens pass through the centre witho^lt deviation. 
 
 We define a plane passing through this centre, perpendicular to the 
 axis, as the principal plane of the lens. 
 
 II. To determine the two focal points of a lens. If a beam of 
 parallel rays, emanating from a very distant luminous point, meets one 
 surface of a positive lens, in a direction parallel to its axis, the rays 
 will, after passing through the lens, meet in a point F. This point is 
 called the principal focus, or principal "focal point," of the lens, and its 
 distance from the centre c of the lens is called the focal length of 
 the lens. 
 
 Similarly, if we present the second surface of the lens to the incident 
 parallel rays in the opposite direction, they will meet in a point F'. 
 
 22 
 
FORMATION OF IMAGES 
 
 This point is the second principal "focal point," and its distance from 
 the centre of the lens c is again a measure of the focal length of the 
 lens. 
 
 No real image can be formed at any position nearer to the centre 
 of the lens than F or F'. It is evident that rays from a luminous object 
 placed at either F or F' would, after passing through the lens, emerge 
 parallel ; if the object were nearer to c, the rays would diverge after 
 passing through the lens. 
 
 F and F' are the \WQ focal points, and possess the property that any 
 ray meeting the lens in a direction parallel to the axis of the lens passes 
 through the focal point on the further side of the lens. 
 
 FIG. 16. 
 
 Every lens (or combination of lenses) may be defined as possessing 
 a centre and two focal points. 
 
 These elements are sufficient for us to determine the position and 
 magnitude of the image of any object. 
 
 We need not now trouble to draw lenses, but indicate them by the 
 principal plane passing through the centre of the lens, and by setting 
 off the positions of the focal points on the axis. 
 
 Let o o represent the axis passing through the lens c ; and F and F' 
 the focal points (CF=CF / ). 
 
 Let us first determine the position of the image of an object a b c 
 graphically. 
 
 From the object a draw a line (or take a ray) parallel to the axis 
 a L, meeting the lens at L. This ray, after refraction, must pass through 
 the focal point F in the direction L Fa'. Now take another ray passing 
 from a through the centre of the lens c. This ray passes in a straight 
 
 23 
 
TELEPHOTOGRAPHY 
 
 line through c and meets the first ray (which took the direction L F a') 
 in the point a', forming the image of a at a'. 
 
 Similarly two rays from c, one meeting the lens parallel to the axis, 
 and the other passing through the centre, will meet in c', forming the 
 image of c at c'. 
 
 We have thus determined the position of the image. Next as to 
 its magnitude. If we compare Fig. 3, illustrating the formation of the 
 image by the pinhole camera, with Fig. 16, we observe that the 
 rays passing through the centre of the lens correspond with those 
 passing through the pinhole, and the proportion existing between the 
 sizes of object and image is identical with the relation between the 
 
 Fie. 17. 
 
 L 
 ? F '' 
 
 >ns 
 C F ] 
 
 g " -. x ..-""'""-*"" 
 
 > ""---._.---"" - s 
 
 c-i 
 
 distances of object and image from the centre of the lens. The 
 magnitude of the image is to that of the object as c b : c b'. 
 
 To express these relations numerically we must introduce an optical 
 law, known as the "Law of Conjugate Foci" which may be deduced 
 from the geometrical construction above. 
 
 If we plot c F and c F' as before, calling c F and c F' each = f, and 
 calling the distance between F' and the object o, equal to x, and the 
 distance between F' and the image i equal to y\ the law tells us that 
 
 f-=xy .... (i) .:'..; ^.v ... 
 
 which means that the focal length of the lens squared, or multiplied 
 by itself, is always equal to the distance between the object and the 
 front focal point, multiplied by the distance between the image and the 
 back focal point. As this generalisation may at first seem a little 
 confusing to the reader, we will interpret the law in another fashion. 
 Plot c, F', and F as before, measure the distance between the object 
 
 24 
 
PLATE III 
 
 Taken with the same 8^" c. de v. lens combined with a 4-in. 
 negative lens, as Plate II., at a distance of 15 ft. (By the Author.) 
 
FORMATION OF IMAGES 
 
 o and the front focal point F', and find what multiple this distance is of 
 the focal length of the lens (in the figure it is five times) ; the distance 
 between the back focal point F and the image i will be the reciprocal 
 of this multiple of the focal length (in the figure of the focal length), 
 o and i are said to be conjugate points, or conjugate to one another. 
 If the object be placed at i the image will be formed at O ; so that 
 object and image are interchangeable. The size (linear) of the image 
 will also be one-fifth of the size of the object ; in other words, the 
 magnification will be one-fifth. 
 
 To take a numerical example : 
 
 Supposing the focal length of the lens f = 10 inches ; then the 
 distance o F' is 5 x 10, or 50 inches ; the distance of the object from the 
 
 FlC. 18. U n S 
 
 I 
 
 
 
 
 c FT 
 
 
 
 tf 
 
 centre of the lens is 60 inches ; the distance i F is - or 2 inches, and 
 the distance of the image from the centre of the lens is 12 inches. The 
 size (linear) of the image is to that of the object as their respectives 
 distances from the centre of the lens, or as 12 : 60, that is as i 15; the 
 magnification is one-fifth. 
 
 If we substitute the values for the focal length of the lens, the 
 distance from the front focal point to the object, and the distance of 
 the back focal point to the image in the general formula expressing the 
 "law of conjugate foci," we shall find that it holds good. 
 
 IOX 10 = 50 X 2 
 I OO = I OO 
 
 In general, then, we notice that the further a given object is from 
 the lens, the smaller will be its image, and the more closely will the 
 
 25 
 
TELEPHOTOGRAPHY 
 
 image approach to the focal point or plane on the further side of the 
 lens ; when the object is very distant, or at "infinity" as it is termed, 
 the image lies in that focal plane. 
 
 Conversely, when the object is brought nearer the lens, the plane of 
 the image recedes from the second focal point and increases in size 
 (although the image is smaller than the object), until it arrives at a 
 distance equal to one focal length beyond the front focal point, or, in 
 other words, when it is twice the focal length of the lens away from the 
 centre of the lens. In this interesting position, image and object are 
 of the same size, and are at equal distances from the centre of the lens. 
 
 If f be the focal length of the lens, c its centre, F' and F the focal 
 points, and o F' be made =f, it follows that F i must =/"; for o F is now 
 
 the multiple one of the focal length, so that F i must be the reciprocal 
 of this multiple, that is to say, one also. Or, from the formula : 
 
 These particular positions of o and i are called the symmetric points, 
 and the planes passing through them the symmetric planes ; they possess, 
 as we have seen, the property that any object situated in one will 
 be reproduced (but inverted) exactly the same size in image in the 
 other. This is called the position of "unit magnification." 
 
 The position of the symmetric points s s' is also remarkable in this 
 respect. If the object is situated beyond one of these on one side of 
 the lens its image is diminished in size (magnification less than unity), 
 and is nearer to the lens than the other : if, on the other hand, the 
 
 26 
 
FORMATION OF IMAGES 
 
 object is situated anywhere between one of them and the focal point on 
 that side of the lens, its image is increased in size (magnification greater 
 than unity), and is further from the lens than the other. 
 
 Thus, o lying in s is exactly reproduced at i in s' ; o' to the left of 
 s is diminished in size at i', and o" to the right of o, between s and F' is 
 increased in size at i". (Note the interchangeability of object and image 
 in the figure.) 
 
 If the object is brought so near to the lens as to coincide with the 
 focal point (or plane through F') we know that, as this point is the 
 position of the focus for parallel rays, the image must be formed at 
 "infinity." Again, if the object be moved nearer still to the lens than 
 this, every ray after passing through the lens will diverge and no real 
 
 FIG. 20. 
 
 i" 
 
 Lens 
 
 
 0' ( 
 
 1 
 
 1 
 1 j_ 
 
 
 
 S 
 
 
 F' 
 
 r I 
 
 s' 
 
 
 
 
 
 
 I 
 
 
 
 image will be formed. (A virtual image is formed in this case, but it 
 will not be necessary to enter here into the formation of virtual images 
 by positive lenses.) 
 
 It is important for following our subsequent reasoning that the 
 reader should always refer the distance of the object from the lens to a 
 multiple of the focal length of the lens, but bear in mind that the 
 multiple he has to deal with to find the magnification is one (focal 
 lengtli) less. To give another example : suppose the lens to be one of 
 10 inches focal length as before, and the object he intends to reproduce 
 is 100 inches from the lens. It is distant 10 times the focal length of 
 the lens, but only 9 times from the front focal point, so that he knows 
 the "conjugate" will be one-ninth of the focal length beyond the back 
 focal point, and also that the " magnification " will be one-ninth. 
 
 Conversely (and this it should be remarked is the usual manner in 
 
 27 
 
TELEPHOTOGRAPHY 
 
 which we shall have to use this law in practice), if we wish to make a 
 certain " magnification " (say one-tenth) with a lens of given focal 
 length (say 10 inches), the distance of the lens from the object must 
 be one focal length more, 10 + i, or 1 1 times the focal length of the lens. 
 
 In general, for a reduction of n times (i.e., a magnification of -) : 
 
 n 
 
 Distance of object from lens=(/z+i) times the focal length of lens. 
 
 Distance of image from lens = 
 
 lens. 
 
 n+ 
 n 
 
 times the focal length of the 
 
 The reader will readily see from the foregoing that as the focal 
 
 FIG. 21. 
 
 points are constant, or fixed, for any given positive lens, this lens can 
 only give larger or smaller images of a given object by placing the 
 lens nearer to it or further from it, in a similar manner to that employed 
 by the pinhole camera with the screen at a fixed distance from the pin- 
 hole (Fig. 3). If we wish to produce a larger direct image of an object 
 at a given distance with an ordinary lens the only way will be to 
 employ another lens in which the focal points are situated at a greater 
 distance from the centre of the lens, or one with a greater (or longer) 
 focal length. 
 
 28 
 
FORMATION OF IMAGES 
 
 Let Fig. 2 1 represent two lenses which differ in their focal lengths, 
 that is to say the distances between their centres and focal points 
 differ. In the upper figure the distant object A B will form an image in 
 the focal plane through F, at a b, of a certain size. In the lower figure 
 the same object will form an image b' a' in the focal plane through F" at 
 b' a'. It is easy to see that the respective sizes of ad, a' b' are directly 
 dependent on the distances of the focal points from the centres of the 
 lenses, or as c F : c' F". In other words, the size of an image given by a 
 lens depends upon its focal length ; and if one lens has a greater (or 
 longer) focal length than another, the sizes of the images given by them 
 respectively will be directly proportional to their focal lengths. 
 
 In general, if one lens is n times the focal length of another, it will 
 give an image n times the size of the other. 
 
 We must impress upon the reader that the focal length of a lens is 
 a measurement and definite characteristic of a lens, but he must always 
 bear in mind that this measurement is carried out under definite 
 conditions viz., that the focal length of a lens is the distance between 
 the centre of the lens and either of the focal points for parallel incident 
 rays. This is most important, as confusion might otherwise arise as to 
 the respective sizes of images for objects that are comparatively close. 
 
 If we compare the sizes of the image of a very distant object (say a 
 building) given by two lenses, one of which has double the focal length 
 of the other, one image will be found to give an image exactly double the 
 size of the other. If, however, we compare the sizes of the image given 
 by the two lenses of a near object, this relation no longer holds absolutely. 
 
 For example, let us compare the sizes of the images given by two 
 lenses of 10 and 20 inches focal length respectively, of an object 
 100 inches from the centre of the lens : 
 
 with the lo-inch lens: - - = io; 101=9; magnification = - ; 
 
 ioo_ i 
 
 20- ,, ,, = 5 5~~ I= 4> \ 
 
 20 4 
 
 so that the sizes of the images are not now as i : 2 exactly. The 
 
 29 
 
TELEPHOTOGRAPHY 
 
 smaller the multiple of the focal length the object be distant, the more 
 will the relation of the sizes of the images differ from that of their true 
 focal length ; if the object be 40 inches distant from either lens, 
 
 the lo-inch lens gives a magnification of-, and 
 the 20- ,, i, 
 
 the proportion being as i : 3 here. 
 
 The usual statement that the right standpoint for viewing a 
 photograph is a distance equal to the focal length of a lens only holds 
 good when all the objects included in the photograph are very distant ; 
 it is not then true of all lenses irrespective of their optical construction. 
 For ordinary positive lenses or lens-systems, images of near objects 
 should be viewed as shown above, the correct viewing distance being 
 practically identical with the distance of the conjugate focus of the 
 nearest foreground object in the image from the centre of the lens. 
 But, as we have asked before (p. 13), how are we to know this from the 
 photograph itself? 
 
 The only way to evade the necessity of asking the question is to 
 avoid including a foreground that is too near, and to employ a lens 
 whose focal length is considerably longer than the longest side of the 
 trimmed photograph. This practice is both cumbersome and expensive 
 when ordinary positive lenses are employed. The advantages of the 
 Telephotographic lens will be compared presently. 
 
 We have, as already stated, endeavoured in this chapter to simplify 
 the study of the formation of images by considering the two principal 
 points of a lens as combined in one, which we have termed the 
 "centre." 
 
 If we still keep to this convention, it must be understood neverthe- 
 less that this "centre" is not necessarily the mechanical centre of the 
 glass lens in the case of a single lens, nor midway between the two 
 lenses forming a combination of positive lenses, as might be supposed. 
 
 If both lenses shown in Fig. 22 are considered thin, the centre c of 
 the equi-convex lens is equidistant from both focal points FF'. In the 
 
 30 
 
FORMATION OF IMAGES 
 
 positive meniscus, however, of the same focal length as the equi-convex 
 lens, the centre c is seen to lie outside the lens itself, but its distance 
 from the two focal points F and F' is still the same. 
 
 Suppose we place the equi-convex lens in a beam of parallel rays 
 coming from a very distant object, such as the sun, and place a screen 
 in the plane of the image, measuring the distance from the screen to 
 the nearest surface of the lens and noting the size of the image, we 
 shall find that on reversing the lens, the distance between lens and 
 screen is exactly the same and the size of the sun's image is unaltered. 
 In either case the distance between lens and screen is approximately 
 equal to the focal length of the lens. In reality it is slightly less. If 
 the thickness of the lens be considered, one-third of the thickness of the 
 
 Fic.22. 
 
 glass lens must be added. Placing now the meniscus lens in the sun's 
 rays, we shall find that if these rays fall upon the convex side of the 
 lens, the distance between the plane of the screen and the nearest 
 surface of the lens is less than in the former case, but the size of the 
 image remains the same. On reversing this lens and presenting the 
 concave surface to the sun's rays, the distance between lens and 
 screen is considerably greater than before, and greater than in the case 
 of the equi-convex lens, but still the size of the image remains the same. 
 The mean of the last two measurements is approximately equal to the 
 focal length of the lens. 
 
 We can arrive very approximately at the focal length of either a 
 single lens or a combination of lenses, by two measurements of the 
 distance of the plane of the image (for parallel rays) for some fixed and 
 convenient point in the lens or lens-mount, by presenting first one 
 surface of the lens to the incident rays, and then the other, and taking 
 the mean of the measurements. 
 
 31 
 
TELEPHOTOGRAPHY 
 
 CO 
 
 2 Q. 
 
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 We conclude this chapter by giving a 
 method of determining very accurately the 
 true focal length of any positive lens-system 
 without involving calculation, but based 
 upon a principle with which the reader is 
 now familiar. 
 
 Mount the lens in a fixed position. 
 Present the surface A of the lens to a beam 
 of parallel rays and thus determine the 
 position of the focal point F. Similarly 
 present the surface B of the lens to a beam 
 of parallel rays, and determine the position 
 of the focal point F'. 
 
 Now place a screen at F with a mark or 
 scale of definite length upon it, and a 
 
 second screen for focusin at 
 
 Plumbed 
 
 with the planes through F and F', on the 
 base of the stand, fix two rules, as shown 
 in the figure. 
 
 The distance between F and F' is only 
 approximately double the focal length of 
 the lens. Remove the screen s, with the 
 definite marking upon it, rather less than 
 half the distance between F' and F to the 
 right of F, and move the focusing screen s' 
 exactly the same distance to the left of F'. 
 An indistinct image of the marking on s 
 will now be seen on s' ; proceed to move s 
 and s' small, but exactly equal, distances in 
 | opposite directions, until the marking upon s 
 is sharply defined and of equal size on s'. 
 s and s' now occupy the positions for 
 "unit magnifications," and we know that in 
 this position each is removed the true 
 3 2 
 
I I 
 LI 
 
PLATE IV 
 
 Taken with a R. R. lens of i6-in. focal length at a'distance of 4 ft., the short distance 
 between lens and sitter has caused the mouth to be exaggerated in size, and the forehead to 
 appear to recede. Compare Plate V. (By Mr. T. Habgood, Boscombe.) 
 
PLATE V 
 
 Taken with the same 8^" c. de v. lens combined with a 4-in. negative lens as employed 
 for Plates II. and III., at a distance of 10 ft. The camera extension is chosen to produce 
 the same size of head as in Plate IV. The image could have been made equally sharp, but 
 the back of the positive element was unscrewed to illustrate the soft effect produced by 
 introducing spherical aberration (see Fig 58). A picture showing this effect should be 
 viewed at a considerable distance. (By the A uthor.) 
 
FORMATION OF IMAGES 
 
 measure of the focal length from the focal points F and F' respectively. 
 By plumbing at s and s' we thus read off on the rule the true focal 
 length of the lens. 
 
 NOTES. 
 
 In Fig. 1 1 we have illustrated the manner in which a ray of light 
 in passing from air through a plate of glass with parallel sides, emerges 
 finally into air. Let us apply the laws of refraction to the case, in 
 order to show that the incident and emergent rays are parallel to 
 each other. 
 
 If we draw a normal PB p' to the surface of the glass at B at the 
 
 Fie. 24. 
 
 Air 
 
 point where the incident ray A B meets it, forming an angle < with the 
 normal, we shall find that after entering the second medium the ray 
 will take an altered course B c, and that B c will form a different angle 0' 
 with the normal at B. The law of refraction tells us that these two 
 angles, termed the angles of incidence and refraction, are in the same 
 plane, and that the sines of these angles bear to one another a constant 
 ratio, depending solely upon the relation of the refractive indices of 
 the two media. Calling the refractive index of air unity, and that of 
 glass the Greek letter p, 
 
 sn = 
 
 sin </>' 
 
 is a constant for these two media ; and in general, in passing from one 
 
 33 c 
 
TELEPHOTOGRAPHY 
 medium of refractive index p. to another of refractive index //, p. sin 
 
 =fjf sin $'. 
 
 Glass has a higher refractive index than air (roughly 1.5), thus the 
 angle $' will be less than ^. 
 
 On meeting the second surface of the glass at c, EC forms the same 
 angle $' with the normal p' c P, and as the ray now passes from a 
 medium whose refractive index is p. into air (refractive index unity), 
 
 /LI sin $ r = sin <f>, 
 
 and hence the emergent ray c D forms the same angle Q with the normal 
 as did the incident ray ; hence c D is parallel to A B or c' D'. 
 
 If the second surface of the plate were not parallel to the first, and 
 the ray formed an angle $" with the normal to this surface, the angle 
 at emergence, $'", would similarly be found from the equation 
 
 /u sin $" = sin q[". 
 
 Let us now apply the laws of refraction to see how rays of light are 
 affected in passing through a lens. 
 
 If we trace the passage of a single ray of light, we may always 
 consider it as passing through a plate of glass whose sides are either 
 parallel or inclined to each other. In the latter case, the particular ray 
 passes through the lens as if it were a prism, the ray, on emerging, 
 being always bent or refracted towards its base, or thicker part. 
 
 Let us trace the course of two rays parallel to the axis which meet 
 either a positive or negative lens. 
 
 The ray A B in either figure meets the lens in the point B ; if we 
 draw a line from the centre of curvature of the surface o to meet E, and 
 draw a line P R through this point at right angles to it (termed a tangent), 
 it is evident that the ray A B may now be considered as meeting a plane 
 surface P B R at B, forming an angle ^ with the normal o B (or perpen- 
 dicular) to this surface. The ray from B takes an altered course B c 
 making a smaller angle <j> r with the normal BO, such that sin ^n 
 sin <'. On the ray arriving at c, join c to the centre of curvature of 
 
 34 
 
FORMATION OF IMAGES 
 
 this surface o', and draw a line through c at right angles to o c, forming 
 the tangent p c s. Before emerging from the lens B c makes an angle 
 <f>" with this normal o c N' ; after emergence, as it passes from a dense, 
 to a rarer medium, it will be bent or refracted from this normal, forming 
 an angle $'" with it, such that ju sin <}>"=sm $'". 
 
 In the case of the positive lens the ray then takes the course CF, 
 meeting the axis in F. F is one of the focal points of the lens, or the 
 locus of its real focus for parallel rays. 
 
 In the case of the negative lens, the ray takes the course c D, being 
 bent or refracted from the axis, but proceeding as from a point v on the 
 
 axis, in front of the lens, v is one of the focal points of this lens, and 
 is the locus of its virtual focus for parallel rays. 
 
 The rays thus traced have passed through the lenses, just as though 
 they had passed through the prisms p R s in drawings, being refracted 
 in either case towards the base of the prism. 
 
 Similarly, if we trace the course of a parallel ray at a different 
 distance from the axis, such as A' B' in either figure, it will be found 
 that its course is the same as through a prism having sides inclined at 
 a different angle, yet finally refracting the ray to the real focal point 
 of the positive lens, and as from the virtual focal point of the negative 
 lens. 
 
 From the above it will be easy to see that a ray of light meeting 
 
 35 
 
TELEPHOTOGRAPHY 
 
 the lens in any direction will, in general, pass through its curved 
 surfaces as if it passed through a plate of glass with sides more or less 
 inclined to each other ; but when the ray in its passage through a lens 
 passes through the centre, the direction of the ray, after refraction, will 
 be parallel to its direction before refraction, or will be affected as if it 
 had passed through a plane plate with parallel sides, as in Fig. 1 1. 
 
 We have drawn attention to the fact (Fig. 14) that there are in 
 reality two "principal," or "focal," points in every lens (or combination 
 of lenses), for it is only when a lens is infinitely thin that they can coin- 
 cide, or become one "optical centre." These two points, and the two 
 focal points, as has already been remarked, are termed the " four 
 
 FIG. 26. 
 
 cardinal points" of a lens. In connection with them we define the 
 planes that intersect the four cardinal points in the axis, perpendicular 
 to the axis, as principal and focal planes. 
 
 For any given lens the principal points are a certain distance apart, 
 depending on the thickness and form of the lens, and the material of 
 which it is composed, and possess the property that light proceeding 
 from any direction towards one of them passes out from the lens as 
 though it had passed through the other. 
 
 If parallel rays are incident upon a lens in either direction, we have 
 seen that F 2 and F : are the focal points of the lens, and that their 
 distances from the optical centre of a thin lens are called the focal 
 length of the lens. When the thickness of the lens is taken into con- 
 sideration, with the two principal points, the true measure of the focal 
 length is the distance between N a and F 2 , or N I and F r The two focal 
 
 36 
 
FORMATION OF IMAGES 
 
 points are always situated at equal distances from their corresponding 
 principal points, or F, N 2 =Fj N L . In other words, any lens or system of 
 lenses has the same absolute focal length whichever surface is 
 presented to incident rays ; but it does not follow that the position of 
 the focal points are equidistant from the surface of the lens nearest to 
 them. 
 
 Fig. 27 represents a case familiar to many photographers. Here 
 we have a meniscus lens with its principal planes P : P 3 passing through 
 the principal points NJ N 2 and FJ F 2 , the two focal points ; N l l = N 3 F y 
 
 FIG. 27. 
 
 Back focal length 
 Back focal length 
 
 It is evident that if the convex side of the meniscus were presented 
 to the light, the distance between the back surface of the lens and the 
 
 o 
 
 focal point in the same direction would be considerably shorter than if 
 the concave surface of the meniscus were so presented ; both images, 
 however, would be of the same size, because the true measure of the 
 focal length is the same in either case, or N X Fj=N 2 F 2 . 
 
 In order to calculate the distances between the principal points for 
 a single lens or combination of lenses, the student is referred to any 
 modern work on geometrical optics. Most positive lenses consist of 
 two combinations. The following formula for calculating the true focal 
 length F, the distance from the back lens to the focal point on the same 
 
 37 
 
TELEPHOTOGRAPHY 
 
 side B F, and the resultant width w, between the principal points of the 
 combination, may prove useful : 
 
 F = 
 
 BF - 
 
 w = w, + w a 
 
 A +/,-*' 
 
 where/! and f z are the focal lengths of the two combinations, a their 
 distance apart, and w l and w z the width between their principal 
 points. 
 
 To determine the position and magnitude of the image of an object 
 
 Fie. 28. 
 
 formed by a thick lens, or a combination of lenses, we have only to 
 represent the four cardinal points and planes of the lens by points and 
 lines as before, setting the principal points and planes at a definite 
 distance apart =w for a single lens, or w for a combination. 
 
 A ray from A parallel to the axis passes from P I to P 2 in a straight line ; 
 from the point where it leaves P 2 , it passes through the focal point F 3 . 
 Similarly, a ray A N I} passing towards one of the principal points, N P 
 emerges from the other principal point, N 2 , in a direction parallel to A NJ, 
 as N 3 A', meeting the former ray in A' and thus determining its position. 
 So that A' B' is the position of the image of the object A B. 
 
 38 
 
FORMATION OF IMAGES 
 
 Again F X N^Fg N,, and both are equal to the true focal length of the 
 lens=/ Calling B Y^X and B' F 2 =jy ; we know that : 
 
 and that the size of A B : size of A' B' : : N : B : N 2 B'. 
 
 From this it is evident that we need not know the distance between 
 the principal points in order to determine the focal length of a lens, 
 provided we know the positions of the two focal points. 
 
 The former method of determining the focal length of a lens illustrated 
 in Fig. 23 will of course apply ; but we give another practical method, 
 
 FiC. 29. 
 
 ^ D ^~ 
 
 
 
 
 
 
 
 
 x F 2 [ 
 
 Lens 
 
 \ , , 
 
 \ 
 
 
 
 1 
 
 
 1 
 
 
 
 
 showing that the result can be ascertained without a knowledge of the 
 separation of the principal points. 
 
 ( i ) Determine the position of the focus of the lens for a very distant 
 object upon the screen of the camera and mark the position upon the 
 base-board ; this is the plane of the back focal point F r (2) Reverse 
 the lens in its flange, and find the position of the focus for the same 
 distant object, measuring the distance of the screen from some fixed 
 point in the lens mount, say the hood. We know that the position ot 
 the other focal point F 2 is the distance D from the hood of the lens. 
 (3) Replace the lens in its normal position with the screen at F I and 
 then remove it an exact distance y further away roughly about one- 
 fourth of its distance from the lens for convenience. (4) Find the 
 
 39 
 
TELEPHOTOGRAPHY 
 
 distance now necessary for the placing of an object o, so that its image 
 is well defined at the new position of the screen at i. (Operations 
 (3) and (4) may be reversed.) 
 
 The distance of the object from the hood of the lens, less D, will be 
 
 its distance x from the front focal point F 2 . Hence f=J xy ; or, if we 
 
 multiply x and y together and extract the square root, we find the true 
 
 focal length of the lens. Supposing x=2", jy=5o, then / 2 =ioo, or 
 
 /=IO. 
 
 40 
 
CHAPTER IV 
 
 THE FORMATION OF IMAGES BY NEGATIVE LENSES 
 
 IF we present either surface of a negative or concave lens to a beam of 
 rays parallel to the axis of the lens, we shall be unable to find a real 
 image of the object from which the parallel rays emanated ; no real 
 focus will be formed by the lens. 
 
 Again, if we bring the object nearer to the lens, until it is in close 
 proximity with it, the lens will still be found incapable of forming a 
 real image. 
 
 It is evident, then, that negative lenses, used alone, will be quite 
 useless for photographic purposes. 
 
 Our object will be to examine the manner in which rays of light 
 are affected by negative lenses, with a view, subsequently, of using 
 them in conjunction with positive lenses, in such a manner that real 
 images can be formed. 
 
 Let us first make an experiment with a negative lens to see its 
 effect upon a beam of parallel rays, and acquaint ourselves with the 
 meaning of a " virtual " focus, by determining its approximate focal 
 length in a practical manner. 
 
 Take a thin disc of any opaque material, such as cardboard, of the 
 same diameter as the lens under examination ; at equal distances from 
 the centre of the disc, and rather nearer the edge than the centre, make 
 two small perforations A, B ; measure their distance apart. If we 
 now place this disc in contact with the lens, and present the disc 
 to the sun's rays, we shall find that the pencils passing through A and B 
 
 41 
 
TELEPHOTOGRAPHY 
 
 will be divergent after passing through the lens. These divergent 
 pencils can be traced as small discs of light upon a screen held behind 
 the lens ; if the screen be made to occupy the position where the 
 distance between these two discs A' and B' is just double the distance 
 between A and B, the distance c F' between the disc and the screen is a 
 rough measure of the focal length of the lens, or is equal to c F. The 
 direction of the pencils A A' and B B' appears to originate at F. F is the 
 "virtual" focus of the lens, and is one of the "focal points" of the 
 lens, F' being the other. 
 
 In negative as well as in positive lenses there are two " principal " 
 
 Fie. 30. 
 
 points ; but here again it will be sufficient for our purpose to consider 
 them as coinciding in one "optical centre." 
 
 From the determination of the position of these three elements in a 
 negative lens, we know : (i) That any ray meeting a lens in a direction 
 parallel to the axis emerges from the lens as though it came from the 
 focal point situated on the same side of the lens as the incident ray ; 
 (2) that any ray passing through the optical centre of the lens pro- 
 ceeds in a straight line. 
 
 We can then, as before, plot a negative lens on paper and indicate 
 it by the principal plane passing through the optical centre of the lens, 
 with its two focal points equally distant on either side. 
 
 42 
 
FORMATION OF IMAGES 
 
 Before proceeding, let us again refer to Fig. 30 to see what it 
 teaches us. We have noticed that parallel rays diverge from the lens 
 as though they proceeded from the focal point on the same side. This 
 fact read alone is unimportant to our investigation ; we must grasp and 
 remember the converse : that rays (A' A, B' B) converging towards the 
 focal point F of the negative lens on the further side leave the lens in 
 a parallel direction ; a focus would be formed by the negative lens at 
 infinity. This is an important, though not practical, conclusion. 
 
 Let us now consider the case of an object placed nearer to the 
 lens, but distant some multiple of the focal length (greater than unity). 
 
 FIG. 31. 
 
 Let o o represent the axis passing through c, the optical centre of 
 the lens, and F and F' the focal points (CF = CF'.) 
 
 We will now determine the position of the virtual image of the 
 object a c b. First consider a ray a L meeting the lens parallel to the 
 axis. This ray after refraction takes the course F a' L, as though the 
 ray emanated from the focal point F. Now take a second ray from a 
 passing through the centre of the lens c ; this ray in passing through c 
 cuts the first (virtual) ray at a', and determines the position of its virtual 
 image. In the same manner we can determine the position of the 
 virtual image of b, at b' ; a' b' is the virtual image of a b, is erect, and 
 lies between the focal point F and the centre of the lens. 
 
 To examine the converse : suppose convergent rays on the left of 
 the lens are proceeding to form a real image a' b' c', and we interpose 
 the negative lens so that a? d b' would fall between c and F as shown 
 
 43 
 
TELEPHOTOGRAPHY 
 
 in the figure, the negative lens will now form an enlarged image of 
 a' c f b' at a b c. 
 
 In Fig. 31 we have supposed the object ac b placed at a distance 
 equal to five times the focal length of the lens, and have seen that the 
 virtual image is formed on the same side as the object. 
 
 The relation between the size of object and image is found as 
 follows : 
 
 Divide the distance of the object from the lens, by the focal length of 
 the lens, and add one ; this is the magnification. (See Notes.) 
 
 In the case before us the object is distant from the lens five times its 
 focal length, hence the " magnification " is 5 + i, or 6, or the virtual image 
 is one-sixth the size (linear) of the object. Further, it is evident that the 
 distance of the object from the lens c c is in this same relation to the 
 distance of the image c c' ; so that c c' is one-sixth of the distance c c. 
 
 Again interpret the converse, for this is the chief interpretation 
 we use : 
 
 If convergent rays on the left of the lens are proceeding to form a 
 real image at a' c' 6', and we interpose a negative lens of known focal 
 length, and find that a real image is formed at acb, we know that the 
 distance of a c b from the lens, divided by the focal length of the nega- 
 tive lens, plus one, gives us the magnification of the image a' c' b' 
 occurring at a c b. 
 
 From Figs. 30 and 31 we see that as the object approaches the lens 
 from infinity the size of the virtual image increases and approaches the 
 lens. If the object be brought up to the plane coinciding with the 
 focal point F, or even nearer to the lens, the same order of things con- 
 tinues, until the object is in contact with the lens, or coincides with the 
 centre of the lens ; here image and object both coincide, and we have 
 the position for unit magnification for a negative lens. 
 
 To impress this, as the case differs from a positive lens, we will 
 illustrate the case when the object is nearer to the lens than its focal 
 point on the same side. 
 
 Taking our two rays whose paths are known : a L, parallel to the 
 axis, emerges as though it originated at F, and a c passes through the 
 
 44 
 
FORMATION OF IMAGES 
 
 centre of the lens ; they cut one another at a', forming the virtual 
 image of a. Similarly b' is the virtual image of 6, and a' b' that of a b. 
 
 Our conclusion from the above observation is : that a real object 
 placed anywhere between the lens and infinity forms a virtual image 
 somewhere between the centre of the lens and its focal point on the 
 same side. And conversely : Convergent rays incident upon a negative 
 lens, proceeding to a focus situated anywhere between the centre of the 
 lens and its focal point on the other side, -will form a real image some- 
 where between the centre of the lens and infinity on that side. 
 
 If, however, convergent rays meeting a negative lens are proceed - 
 
 Fic.32. 
 
 Lens 
 
 ing to a focus anywhere beyond the focal point on the other side no- 
 real image can be formed by the negative lens. 
 
 If we examine the convergent pencils (2), Fig. 33, proceeding 
 towards the focal point F, we see that they emerge parallel to the axis, 
 to form an image at infinity. It is easy to see that if they converged 
 to a point beyond F they would no longer emerge parallel, but become 
 divergent, and thus could not form a real image. 
 
 As a matter of interest let us now illustrate the facts arrived at in a 
 comparative manner. 
 
 In ( i ) the rays converge towards a point anywhere between the lens 
 and the focal point F ; a real image is formed at R. 
 
 In (2) the rays converge towards the focal point F and emerge 
 parallel. 
 
 In (3) the rays converge towards a point i, beyond the focal point F ; 
 
 45 
 
TELEPHOTOGRAPHY 
 
 they diverge, as from its conjugate, a virtual image at v, and no real 
 image is formed. 
 
 FIG. 33. 
 
 In (4), similarly, the rays converge towards the symmetric point s 
 (beyond the focal point), diverging from the lens at the same inclination 
 
 46 
 
FORMATION OF IMAGES 
 
 as the incident rays, and as though they originated in the virtual 
 symmetric point s'. 
 
 If we reverse (3) we see the conditions for convergent rays pro- 
 ceeding to a point beyond the symmetric point, and in general confirm 
 our conclusion that no real image can be formed by a negative lens 
 when the rays converge to a point beyond its focal point on that side of 
 the lens. 
 
 We give in conclusion a practical method of determining the focal 
 length of a negative lens with accuracy : 
 
 1. Focus accurately the image of some well-defined object with any 
 ordinary positive lens, and measure the size of the image. 
 
 2. Place the negative lens, the focal length of which we wish to 
 determine, a short distance within the convergent beam from the posi- 
 tive lens. Then focus the image accurately formed by the combined 
 lenses and measure its size. Note : 
 
 (a) The distance of the screen from any fixed point on the mount- 
 ing of the negative lens ; call this D. 
 
 (b) The magnification that has occurred to the image formed by the 
 positive lens alone ; call this M. 
 
 3. Now move the negative lens a little nearer to the positive lens 
 (N.B. Keep the positive lens in a faced position), and focus accurately 
 a second time upon the screen, and as before note : 
 
 (c) The distance of the screen from the same fixed point on the 
 mounting of the negative lens ; call this D'. 
 
 (d) The magnification of the image now formed by the positive lens 
 alone ; call this M'. 
 
 The focal length of negative lens = 
 
 D D 
 
 M' M* 
 
 NOTESj 
 
 The four " cardinal points " of a negative lens, as in the case 
 of a positive lens, are the two principal points, and the two focal 
 
 47 
 
TELEPHOTOGRAPHY 
 
 points. Here again the principal points are a certain distance apart, 
 dependent upon the thickness and form of the lens, and possess the 
 property that light proceeding from any direction towards one of them 
 
 Fie. 34. 
 
 passes out from the lens as though it had passed through the other. 
 The relation F I N X = F 2 N 2 in Fig. 34 always holds good, so that we 
 may trace the course of rays through a thick lens by plotting the two 
 
 FIG. 35. 
 
 principal planes passing through the two principal points in the axis, 
 and the two focal points on either side. 
 
 A ray A P I passing from A parallel to the axis (Fig. 35) meets the 
 focal plane P I NJ in P I and emerges from P 2 as though it originated at F I : 
 similarly the ray A NJ meeting the principal point N I emerges from N 2 in a 
 direction parallel to A N I i.e., in the direction a N 2 ; the point a, where 
 
 48 
 
PLATE VI 
 
 These three photographs are all untouched, the normal-sized eyes are those of children. 
 Taken with the same Telephoto combination as Plates II., III., and V., at a distance of 
 4 feet in all three cases. The magnified adult eye was obtained by using a greater 
 extension of camera. Exposure, small eyes, 3 seconds in an ordinary room; large eye 
 25 seconds in a badly lighted studio. (By the Author.) 
 
FORMATION OF IMAGES 
 
 N 3 a meets P 2 F V determines the position of the virtual image a of the 
 object A. 
 
 In the same manner we can find the image of any other point in 
 the object A B, and thus determine the position of the entire virtual 
 image a b. 
 
 The relation between the size of the object A B and its image a b is 
 found by our interpretation of the law of conjugate foci : 
 
 xy = f. 
 
 V 
 
 As image and object are here both on the same side of the lens 
 
 x N! B f, and y = b F ; so that when x = n + i times/ y = f. 
 
 n + i 
 
 To take a numerical example : suppose/" = 2 inches, and the object 
 is 10 inches from it ; here n = 5 times, so that 
 
 * = (5 + i) 2 and JK = (~ -) 2 ; 
 
 /9 
 - = xy 
 
 12 x : 
 
 / =2. 
 
 Conversely, in examining a real image formed by a negative lens 
 of 2 inches focal length used in conjunction with any positive system, 
 we find this real image is 10 inches distant from the negative lens, and 
 know that it has produced a magnification (very nearly) of \ + i or 6 
 times. 
 
 In dealing with thick lenses, the measurement should of course be 
 taken from the principal point of emergence, so that a slight error may 
 arise. The position of the principal points in negative lenses differs 
 with their form and thickness. 
 
 In the double concave lens A (Fig. 36) both are contained within the 
 glass ; in a plano-concave B one is always on the axis where the concave 
 
 49 D 
 
TELEPHOTOGRAPHY 
 
 surface cuts it ; and in the negative meniscus, one may fall within the 
 lens or both may be outside, as shown in c and D. 
 
 In D we note that the ray a b proceeding to N P and which passes 
 through the centre of the lens (i.e., towards c), emerges from it as c d 
 parallel to a b and passes through the other principal point N 2 . 
 
 In the construction of negative lens-systems used in practice, the 
 principal points do not generally lie outside the lenses, so that only 
 very small or negligible errors come in when determining "magnifica- 
 tion " by the above process. 
 
 5 
 
CHAPTER V 
 
 THE FORMATION OF ENLARGED IMAGES 
 
 PART I. By two Positive lens-systems. 
 
 Part II. By a Positive system and a Negative system combined or 
 the TELEPHOTOGRAPHIC LENS. 
 
 PART I. 
 
 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 
 
 FIG. 37. 
 
 Lens 
 
 positive lens, which in its turn forms a second image of the first one, 
 produced by the first lens. 
 
 This process is termed enlargement by "secondary magnification." 
 The lens L : (Fig. 37) forms an inverted image L X of an object at o ; if 
 we place a second lens L 2 behind this real image ij (although formed in air) 
 at any distance greater than the measurement of its focal point F 2 from 
 the lens, a real image of I 2 must again be formed. If the distance 
 between the second lens L 2 and i : is greater than the focal length of L 2 , 
 
 51 
 
TELEPHOTOGRAPHY 
 
 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 I 2 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 i : 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 ^ given by the first lens L X 
 will be increased by the second positive lens L 2 , as the curvature is 
 wrongly disposed for reproduction on a plane surface at I 2 . 
 
 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 
 
 52 
 
NORTH 
 
 EAST 
 
 WEST 
 
 * 
 
 PLATE VII 
 
 SOUTH 
 
 "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 i\ in. in diameter. Enlarged 
 in telescope by a Dallmeyer telephoto lens to 29 in. Taken September u, 1898." 
 
 (Notes from the Royal Observatory, Greenwich.} 
 
FORMATION OF ENLARGED IMAGES 
 
 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, FlG.38. 
 
 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 plano- 
 convex 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 
 
 53 
 
TELEPHOTOGRAPHY 
 
 the Telephotographic lens that we can imagine, with the components 
 here arranged so as to give the greatest possible focal length. 
 
 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. 
 
 Parallel rays incident upon the lens A (Fig. 39) used alone converge 
 towards the focus F at a definite distance from the lens A ; similarly, 
 parallel rays incident upon B diverge as from the virtual focus F', F' being 
 the same distance from the lens B as both have the same focal length. 
 
 It is evident that when F X is made to coincide with F 2 , incident 
 parallel rays will emerge parallel. 
 
 In the particular case we have chosen as a preliminary illustration, 
 
 FIG. 39. 
 
 on account of its simplicity, as the focal lengths of the two lenses are 
 identical, they must, as is here seen, be placed in contact ; but in general 
 the focal length of the compound lens F is infinite, when positive and 
 negative lenses are separated by a distance equal to the difference of their 
 focal lengths (/i /~ 2 ). 
 
 Let us now separate these lenses gradually and observe what 
 happens : 
 
 Parallel incident rays upon the positive lens A (Fig. 40) are rendered 
 convergent and proceed to form a focus at F : ; if they are intercepted by 
 the negative lens B separated by an interval a from A they are rendered 
 less convergent, and proceed to form a focus at F, as though they came 
 from A' and not from A. The distance A' F is now the focal length of 
 the compound lens, when the two lenses composing it are separated by 
 the interval d. 
 
 54 
 
FORMATION OF ENLARGED IMAGES 
 
 Note. In general a (see Fig. 40) represents the measurement of the 
 entire separation between positive and negative lenses. 
 
 f \~~fz * s tne distance the component lenses must be separated in order 
 that the focal length of the compound lens shall be infinite. (In the 
 present case as/i / 2 =o, the lenses are in contact.) 
 
 d represents the measurement of any increase in the separation 
 greater than the difference between the focal lengths of the component 
 lenses /J _/,. (In the present case, d=a because f^f^] (See Notes.) 
 
 FIG. 40. 
 
 a (here =d) 
 
 A 
 
 Equivalent focal length 
 a=f, ; 
 
 Equivalent focal length 
 
 If we know/j, f v the focal lengths of the component lenses, a the 
 entire separation, and d the interval as defined, we can find the focal 
 length of the compound lens F, and its back focal length B F (see figure) 
 from the following simple formulae : 
 
 F - 
 
 d 
 
 (3) 
 (4) 
 
 which tell us that : 
 
 The focal length of the compound lens is found by multiplying the 
 
 55 
 
TELEPHOTOGRAPHY 
 
 focal lengths of its two components together, and dividing by the 
 interval (d) of separation greater than the difference of their focal 
 lengths. 
 
 The back focal length, or distance from the negative lens to the 
 screen, is formed by multiplying the focal length of the negative lens 
 by the difference between the focal length of the positive lens and the 
 entire separation, and dividing by the interval (d) of separation greater 
 than the difference of their focal lengths : 
 
 Suppose the lenses A and B, Fig. 40, are both of 6 inches focal 
 length, we see that : 
 
 If d = O, F = OQ BF 8 
 
 = To"> = 36o; = 354" 
 
 = i, =3 6 ; =3 
 
 = 2, = 18 ; =12 
 
 = 3, = 12 ; =6 
 
 = 4, =9', =3 
 
 = 6, 6 ; =o 
 
 t ( 
 
 One of the most valuable practical features of this lens arises from 
 the fact that the back focal length is shorter than the true focal length 
 of the compound lens, as illustrated above. This is much more pro- 
 nounced where the negative lens has a shorter focal length than the 
 positive lens, as will be shown later. 
 
 By the above simple combination of two lenses of equal focal length, 
 but of opposite power, we have determined the following general 
 characteristics of any Telephotographic system : 
 
 (1) The lens has an infinite focal length when the component lenses 
 are separated by a distance equal to the difference of their focal 
 lengths. 
 
 (2) Its focal length decreases from infinity to diminishing finite focal 
 lengths as we increase this separation, until, 
 
 (3) When the lenses are separated by a distance equal to the focal 
 length of the positive lens, the focal length of the compound lens is 
 
 5 
 
PLATE VIII 
 
 "Photograph of the Eclipse of January 22, 1898. Taken at Sahrdol, India, 
 by the Astronomer Royal. Instrument used, Thompson photographic refractor, 
 9 in. in diameter, full aperture, focal length 8 ft. 6 in. Image of the Sun in primary 
 focus i in. in diameter. Enlarged in telescope by a Dallmeyer telephoto lens to 
 4 in. Exposure f second." (Notes from the Royal Observatory, Greenwich.) 
 
FORMATION OF ENLARGED I 
 
 equal to this (see Fig. 40) giving its shortest focal length. In other 
 words, until the interval d is equal to the focal length of the negative 
 lens, or the negative lens has been separated from the position for 
 emergent parallel rays (as in i) by an interval equal to its focal 
 length. 
 
 (4) The back focal length is always shorter than the true focal length, 
 except in the positions of its longest and shortest focal lengths ; but 
 neither of these two positions is of practical value. We cannot have a 
 camera of infinite length, nor should we place the plate in contact with 
 the negative lens. 
 
 Let us now take a general case, applying the information we have 
 gathered from our simple particular case, in order to examine conditions 
 that are not included in it. 
 
 Let the focal length of the negative lens f z be shorter than that 
 of the positive lens/^. If the lenses are placed in contact, it is easy 
 to see that no real image can be formed, for the combination would then 
 be equivalent to a lens of negative focal length. For lenses in con- 
 tact, the following simple relation holds good : 
 
 5 ~7, A 
 
 so that if/" 2 is less than/^, F must be a negative quantity. (See Notes.) 
 The focal length of the compound lens continues to be negative on 
 separating the lenses, Fig. 41 (i), until the separation a is equal to the 
 difference of their focal lengths, or until we arrive at a separation when 
 d=o ; here the rays emerge parallel or the focal length is infinite (2), as 
 we have seen. 
 
 On increasing the separation (3), or making d a definite quantity, the 
 focal length decreases until d=f 2 , or the whole separation a=f v 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/ r 
 If we increase the separation still further, (4), the negative lens forms a 
 virtual image of the real image formed at/ x . 
 
 57 
 
TELEPHOTOGRAPHY 
 
 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., Fig. 33.) 
 
 (I) 
 
 Focal length is negative 
 
 (2) 
 
 d = o 
 
 Focal length is infinite 
 
 (3) + 
 
 Negative lens forms virtual image of real image 
 formed by positive lens at f { 
 
 In (i) they converge towards a point beyond the focal point of the 
 negative lens, and therefore emerge divergent, giving a virtual image. 
 
 58 
 
FORMATION OF ENLARGED IMAGES 
 
 In (2) they converge towards the focal point of the negative lens 
 and therefore emerge parallel ; do. 
 
 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 ^. positive quantity greater than o and less than/" 2 . 
 
 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 v 
 (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 / : and / 2 , we know the focal 
 length of the compound lens for any value of d greater than o ; for 
 
 F = 
 
 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. 
 
 59 
 
TELEPHOTOGRAPHY 
 
 If we now separate them by any greater interval d, say f of an inch, 
 the focal length 
 
 3x6 .1 
 
 F = - = 24 inches. 
 
 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 accom- 
 plish. 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 
 interval.^ 
 
 As in the case of ordinary positive lenses, we have now to deter- 
 mine 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 L : and L 3 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, "Telephoto- 
 graphic Systems of Moderate Amplification," 1893, p. n, 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 under- 
 stood when it is considered as consisting of two separate parts, as described further on, 
 under B. 
 
 60 
 
PLATE IX [. & 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 aB 
 patent portrait lens and high power tele-attachment. Camera extension from 
 back of negative attachment 19 inches. Portrait lens was closed to -g. 
 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.) 
 
PLATE X 
 
 [. &: H. Spitta, Photos. 
 
 " Upper Picture, View of the Saas Grat from Saas Fee. Photographed 
 with Ross 3-inch portable symmetrical g- yellow screen. Edward's iso- 
 medium plate, exposure three seconds. Hour 8.30 A.M. Mountain about 
 three miles distant. The portion included in the telephoto view is that 
 immediately under the two asterisks. 
 
 " Lower Picture, Telephoto The Dom from other side of Saas Valley. 
 Dallmeyer 2B patent portrait lens and high power tele-attachment. Camera 
 extension from back of negative attachment 20 inches. ^ on portrait lens. 
 Edward's iso-medium plate with yellow screen. Hour 9 A.M. Exposure 12 
 seconds. Mountain 4^ miles distant." (Dr. E. Spitta's description.) 
 
FORMATION OF ENLARGED IMAGES 
 
 always shorter than that of the positive lens, hence we may represent f\ 
 as being a multiple of m (greater than one) of/~ 2 ; 
 
 >=4 (5) 
 
 /2 
 
 or /i m fz (6) 
 
 Let L! and L 2 represent the positive and negative lenses respectively, 
 Fig. 42, and <?fthe interval. If we plot/j, the focal point of the positive 
 lens to the left of the lens L : , and/~ 2 , the focal point of the negative lens 
 to the right of the lens L 2 , it can be shown that * : 
 
 (1) The front focal point of the whole system F I is distant from the 
 front focal point of the positive lens l to^ = m F ; 
 
 (2) The back focal point of the whole system F 3 is distant from the 
 
 T7 
 
 back focal point of the negative lens F 3 to/~ 3 = . (See Notes.) 
 
 Trt- 
 
 Hence the distance between the front focal point of the whole system 
 and the front lens : 
 
 F! L! = m F + / ; 
 
 and the distance between the back focal point of the whole system and 
 the negative lens : 
 
 
 In the case of an ordinary positive lens of focal length /j we found 
 that the position of its focal points were each equal to/" on either side 
 
 of the lens respectively; again, for a given " magnification " of -: 
 
 n 
 
 calling the distance of the object from the lens 0, and the distance of 
 the image from the lens i, 
 
 o = nf + /; 
 
 n 
 
 For a similar "magnification" with the Telephotographic lens, 
 
 * Czapski, " Theorie der Optischen Instrumente nach Abbe." 
 
 61 E 
 
TELEPHOTOGRAPHY 
 
 C\J 
 
 6 
 
 62 
 
FORMATION OF ENLARGED IMAGES 
 
 calling o the distance of the object from the positive element and I the 
 distance of the image from the negative element, 
 
 (7) 
 
 n nt 
 
 To compare these results, let/" = F ; hence 
 
 n F = o F ; and 
 
 I F = i F. 
 
 n 
 
 If we neglect the separation between positive and negative lenses, 
 
 = F + mF+f^, 
 
 *-*-* + -/,; 
 
 or, written in another form : 
 
 = o + (F (m - i) +/J (9) 
 
 1 = i - ( F ( i - ) -/ 2 ) (10) 
 
 m 
 
 From the last two equations* it is evident that using a Telephoto- 
 graphic lens in place of an ordinary positive lens of identical focal 
 length : 
 
 (1) The distance of the object must be greater than with an 
 ordinary positive lens for the same " magnification " an advantage in 
 perspective. 
 
 (2) The distance of the negative lens to the plane of the image 
 (or camera extension) is smaller an advantage in mechanical 
 means. 
 
 * D. P. Rudolph, " Gebrauchsanleitung fur Tele-Objective," May 1896. 
 
 63 
 
TELEPHOTOGRAPHY 
 
 From the quantities contained in the brackets in equations (9) and 
 (10), it is evident that the greater we make m the more pronounced 
 will the advantages of the Telephotographic lens become with respect 
 to convenience of usage, and in respect also of the better perspective 
 given by a greater distance between lens and object for a given 
 "magnification." 
 
 Note. Equations (7) and (8) must be remembered and applied in 
 
 conjunction with the general formula F = -i/r (which determines the 
 
 a 
 
 focal length of the compound system) to find the necessary distance 
 of object from the front lens of the system for a given magnification, 
 and to ascertain the requisite camera extension. 
 
 This method, although elegant in theory, necessitates further calcu- 
 lation to arrive at the intensity of the equivalent or compound lens for 
 the time being. This may readily be done by making the diaphragm 
 apertures of definite measurement, in contradistinction to " relative 
 apertures," by dividing the focal length of the lens (for a given interval 
 d} by the aperture used. 
 
 When the object is very distant, or as we say at infinity, it is 
 evident that no advantage is derived from the property of the 
 Telephotographic lens shown in equation (9), although the 
 advantage derived from the condition in equation (10) always 
 exists. Referring to equation (3) when n is small, or of the 
 same order as m, then we find the increased distance between 
 object and lens a great advantage, as will be seen when dealing 
 with the subject of portraiture ; but when n is great, then in 
 becomes insignificant in comparison, and no advantage is practically 
 attained. 
 
 Having ascertained the position of the two focal points ? 1 F 2 , 
 let us proceed to find the position of the principal points P I i> 2 , 
 Fig. 42. 
 
 It is evident that their distance apart, 
 
 P l to P 2 = F x tO F a 2 F. 
 
 64 
 
FORMATION OF ENLARGED IMAGES 
 
 The whole distance 
 
 F! to F 2 = m F + 2/i + d 2/ 2 + - F ; 
 
 1 ( f f \ 2 ( 
 
 but 2 F = , > 
 
 Hence P I to P 2 = -. (/j / 2 + d] 2 (11). 
 
 P! and P 2 are equidistant from F X and F 2 , as in any positive system, 
 and thus their positions and width are determined. 
 
 Equation (u) shows us that when the interval d is small, the 
 principal points are widely separated, so that with the Telephotographic 
 lens we cannot consider them as coinciding. 
 
 Let us now see how to determine the position and size of the image 
 of an object. 
 
 Plot the two principal points of the lens p l P 2 (which here lie outside 
 the lens) and their corresponding focal points F I F 2 (see Fig. 42 for 
 convenience of following the disposition of the cardinal points). 
 Let A B be an object n times the focal length of the combination 
 distant from the focal point F I( thus B F l = n F. The ray A p lf parallel to 
 the axis, passes from P 2 through the focal point F 2 in the direction 
 P 2 F.,A / ; the ray A N I( proceeding to the front principal point N P proceeds 
 from the second principal point N 2 in a direction parallel to A N X , or in 
 the direction N 2 A', meeting the first ray in A'. A' is then the image of 
 A ; and A' B' the image of A B. As B F I = n F, we know from our previous 
 
 study of a positive lens, that B'F O = - F. Again the size of 
 
 n 
 
 A B : A' B' : : n : I. 
 
 Let us now give a numerical example comparing a Telephoto- 
 graphic lens with an ordinary positive system of the same focal length. 
 (See (2) and (3) Fig. 42.) 
 
 65 
 
TELEPHOTOGRAPHY 
 
 Let the focal length of the ordinary positive lens be 24 inches. 
 
 Let the focal lengths of positive and negative lenses of the Tele- 
 
 photographic system be 6 and 3 inches respectively ; -- = 2, or m here 
 
 = 2. To make this equivalent to the 24-inch lens, the interval d must 
 
 , o r i_ 6 x 3 
 
 be f of an inch : 3 - = 24. 
 
 Suppose we want to produce an image J of the size of the object 
 A B. 
 
 In both cases B F I = 4 x 24 =96, and similarly F 2 B' = = 6 inches, 
 
 4 
 and therefore A B : A' B' : : 4 : i in each case. 
 
 In the case of the Telephotographic lens the distance of the object 
 
 () () (/.) 
 
 from the lens must be 4 x 24 + 2 x 24 + 6 = 150 inches ; 
 but with the ordinary lens only 
 
 () 
 
 (4 + i) 24 =120 inches. 
 
 Again for camera extension with the Telephotographic lens 
 
 24 + 4 _ = ,- 
 
 but with the ordinary lens 
 
 24 + = 
 
 4 
 
 w 
 
 The convenience of the shorter camera extension is evident and 
 very marked. 
 
 The greater distance between lens and object is of great importance 
 from the point of view of perspective, for the reader must bear in mind 
 that the position and magnitude of the image of an object derived from 
 the four cardinal points, although accurate, does not trace the course of 
 
 66 
 
FORMATION OF ENLARGED IMAGES 
 
 those rays which in reality produce the image. In the example above 
 it is evident that the ordinary positive lens, being nearer to the object, 
 includes it under a greater angle than does the Telephotographic lens 
 at a greater distance. When the distance of the object is very great 
 the advantage of course ceases. It may be stated very approximately 
 that : The distance of the object from the lens determines the perspective, 
 We shall refer to this more fully later. 
 
 NOTES ON A. 
 
 If two lenses, f v f y of positive and negative focal length respec- 
 tively, are separated by a given distance a between their principal or 
 nodal points, the focal length of the combination 
 
 A + -A 
 
 If we make d = f l f^ a=o, a = fi />', or when the lenses are 
 separated by a distance equal to the difference of their focal lengths 
 d =o and the focal length of the combination is infinite. 
 
 I f d = o, or is any interval greater than the difference of the focal 
 lengths, and equal to or less than/^, the formula takes the form 
 
 F - 
 
 d 
 
 When a = f v df-^ f z /j= - f z , or the interval d is equal to the 
 focal length of the negative lens ; the condition when the combination 
 has its shortest focal length ; F =/j. 
 
 *! is some multiple of/" 2 , we may say 
 
 /i = f 9 
 
 where m is the multiple. 
 Substituting in : F =&; it is evident that 
 
 G/ 
 
 *= L <4'); 
 
 m d 
 
 67 
 
TELEPHOTOGRAPHY 
 and also 
 
 r m ^~d'' 
 
 The distance of the front focal point of the combination from the 
 front focal point of the positive lens = (A-) and /. = m F. 
 
 Similarly the distance of the back focal point of the combination from 
 
 the back focal point of the negative lens = (^f ) and .. =. F, and 
 
 v a m 
 
 hence : 
 
 Distance of front focal point from positive lens = m F +f r 
 
 ,, ,, back ,, ,, ,, negative lens = F /,. 
 
 m 
 
 METHOD B. 
 
 Let us now consider the Telephotographic lens as consisting- of 
 two separate parts. 
 
 The positive element may be considered as forming an image of 
 definite size, of a given object, dependent upon its focal length, and 
 the negative element may be considered as enlarging the image which 
 the positive lens would have formed by itself. 
 
 In general, if one positive lens is n times the focal length of another 
 we have seen that the image produced by the one will be n times as 
 large as that produced by the other. From this it is evident that if we 
 increase the size of any given image n times, this enlarged image will 
 be identical with that produced by a lens whose focal length is n times 
 the focal length of the lens that produced the original image. 
 
 In Chapter III. we have ascertained how images of either near or 
 distant objects are formed by a positive lens ; and in Chapter IV. we 
 found the law for finding the " magnification " of the image of an object 
 by a negative lens : " Divide the distance of the object from the lens, 
 by the focal length of the lens and add one." The image formed by a 
 negative lens alone is virtual, and as the above law shows us that a 
 
 68 
 
QJ - 
 _- 
 
 1-1 -5 
 
 D j_, 
 
 
 to < 
 
 C O 
 
 <u o 
 
 -o -^ 
 
 rt " 
 
 O c 
 
 O 
 
- c 
 
 ^ S 
 
 E 3 
 
 C8 g 
 
 2 6 
 
 s 
 
 
FORMATION OF ENLARGED IMAGES 
 
 diminished virtual image is formed by a negative lens of a real object 
 we must invert the conditions and form a real image of a virtual object ! 
 (Image and object are always interchangeable ) 
 
 This is precisely what we do accomplish in the Telephotographic 
 construction. 
 
 The positive lens L P of focal length f v would form a real image at 
 a 6, but the rays are intercepted by the negative lens L 2 of focal length 
 f We may then consider ab a new "virtual object," a real image of 
 which A' B' is formed by the negative lens L 3 . 
 
 In this method of treating the subject we shall always refer the 
 size of the final image A' B' to the size of the image a b which will be 
 formed by the positive lens alone. 
 
 We repeat that in speaking of relative sizes, we refer to linear 
 " magnification," unless otherwise stated. 
 
 In the Telephotographic lens we may place the screen at any 
 distance we choose from the negative lens, and in order to find how 
 many times we have magnified the image formed by the positive lens 
 alone, we have seen that we must divide this distance by the focal 
 length of the negative lens and add one. 
 
 Calling M the magnification, and E the camera extension (distance 
 between negative lens and screen), and f the focal length of the nega- 
 tive lens : 
 
 E 
 
 M = -= 
 
 Rule. To find the magnification : divide the camera extension by 
 the focal length of the negative lens and add one. 
 
 Conversely, 
 
 Rule. To find the camera extension necessary for a certain 
 magnification : multiply the focal length of the negative lens by the 
 magnification less one. 
 
 E =/ 8 (M - i) ....... (13) 
 
 These two rules apply for either near or distant objects. For a 
 near object the focal length of the positive lens may be said to be 
 
 69 
 
TELEPHOTOGRAPHY 
 
 CO 
 
 <t 
 g 
 
 LL 
 
 Principal plane of positive system 
 6 inches focal length 
 
 Principal plane of negative system 
 3 inches focal length 
 
 Focal pjane of positive lens 
 
 Focal plane of 
 
 -^telephotographic lens 
 
 70 
 
FORMATION OF ENLARGED IMAGES 
 
 temporarily increased and the image of a near object produced by it is 
 larger than when the object is distant, obeying the law of conjugate 
 foci. The conditions for the magnification of this image are not, how- 
 ever, interfered with. 
 
 If the object is very distant (the position of the focus of the positive 
 lens being that of its focal point) we can at once derive the focal length 
 of the Telephotographic combination for any given magnification. It 
 
 is simply 
 
 = M/ I; F = M/ (14) 
 
 Rule. To find the focal length of Telephotographic lens for any 
 chosen extension of camera : multiply the focal length of the positive 
 lens by the magnification. 
 
 This may also be found in a perhaps simpler manner from the 
 following consideration. As the positive lens/j is some multiple of the 
 negative lens/ 2 , if we call this m, then m =, and the focal length of 
 
 JZ 
 
 the combination for a distant object, 
 
 F = mE +/ (15) 
 
 Rule. The focal length of a Telephotographic lens is equal to m 
 times the camera extension plus the focal length of the positive lens. 
 Let us now apply these rules to the example illustrated in Fig. 43. 
 
 + f 
 
 Here/! = 6 inches ; f z = 3 inches ; E = 9 inches, and-^ 1 m = 2. 
 
 J 2 
 
 Hence, 
 
 o 
 
 M = ^ + i = 4 ; 
 
 O 
 
 and 
 
 E = 3 (4 - i) = 9, 
 
 or the image is four times as large as that given by the positive lens 
 alone, and it is evident that : 
 
 F = 4 x 6 = 24 (from (14) ); 
 or again, 
 
 F = 2 x 9 + 6 = 24 (from (15) ). 
 71 
 
TELEPHOTOGRAPHY 
 
 We thus see that with a camera extension of only 9 inches from 
 the negative lens, we can obtain an image of the same size as that 
 given by an ordinary positive lens of 24 inches focal length, requiring 
 this length of camera ! 
 
 In other words, the true focal length is the distance between p and 
 F, although the distance between p" and F is all that is necessary to 
 obtain it. As in ordinary positive systems, p is one of the principal 
 points and F one of the focal points of the Telephotographic system. 
 
 By treating the lens in this manner we do not necessarily know the 
 separation of the principal points or planes of the two components, and 
 for distant objects the knowledge of the distance between the principal 
 points and planes of the whole system is immaterial. For extreme 
 accuracy in the results, we ought to know the position of the principal 
 point or plane of the negative lens, as it should be from this point that 
 we set the camera extensions. In practice the mechanical centre of 
 the thickness of the negative lens is very nearly the position of its 
 principal point, and negligible errors only are likely to creep in. 
 
 It is perhaps needless to say that the separation of the two elements 
 determines the plane of the final image, and we have to adjust the 
 separation of the two lenses mechanically until the image is well defined 
 upon the screen in the position we have assigned to it, in order to bring- 
 about the required magnification. 
 
 Again, by considering the final image as a magnification of the 
 image produced by the positive lens alone, we see, at once, from first 
 principles, how to determine the comparative illumination of the two 
 images, which decides the relative photographic exposures. 
 
 Suppose we know the correct exposure to give with the positive 
 lens alone, and we magnify this image by means of the negative lens a 
 certain number of times (linear), the surface covered is the square of 
 the linear dimension ; hence if t is the correct time of exposure to give 
 for the positive lens alone, the correct exposure for a given magnifica- 
 tion (linear) with the Telephotographic illumination is : 
 
 T, the exposure = M 2 t (16) 
 
 72 
 
FORMATION OF ENLARGED IMAGES 
 
 Rule. To find the correct exposure with the Telephotographic lens : 
 Multiply the time of exposure necessary for the positive lens alone by 
 the square of the magnification. 
 
 This result is identical with the following : 
 
 Rule. To find the intensity of the Telephotographic lens : Divide 
 the intensity of the positive lens by the magnification. 
 
 We shall refer to intensity in the next chapter, but may point out 
 here that to find the relative exposures of two lenses we have to square 
 the denominators of the fractions expressing them. So that if the 
 intensity of the positive lens alone i = -, where a is the aperture, and /j 
 the focal length, the intensity of the Telephotographic combination for 
 
 a magnification of M times = or the relative exposures are as : 
 
 M/ 
 
 // : (M//) or// : F 2 . And this is the same thing as saying that with a 
 given aperture, or definite size of diaphragm of the lens, the relative 
 exposure for the positive lens alone and the Telephotographic combina- 
 tion are as the squares of their focal lengths. 
 
 If we examine Fig. 43, we shall see that only a comparatively small 
 part of the entire image formed by the positive lens is taken up and 
 magnified by the negative lens; the " drawing "of this small area is 
 identical with that of the final image, but of different scale. It is evident 
 that the scale is dependent upon the magnification employed. The 
 magnification is due to a multiple of the focal length of the positive 
 lens, produced at a distance which is only a (nearly equal) multiple of 
 the (shorter) focal length of the negative lens ; hence it is evident 
 that the correct viewing distance of the image cannot be from 
 the distance it is removed from the lens, but a considerably greater 
 distance ! We shall examine the correct position in the next 
 chapter. ^ 
 
 Let us now investigate, more particularly, the employment of 
 the Telephotographic lens in forming images of near objects, an 
 application of great practical interest and importance to photo- 
 graphers. 
 
 We have seen that when we require to produce a certain " magni- 
 
 73 
 
TELEPHOTOGRAPHY 
 
 fi cation " with an ordinary positive lens, the following relations 
 exist: 
 
 Distance of object = (n + 
 
 n + i r 
 
 image = -/ r 
 
 n 
 
 We have now only to decide how many times we wish to increase the size 
 of this image to obtain the desired magnification, for we know that the 
 
 size of the image formed by the positive element is -, the actual size of 
 
 wit 
 
 the object. Let M represent the magnification given by negative lens, 
 as before, and- the entire "magnification" we wish to bring about 
 
 N 
 
 between the object and final image by the whole system. 
 
 
 - =- X M ........ (I 7 ) 
 
 N n 
 For equal size N = i ; /. M = n 
 
 i ir I I n 
 
 half ,, - = - ; .'. M = - ; 
 
 N 2 2 
 
 T- II n J 
 
 ror quarter size - = - ; ' M = - ; and so on. 
 
 N 4 4 
 
 EXAMPLE. Suppose the focal length of the positive element /i=io 
 inches, that of the negative lens/ 2 =4 inches, and the object is 80 inches 
 distant, and we wish to reproduce it in half natural size. 
 
 The lens/j produces an image \ the size of the object ; we require 
 
 the final image to be but - or - = - ; hence we must magnify the image 
 
 2 N 2 
 
 given by/i, 3^ times, or make M = 3^. 
 
 i i 7 i 
 
 - = - x L = _. 
 
 222 
 
 applying the formula : 
 
 E = / 2 (M - i ) 
 
 = 4(3i" = 
 74 
 
FORMATION OF ENLARGED IMAGES 
 
 or we require a camera extension of 10 inches to arrive at the final 
 magnification wanted. 
 
 Let us now determine the true focal length F of the Telephoto- 
 graphic system that has produced the result. 
 
 It is obvious that one of the focal points FJ, or the position of its 
 focus for parallel rays, must be somewhere between the negative lens 
 and the screen. 
 
 If we call its distance from the negative lens F L 2 =x, F s must be 
 
 p* 
 
 - ; calling E=the camera extension as before, we have the two following 
 relations : 
 
 x = E - ; 
 
 N 
 
 F = m x + /i ; 
 hence 
 
 F = m (E -) -|- yj ; 
 or 
 
 F(S+ !).- +/.j 
 V N /l ' 
 
 F = 
 
 ,m >. 
 (- + i) 
 
 X 
 
 In the example given m = = 2^-,/j = 10, E = 10, and 1 = 1 
 
 4 N 2 
 
 /2i v 1 
 
 F (-* + i) = 2$ x 10 + 10; 
 
 if F = 35; 
 F = 15*. 
 
 The knowledge of the true focal length is necessary for determining 
 the intensity of the lens, and therefore equation (18) must be remembered 
 and applied. It will be noted that the result obtained is identical with 
 that given by (8). 
 
 Knowing that F=i5f", the distance between object and image to 
 bring about the magnification of J must be (or would be thought to be) 
 
 75 
 
TELEPHOTOGRAPHY 
 
 4j F or 70 inches ; but (neglecting the separa- 
 tion of positive and negative lenses) the whole 
 distance = 80" (distance of object from positive 
 lens) + 10" (camera extension from negative 
 lens = E) or 90 inches, hence the separation of 
 the principal points of the whole system is 
 9070, or as much as 20 inches! 
 
 If we required an ordinary positive lens- 
 system to give the same ''magnification" (J), at 
 the same distance from the object, its focal length 
 
 Q 
 
 would have to be , or 27 inches nearly, and 
 
 \) 
 
 the camera extension 40 inches. 
 
 The photographer will see at once the ad- 
 vantage gained by using the Telephotographic 
 lens, giving the same size of image at the same 
 distance as the ordinary lens of longer focal 
 length : ( i ) in respect of rapidity, if equal effec- 
 tive apertures are employed, or (2) in respect of 
 greater " depth of focus," if both lenses are used 
 at the same intensity, the ratio of the effective 
 aperture to focal length being the same in each 
 case. 
 
 Equation (18) shows us that when N is very 
 great, the above advantages of the Telephoto- 
 
 4M 
 
 graphic lens no longer hold good, for F ( h i) 
 
 then becomes F (^ + i ), or is equal to F, and the 
 equation becomes as before: F=m E+f r (See 
 Equation (15).) 
 
 Let us now proceed to find the distance that 
 must intervene between the object and the 
 Telephotographic lens for a given " magnifica- 
 tion " of -' when its focal length is known. 
 
 N 
 
 76 
 
s 
 
 \N 
 
 a 
 
 xi .2 
 
 o .o 
 
 X! 'S 
 
FORMATION OF ENLARGED IMAGES 
 
 In the first place we must determine the distance of the focal point 
 from the negative lens in order that it may correspond to the focal 
 
 p 
 
 length F chosen, and to this add - for the given magnification, thus 
 
 determining the entire camera extension E that will be required. 
 
 Now we must determine the magnification given to the image 
 formed by the positive lens/~ 1( to bring about the final relation between 
 object and image, as from the size of the image formed by/^ we at 
 once find the necessary distance for the object to be placed : 
 
 as before 
 
 M = 5+1, 
 
 fz 
 and 
 
 I M t 
 
 N n ' 
 or 
 
 n = M N (19) 
 
 and the distance of the object 
 
 = /i( + l) C P( 2 ) 
 
 Example : Take the case of the Telephotographic lens illustrated in 
 Fig. 43 where the focal length is 24 inches. To find the necessary 
 distance between object and lens for a magnification of . 
 Here 
 
 E = 9 4- ^ = I 3 |; 
 
 \J 
 
 M = 1^ + i = sl; 
 
 3 
 
 i i 
 
 _ = _ or N = 5, 
 
 N 5 
 
 11 = ^r x 5 = 28, 
 
 \j 
 
 or the distance of object=6 (28 + 1) = 174 inches. 
 
 The principal points are Jiere separated by a distance of 174- 
 (6 x 24 + 1 5)= 1 5 inches. 
 
 77 F 
 
TELEPHOTOGRAPHY 
 
 For an ordinary positive system of the same focal length 
 Distance of object =yj (N + i) = 144 inches. 
 image - f, (^~) = 28|. 
 
 In other words the ordinary lens must be placed in the position where 
 the refraction caused by the Telephotographic lens appears to originate. 
 (See Fig. 43.) 
 
 We thus confirm again our conclusion that a greater distance 
 must intervene between object and lens with a Telephotographic 
 lens than with an ordinary positive system, both having the same 
 focal length, in order to produce the same size of image, or the same 
 magnification. 
 
 If both lenses have the same intensity, or ratio of effective aperture 
 to focal length, the Telephotographic lens has the advantage (i) in 
 giving better perspective, and (2) in greater "depth of focus." 
 
 It must be remembered, however, that under these particular 
 circumstances the Telephotographic lens will require a longer exposure 
 than the ordinary lens in the proportion of the square of their distances 
 from the object; in our particular case as (i74) 2 : (i44) 2 , or very 
 nearly as 3 : 2. 
 
 Very little consideration will show the reason for this. When 
 images of the same size are produced by either type of lens worked at 
 the same intensity and at the same distance, the relative exposures 
 must be the same ; but here, although the size of the image is the 
 same in both instances, the distance the light has to travel from the 
 object before reaching the Telephotographic lens is greater, and the 
 comparative illumination of the two images obeys the " law of inverse 
 squares." 
 
 The reader will find more examples illustrating the use of the lens 
 for photographing near objects in Chapter VII. on the "Application 
 of the Lens." 
 
 To sum up, this method (B) seems to offer the following advantages, 
 to the photographer : 
 
 78 
 
FORMATION OF ENLARGED IMAGES 
 
 (1) It only extends the already familiar principle of producing 
 images of objects in a given scale. 
 
 (2) The magnification of the original scale carries with it direct 
 information on the question of correct exposure. 
 
 (3) The determination of the "equivalent" lens of the system is 
 arrived at more readily than in the method (A), when it is necessary to 
 find it. In (A) it is always necessary, and involves a knowledge of the 
 " interval " between the component lenses, as well as their focal lengths. 
 In the method (B) the knowledge of the " equivalent " lens is only really 
 necessary in the case of photographing near objects. 
 
 (4) Fewer preliminary considerations are required in arranging the 
 scale for the final image. The distance between object and lens 
 decides the scale given by the positive lens, and the subsequent 
 magnification necessary is immediately known and attained. 
 
 (5) Less mental effort or calculation is required for equally accurate 
 results. 
 
CHAPTER VI 
 
 THE USE AND EFFECTS OF THE DIAPHRAGM, AND THE IMPROVED 
 PERSPECTIVE RENDERING BY THE TELEPHOTOGRAPHIC LENS 
 
 IN determining the position and magnitude of the image of an object 
 we have hitherto only made use of certain functions of a lens or lens- 
 system, and, moreover, considered the latter as perfectly free from all 
 aberrations, including distortion. 
 
 Reference to the four "cardinal" points is of great value and 
 simplicity in this respect, but it is obvious that these geometrical 
 constructions do not in reality trace the actual course of the rays which 
 form the images. This is particularly obvious in reference to the 
 Telephotographic construction. (See Fig. 42.) The rays utilised to 
 determine the position, &c., of the image may not even pass through 
 the lens at all. 
 
 It may be the mounting of the lens itself or the aperture of the 
 diaphragm which limits and determines the portions of the lenses 
 themselves that are utilised in the production of the various points 
 forming the entire image. In Fig. 45 (i) shows that rays at a certain 
 obliquity to the axis cannot pass the lens at all, but are intercepted by 
 the mounting of the lens ; (2) shows that the diaphragm with a given 
 aperture in one position allows the entire pencil of rays at a given 
 obliquity to pass through both lenses, a definite portion of each 
 combination being utilised to form the image ; (3) shows that if the 
 same diaphragm be placed in a different position the same pencil of 
 rays meeting the lens at the same obliquity as in (2) is almost entirely 
 
 80 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 cut off, but the figure shows that new portions of the positive and 
 negative lenses are now utilised to form the image. 
 
 From diagrams (2) and (3) it is obvious that the size of the 
 diaphragm will not only affect the different portions of the two lenses 
 that are brought into play in forming the image, but also affect the 
 illumination of the image, and the extreme obliquity at which a pencil 
 of rays may pass through both lenses. 
 
 Fic.45 
 
 A glance at Fig. 46 will show the position in which the diaphragm 
 should be placed in order to transmit the greatest angle ; this is seen 
 to be the crossing point of those rays which traverse both lenses from 
 their extreme edges. The diaphragm now also occupies the position 
 for the greatest equality of illumination. If we project the extreme 
 incident rays to meet in the axis, they form an angle o, which 
 determines the extreme angle included when no diaphragm is 
 employed. 
 
 81 
 
TELEPHOTOGRAPHY 
 
 Let us now examine the effect of the diaphragm in greater detail. 
 
 On Rapidity. In comparing the rapidity of two lenses, it is obvious 
 that the one which gives an image of greater intensity, or possesses a 
 higher degree of illumination than the other, is the more rapid of the 
 two. In general we form an idea of rapidity of a lens by defining its 
 Intensity ; this we will denote by i. 
 
 The intensity is the ratio of the diameter of the effective aperture 
 to the focal length of the lens. Calling a the diameter of the effective 
 aperture and /the focal length, 
 
 I=J (20) 
 
 It is important that we should clearly understand the meaning of 
 
 FIG. 46. 
 
 the "effective" aperture. If a beam of parallel rays (Fig. 47) is 
 incident upon a positive lens A, having a certain focal length/ the rays 
 converge after passing through the lens and meet in a point F, its focal 
 point. The diameter of A A is the effective aperture of the lens, as 
 none of the rays incident upon it are intercepted after convergence. If 
 we place diaphragms B B, c c, of smaller diameter than A A, behind the 
 lens as in (i), in positions which just allow the entire cone of rays A F, A 
 to pass, the diameters of B B and c c have the same effective apertures 
 
 as A A. Calling a the diameter of A A, the intensity in each case is -. 
 
 If, however, the diaphragm B' B' intercepts any of the rays transmitted 
 
 82 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 through A A as in (2) the effective aperture becomes then A' A'; calling 
 b the diameter of A' A', then the intensity is -^ 
 
 For various reasons it may be necessary to reduce the diameter of 
 the full effective aperture, and to accomplish this we make use of 
 diaphragms whose effective apertures are arranged to have certain 
 intensities. The intensities assigned to the diaphragms are indicative 
 of the relative exposures necessary for each, and they are arranged so 
 that the- latter are easily comparable. The term " stop " is synonymous 
 with "diaphragm." 
 
 As the Telephotographic combination is used to give a great 
 Variety of focal lengths, it is most convenient to adopt a system of 
 
 FIG. 47. 
 
 ABC 
 
 A B 
 
 diaphragm notation that has direct reference to the focal length of its 
 positive element. 
 
 The stops are denoted by the ratio of the focal length of the lens to 
 
 f f 
 
 the effective aperture. Thus if J ~ = 8, then the stop is called -4 or its 
 
 a 8 
 
 intensity is < 
 
 o 
 
 Fig. 48 shows the intensities (usually engraved on positive 
 lenses) and relative rapidities of the diaphragm notation based upon 
 the above system. In general, if the diameter of the aperture is 
 known, with the focal length of the lens, and we express the intensity 
 as above, the comparative exposures are as the squares of the denomi- 
 nators of the stop notation. Example : the relative exposures of stops 
 
 /_.,/ 
 
 * and are as io 2 : 
 
 10 i c; 
 
 , or as i : i\ (not given in the figure). 
 
TELEPHOTOGRAPHY 
 
 In the last chapter we have considered the Telephotographic lens 
 from two different standpoints ; the method of treating it (B) will readily 
 
 rure 48. 
 
 fntensities 
 and 
 
 = unit 
 
 Af-.anqle =2 36' 
 
 ^ angle = J 
 
 32 
 
 (A) - J 
 
 At JC -mote = 55 
 
 Taking ijfd as f/ie limit of inc/isfinctness a/lowed. 
 
 SCALE, 3/4. 
 
 commend itself for arriving at comparative exposures. It is only 
 necessary to multiply the exposure required for the stop notation 
 
 84 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 indicated on the positive lens by the square of the magnification, and 
 we know the exposure to be given for the Telephotographic lens. 
 The knowledge of the effective aperture in some Telephotographic 
 constructions is most important because the stop is sometimes consider- 
 ably removed from the front converging lens. The absolute 
 measurement of its diameter would be very different from its real 
 effective aperture, and if used in place of the latter as a basis of calcula- 
 tion would lead to very great discrepancies, and consequent failure in 
 the correct timing of exposures. 
 
 Fig. 48^ exhibits at a glance the meaning of a "rapid" as 
 distinguished from a "slow" lens. For convenience we have illustrated 
 a lens of 4 inches focal length, but it is evident that the cones of 
 light will be of the same shape, or the rays will cross at the same angle, 
 for any given intensity, no matter what the focal length of the lens may 
 be. The figure also shows that rapid lenses have less " depth of 
 focus " than slow lenses, but we shall refer to this further on. 
 
 In designing a Telephotographic combination we must carefully 
 consider the purpose for which it will be employed. If we take a 
 positive lens of high intensity we can convert it into a Telephoto- 
 graphic system by combining it with a negative lens, which may be 
 destined for either rapid work, or, on the other hand, to attain high 
 magnification. For example, if we take a positive lens, having an 
 intensity of //4 we can employ a negative lens to magnify the image 
 three times, and yet still have a fairly rapid lens in the combination, of 
 intensity //i 2. Again, if high magnification is the aim, we can magnify 
 the image given by the positive lens as much as sixteen times and the 
 combination still has a reasonable intensity off/64. 
 
 On the other hand, if we take a positive lens of only moderate 
 intensity, say //8, and combine it with a negative lens, we can only 
 expect to get small or moderate amplifications without necessitating a 
 very low intensity in the Telephotographic combination. 
 
 The Lowest Intensity Permissible. In treating of diffraction, Lord 
 
 * From "A Simple Guide to the Choice of a Lens." (J. H. Dallmeyer, Ltd.) By 
 the Author. 
 
 85 
 
TELEPHOTOGRAPHY 
 
 Rayleigh has demonstrated that the lowest intensity permissible without 
 introducing the disturbing effects of diffraction is a ratio of aperture 
 to focal length of i : 71, or fjji. 
 
 This conclusion has a very important bearing on the use of the 
 Telephotographic lens. Suppose the intensity of the positive element 
 is fl% for example, and we wish to produce a magnification of five 
 times, the combination will have an initial maximum intensity of ^40. 
 We might very likely stop down the positive lens to/7i6, or even less, 
 with the object of getting finer definition. If the stop //i 6 in the positive 
 lens were employed, we should convert the intensity of the whole 
 system into //So, which is in reality too small for the finest definition. 
 
 We must then always remember that: the intensity of the positive 
 element of the system divided by the magnification must not be less 
 than //; i. 
 
 On Covering Power, or the size of plate covered at a given intensity. 
 Referring to Fig. 49, the diameter of the circle beyond which no light 
 can pass being called D, the effective aperture of the positive lens di 
 and the diameter of the negative lens d a , and, as before, if/i,/" 2 , represent 
 their focal lengths, a the separation, and E the camera extension from 
 the negative lens, it can be shown that : 
 
 _ E f , , 
 
 + / M/ 2 [E (/,-/.) +//JJ 
 
 Approximate formula for maximum circle of illumination 
 
 A A- A 
 
 In the example shown in Fig. 43 d, = 7/8", d z = 5/ 4 ",/i = 6",/ 2 = 3", 
 and E = 9 inches. Hence 
 
 D = f (* x 3 + I * 6) = IQ inches< 
 
 3 
 
 These formulae only require a knowledge of arithmetic to arrive at the 
 
 86 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 result. The result by the approximation, loj, differs very slightly 
 from that of the more complicated formula, which gives IO T ^ as the 
 diameter of the field. 
 
 If we employ a diaphragm and so reduce the effective aperture of 
 d^ we must substitute its value in the formula to find the circle of 
 illumination covered, or the diameter of the field. Say its effective 
 aperture is \ inch, then D = 8 inches. 
 
 In the formula it is evident that d } f z may become very small when 
 the effective aperture d l is also very small. 
 
 FIG. 49. 
 
 If we neglect this quantity we find the minimum circle of illumina- 
 tion for any lens 
 
 = (M - I) (1&,\ 
 Jl ~/2 
 
 where M is the magnification as before. 
 In the case under notice 
 
 6 x R 
 D min. = (4 i) * = 7! inches. 
 
 6 - 3 
 
 The circles of illumination must determine the size of the plate that can 
 
 87 
 
TELEPHOTOGRAPHY 
 
 be covered ; the diagonal of the plate must not be more than the 
 diameter of the circle covered, or the corners of the plate will be " cut 
 off," or not illuminated. It is advisable to arrange that the circle of 
 illumination is greater than the diagonal of the plate for the smallest 
 effective aperture likely to be used. We give here the diagonals of the 
 sizes of plates in ordinary use. 
 
 Diagonal or minimum diameter 
 Size of plate. of circle of illumination. 
 
 4 x 3* ' 5-4 l 
 
 5x4 6.4 
 
 6| x 4 f 8 
 
 8 x 6J 10.7 
 
 10 x 8 12.8 
 
 12 X 10 15-6 
 
 15 X 12 I9- 2 
 
 18 x 16 24.1 
 
 22 X 2O 29.7 
 
 25 x 21 3 2 -7 
 
 30 x 24 38.4 
 
 On the angle included by the combination. 
 
 Calling a the extreme angle, F the focal length of the Telephoto- 
 graphic lens, and D the diameter of the circle of illumination, 
 
 -T D 
 
 a = 2 tan . 
 
 2 F 
 
 In the case illustrated D=IO. i and F=24 ; 
 
 a = 2 tan ~ : 77- = 2 tan ~~ I .210416. 
 
 48 
 
 From a table of natural tangents we find that .210416 corresponds 
 to an angle of 1 1 53', and hence the extreme angle that can be included 
 is 23 46'. As the effective aperture of the diaphragm is decreased the 
 diameter of the circle of illumination becomes less, or less angle is 
 included as we stop down the lens. 
 
 88 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 It will be found, however, that when the lens is used to its utmost 
 limits in respect of covering power, whatever stop is employed, the 
 angle included is approximately a constant for any extension of camera ; 
 if the lens is used to cover a definite size of plate at different extensions 
 of camera, it is obvious that the angle included on that plate is variable, 
 diminishing as we increase the magnification. 
 
 On Equality of Illumination. Speaking of lenses generally, one 
 form may lend itself more readily than another to transmit the full 
 pencil of light over a greater angle, but no lens can in reality give equal 
 illumination over the entire plate. This inequality is an inherent defect 
 of every form of lens producing an image that is to be received upon a 
 plane at right angles to the axis of the lens. It is most apparent when 
 the combinations of the lens-system are separated by a considerable 
 distance, particularly if used without a diaphragm. The construction 
 of the Telephotographic lens necessitates a comparatively large separa- 
 tion of the elements composing it, even when m, or-^' is small. Under 
 
 /3 
 
 these conditions the full pencil of rays from the front combination can only 
 emerge from the back combination (without being cut off) over a very 
 few degrees from the axis of the lens, or the centre of the plate. The 
 tube of the lens then very rapidly commences to cut off the full pencil, 
 and the worst conditions for equality of illumination are brought about. 
 A lens is readily examined to test the field over which the full 
 pencil is received, by focusing upon a bright object, such as a candle 
 or small gas flame, and racking the screen in a little, until the image 
 becomes a bright disc of light. If we now move the camera so that 
 the image gradually passes from the centre towards the edge of the 
 screen, and observe how far the disc continues circular, we can follow 
 how far the best conditions for equality of illumination are fulfilled ; as 
 soon as the disc commences to become cut off, the full oblique pencil is 
 no longer received upon the plate. If this operation is conducted, in 
 the first place, without a diaphragm, we shall find that equality of 
 illumination can be attained over a greater angle as the size of the 
 diaphragm decreases, but at the expense of intensity. 
 
 89 
 
TELEPHOTOGRAPHY 
 
 Even when the best conditions for equality of illumination are main- 
 tained, still the illumination of the plate rapidly decreases with the angle 
 of obliquity. We state the case generally here as it is essential that 
 we should choose our positive element, so that it, at any rate, shall 
 transmit the full pencil of rays to the negative lens at the extreme 
 obliquity. 
 
 Presuming that a full pencil passes through a lens at any obliquity 
 of incidence, the quantity of light passing axially through the lens, as R R, 
 
 FIG. 50. 
 
 is greater than that which passes obliquely, the latter varying as the 
 cosine of obliquity. Again the oblique pencils r r are brought to a 
 focus at/i more distant from the aperture of the lens L than the central 
 pencil at F, the illumination varying according to the "law of inverse 
 squares " when the plate is at right angles to r f, as at //. Now 
 L F and L/" vary with the secant of obliquity, and hence the illumination 
 at F and f (on the plane / p) will vary as 
 
 cos x 
 
 sec 2 9 
 
 9 o 
 
 = cos 3 e. 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 But the illumination on p p as compared with that of pp decreases 
 
 again in the ratio of cos0 (or as -). Hence the final illumination 
 
 sec 8' 
 
 varies as cos 4 0, or as the fourth power of the cosine of the angle of 
 obliquity. 
 
 The following table shows the illumination of the plate given by an 
 ideally perfect lens as regards transmitting the full incident pencil at 
 various obliquities. 
 
 Quantity of light passing 
 
 Angle of obliquity through at the pupil Illumination of image 
 = d. = cos 0. = cos 4 6. 
 
 O I.OOO I.OOO 
 
 5 -996 .985 
 
 10 .985 .941 
 
 15 .966 .870 
 
 20 .940 .780 
 
 25 .906 .675 
 
 30 .866 .562 
 
 40 .766 .344 
 
 45 -707 -250 
 
 50 .643 .171 
 
 Now, although this table shows that the illumination rapidly decreases 
 for the greater angles of obliquity (one half when 60 and only one 
 quarter when 90 are included upon the plate), the loss of light for 
 small obliquities is seen to be very small up to 20 (that is 10 either 
 side of the axis). The Telephotographic lens is seldom constructed to 
 include a larger angle than this, so that we can readily choose a positive 
 element which shall transmit light most favourably for equality of 
 illumination ; but the separation of the elements, their diameters, and 
 the position of the diaphragm must determine the limits for this condi- 
 tion in the compound system. 
 
 On Distortion. If we place a diaphragm at any distance either 
 before or behind a single positive lens, distortion of the image produced 
 by it takes place, due to the fact that no single lens can be made free 
 from spherical aberration, curvature of field, &c. ; a reference to 
 
 91 
 
TELEPHOTOGRAPHY 
 
 Fig. 5 1 will make the matter clear : a beam of rays parallel to the axis 
 of the lens L forms a focus at a point F in the axis ; if the parallel beam 
 i^RRg falls upon the lens obliquely, its focus (or more correctly its 
 approximate focus) will be found at a point / which is not situated in 
 the same plane as F, but if these rays are produced they will meet the 
 focal plane of the lens through F in the points r^ rr y If we place a 
 small diaphragm in contact with the lens, distortion will not take place, 
 as both r^ r z are symmetrically situated with respect to the ray Rr. If 
 
 FIG. 51. 
 
 we remove the diaphragm from the position of contact, and place it in 
 front of the lens in the position of S 1} the rays R X R only can traverse the 
 upper portion of the lens L, and are received upon the plane through F 
 in the points r r^ : the effect being to displace the ray RJ r towards the 
 centre of the image plane, the points which are most displaced being 
 those furthest away from the centre ; giving rise to what is known as 
 "barrel shaped" distortion. If, on the other hand, we place the 
 diaphragm in a position s 2 behind the lens, it will be seen that the rays 
 R R 2 pass through the lower half of the lens L and are received upon the 
 image plane in the points rr y The effect is to displace every point 
 outwards from the centre, giving rise to what is known as " pincushion " 
 distortion. These effects of distortion are best illustrated in the 
 
 92 
 

 
 o 
 
 o 
 
 ,H 
 

Or 
 
 
 USE AND EFFECTS OF 
 
 rendering of a square or rectangular object as shown in the 
 figure. 
 
 The figure has served to illustrate the manner in which distortion is 
 produced by an uncorrected single lens ; the same effects are noticeable 
 in any single positive combination, and arise from the fact that, although 
 adequate correction or defining power may be brought about in the 
 axis of the system, it is impossible to remove spherical aberration, coma, 
 curvature of field, &c., in the eccentrical pencils. These ill effects are 
 reduced by employing a diaphragm which gives rise to the effects of 
 distortion as indicated above. 
 
 The distortion of the image is in reality brought about by inherent 
 defects in the lens itself, and not by the diaphragm employed ; for 
 example, if we place a diaphragm either before or behind an optical 
 system which is perfectly corrected, such as a rapid rectilinear, stigmatic 
 lens, &c., it will not bring about distortion in the image, and from this 
 it will be obvious that were we enabled to produce a single combina- 
 tion absolutely free from all aberrations in the eccentrical pencils, the 
 position of the diaphragm with regard to it would have no effect as 
 regards distortion and have no influence in producing it. 
 
 From the above remarks it will be evident that the position of the 
 diaphragm with respect to a single negative lens when placed in front 
 of the latter will be to displace the pencils of rays falling upon it 
 outwards from the centre. Hence, if a diaphragm be placed between 
 a single positive and single negative lens, the effect will be to give 
 " pincushion " distortion to the image formed by the positive lens alone, 
 which in its turn will be emphasised by the negative lens in the final 
 
 image. If we call -^ = m as before, the "pincushion" distortion 
 
 /2 
 
 increases as m increases. A Telephotographic system, then, which has a 
 single positive combination combined with a single negative combination 
 with 1 a diaphragm placed between must give this form of distortion in an 
 inadmissible degree, even when m is low, except for pencils very near the 
 axis, and in an impossible degree when m is great, or the lens is employed 
 to cover a plate approaching the limits of its circle of illumination. 
 
 93 c 
 
TELEPHOTOGRAPHY 
 
 If the positive element is a single combination with the diaphragm 
 placed in front as in a " single landscape lens," which produces " barrel 
 shaped " distortion per se, it can be combined with a single negative 
 element, and form a Telephotographic system which is non-distorting. 
 The chief drawback to this arrangement is the low intensity of the 
 positive lens and consequently that of the entire system when fine 
 definition is aimed at.^ 
 
 The "pincushion" distortion involved in a Telephotographic lens 
 composed of a single positive element of high intensity combined with, 
 a single negative lens soon led the author to abandon this form of lens, 
 replacing the single front lens by a positive combination of high inten- 
 sity free from distortion in itself, combining it with a negative combination 
 constructed to give the minimum distortion even when m is very high. 
 
 The extra reflecting surfaces of the lenses thus combined constitute 
 a theoretical disadvantage as regards the brilliancy of the image ; but 
 this is not found of practical moment. The more complicated system 
 seems to warrant the expenditure of optical means to remove a palpable 
 defect. 
 
 On the "Pupils" of a Lens-system. Professor Abbe" has defined 
 these as extending the significance of the diaphragm or stop. We may 
 consider each separate stop of a lens-system as forming an image by 
 the lenses which are in front of it (that is towards the object). The 
 stop whose image thus formed appears under the smallest angle from 
 the object is defined as the " Aperture Stop," and its image is called 
 the " Entrance Pupil " of the lens. Similarly the image of the 
 " Aperture Stop " formed by the lenses succeeding it, that is towards 
 the image, is termed the " Exit Pupil." The " Entrance Pupil " and 
 the " Exit Pupil " bear to one another the same relation as object and 
 image referred to the whole system. (See Notes.) These "Pupils" 
 have a very important and interesting bearing upon the study of 
 
 * The author constructed a lens of this form for Mr. J. S. Bergheim to be used in 
 portraiture. As Mr. Bergheim desired to produce " soft " images, the single positive 
 element was made of high intensity, the spherical aberration necessarily introduced 
 giving the softness aimed at, but the combination is free from distortion. 
 
 94 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 optical instruments. Von Rohr points out their bearing upon the 
 correct method of viewing the perspective drawing given by a lens, 
 and also upon the subject of " depth of focus," which is referred to 
 below. 
 
 Perspective. If we put a photographic lens in the orifice of a dark 
 chamber so that it may form an image of any object situated outside, 
 we can take a screen and place it at any distance we choose at (or 
 beyond) the focal point of the lens, and thus receive upon it sharp 
 images of distant objects or nearer objects according to the position in 
 which the screen is placed. In other words, we can only have one 
 plane in the field of the object, or the external field, which is strictly in 
 focus at one time. 
 
 On the other hand, when we regard the external field, in order to 
 form a correct idea of the perspective which will be produced in the 
 resulting image upon the screen, we must first select the particular 
 plane in the field of the object for which we shall focus sharply ; we 
 must then consider the appearance of objects situated before or behind 
 this particular plane as projected upon it ; we then know, provided 
 that the lens is non-distorting, that the perspective of the image will 
 exactly reproduce the object plane and the projections of objects before 
 or behind it, on to it, in some definite proportion. The perspective, 
 then, is determined by the distance between the entrance pupil of the 
 lens, through which pass all rays from the field of the object, and the 
 chief plane for which we have focused. The entrance pupil and the 
 exit pupil of the lens become the centres of perspective for object and 
 image, and the image itself is an exact facsimile of the perspective 
 produced upon the chief plane in the field of the object ; it is usually 
 reduced in size in some proportion n : 1. Now, the size of the image 
 itself does not give us any indication as to the correct point of sight, or 
 distance from which it should be viewed. In order to discover this, 
 we must place the image between the entrance pupil of the lens and 
 the chief plane for which we have focused, in such a position that its 
 projection exactly coincides with the objects in the object field. 
 
 In the case of employing a very small stop in the lens, all objects 
 
 95 
 
TELEPHOTOGRAPHY 
 
 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 con- 
 sidered 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 
 
 FIG. 52. 
 
 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. 
 
 If a represents the aperture of the entrance pupil, Fig. 52, and oo 
 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 indistinct- 
 ness which will be found on the image plane when a reduction of n 
 times takes place. This consideration leads to an interesting inter- 
 pretation of the subject of "depth of focus," to which we shall shortly 
 refer. 
 
 96 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 The correct distance from which an image formed by an ordinary 
 photographic lens should be viewed is commonly defined to be a dis- 
 tance 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, 
 
 ^u n + i r 
 
 so that x = - / ; 
 n 
 
 and if n be infinite x f, which corresponds with the rule to view land- 
 scapes 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 + gnt] ; g = i, or is > i ; 
 and the correct viewing distance 
 
 x = 
 
 n 
 
 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 
 
 97 
 
TELEPHOTOGRAPHY 
 
 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. Lt 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 oppo- 
 site 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 photographer is apt to approach 
 his subject and include it under a large angle for the purpose of obtain- 
 
 Fic.53. 
 
 ing 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. 
 
 Depth of Focus (Von Rohr's interpretation). The conception of 
 the " Entrance Pupil" of a lens and its separation from the chief plane 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 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 indis- 
 tinctness. 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 indistinct- 
 ness greater than one-hundredth of an inch, it is said to appear 
 "sharp." 
 
 In general, if we take i as the limit of indistinctness permissible in 
 the image, and we reproduce the object in the proportion of n : i, the 
 circle of indistinctness for any point in the field of the object projected 
 upon the object plane for which we have focused would be n times i, 
 or n i. Referring to Fig. 52, the circles a' and a" projected on to the 
 chief plane of the object from the points P P' are, of course, n times as 
 
 99 
 
TELEPHOTOGRAPHY 
 
 great as the circles of indistinctness to which they correspond in the 
 image. Using the same notation as before, calling d the distance 
 between the chief object plane and the " Entrance Pupil," b the distance 
 of the point p in front of this plane, and c the distance of the point P' 
 behind it, a the diameter of the " Entrance Pupil," and i the limit of 
 indistinctness in the image, 
 
 dn i 
 
 b = 
 
 c = 
 
 a + m 
 
 dni 
 a n i 
 
 b is here the front depth of field, and c is the back depth of field, the 
 whole depth being 
 
 2 dn ia 
 
 b + c = 
 
 d' n 1 i 2 ' 
 
 The size of the diverging circles a' and a" is not only dependent upon 
 the diameter of the " Entrance Pupil," but also on its separation from 
 the chief plane for which we have focused. 
 
 Fig. 54 clearly shows that these circles decrease when the 
 separation d increases. To put this more clearly, we see from the 
 former figure that 
 
 b a 
 
 a = 
 
 d - b' 
 
 now if we increase d by h the formula becomes 
 
 i b a 
 
 a = 
 
 d + h b' 
 
 If </is very great compared with d b, or, in other words, if the point P 
 and the principal object plane are both widely separated from the 
 ' Entrance Pupil," the effect of further removing the " Entrance Pupil " 
 becomes indifferent. Thus we see the advantage gained by the Tele- 
 
 loo 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 photographic lens in producing sharper or better defined images of 
 near objects, giving the effect of greater depth of focus, and that the 
 advantage ceases for very distant objects. The reason for this greater 
 depth of focus in the Telephotographic lens lies in the smaller angles 
 subtended by the " Entrance Pupil " from points in the object, as its 
 distance is greater than for a lens of ordinary construction. Supposing 
 the angle subtended is 2 u, then 
 
 tan u = 
 
 a 
 
 2 (d + 
 
 In conclusion we find that a Telephotographic lens of the same intensity 
 as an ordinary positive lens gives greater depth of focus than the latter 
 
 Fie. 54. 
 
 when used to photograph near objects, although this advantage 
 gradually diminishes when the distance of the object increases, and is 
 finally lost when the distance of the object becomes very great. It 
 must be remembered, however, that the greater separation of the 
 " Entrance Pupil " of the Telephotographic lens from the object, in 
 circumstances where this advantage occurs, will necessitate an increase 
 of exposure depending upon the " law of inverse squares " as already 
 pointed out. 
 
 Depth of Focus (usual interpretation). Our method of treating the 
 Telephotographic lens, under the heading B, enables us again to 
 
 101 
 
TELEPHOTOGRAPHY 
 
 simplify the question of depth of focus applied to the construction. If 
 the positive element of the system be considered alone, we may apply 
 the well-known formulae for front and back " depth of field " in the 
 usual manner, and if the result is to be regarded as a pictorial repre- 
 sentation, we may neglect the effect produced by the magnification of 
 the admissible circles of indistinctness which have been formed by the 
 positive lens alone, because the more we magnify the primary image, 
 the greater will be the distance from which the picture may be expected 
 to be viewed. (This of course actually occurs in an ordinary " enlarge- 
 ment " from a photographic negative.) In selecting the circle of confu- 
 sion of one-hundredth of an inch as sufficiently small when viewed at 
 the normal distance of vision to appear practically sharp, we are guided 
 by the fact that at a distance of about 12 inches this measurement 
 subtends an angle of only three seconds of a degree. It is obvious that 
 if we view the result obtained by the Telephotographic lens when a 
 certain magnification has taken place, at a correspondingly greater 
 distance than that at which we should view the result made by the 
 positive lens alone, the increased circles of indistinctness will still only 
 subtend the same angle at the eye, and therefore will appear equally 
 well defined. If, on the other hand, we require the final image pro- 
 duced by the Telephotographic lens to have a definite degree of sharp- 
 ness which shall not exceed one-hundredth of an inch, it will only be 
 necessary to substitute the numeral M 100 (representing M times 100) 
 for 100 in the formulae, wherever 100 occurs, in order to attain the 
 same limit in the final image, whatever M may be ; M as before being 
 the magnification. 
 
 For the sake of uniformity and greater simplicity we here give 
 formulas for depth of focus which have reference to the relation between 
 the size of object and image (or their distances from the focal planes of 
 
 a positive lens), - as before being " the magnification " of the image. 
 n 
 
 Calling f the focal length of the positive element, a its effective 
 aperture, I = - its intensity, (n+i)/ the distance of the object from the 
 lens, 
 
USE AND EFFECTS OF DIAPHRAGM 
 the distance beyond which all objects will be sufficiently well defined 
 
 = ioo a/ + / (22) 
 
 or ioo times the effective aperture multiplied by the focal length + the 
 focal length of the lens ; or 
 
 = IOO I/ 2 +/ . ^ '. . . . . (22 a ) 
 
 When we focus upon a near object the front depth 
 
 nf(n + i) 
 ioo a + (n + i) ' 
 
 or 
 
 n times the distance of the object 
 ioo times the aperture + (n + i)' 
 
 or 
 
 /( + ( 2 ,\ 
 
 IOQI/+ (n + i) 
 
 The back depth 
 
 nf(n -4- i) 
 
 IOO (tt + i) ' 
 
 or 
 
 n times the distance of the object t 
 ioo times the aperture (n + i)' 
 
 or 
 
 */( + t A \ 
 
 ioo if (n + i) 
 
 Example. An object is placed at a distance of 20 ft. from a Tele- 
 photographic lens composed of a positive lens /j of 10 inches focal 
 length, working at an intensity I=J, and a negative lens/ 3 of 5 inches 
 focal length ; the primary image being magnified 4 times, or M=4. 
 
 In order that the primary image shall not include circles of indis- 
 tinctness greater than i /ioo we find, as - = . 
 
 n 23 
 
 103 
 
TELEPHOTOGRAPHY 
 Front depth 
 
 = '3/. (3 + = 20 inches . 
 
 IOO /- / v 
 
 /I + (23 + I) 
 
 Back depth 
 
 33/, (23 4 
 
 IOO / / 
 
 /i - ( 2 3 + 
 
 = 
 
 Now, if we place the focusing screen at a distance of 15 inches from 
 the negative lens, we shall obtain a magnification of four times. Should 
 the result be regarded from the pictorial point of view, it will not be 
 necessary to pay attention to the fact that we have magnified the primary 
 image, for the reasons stated above. 
 
 But if we do not wish the limit of indistinctness to exceed " m 
 the final image, then the front depth 
 
 ' = 5-4 inches. 
 
 Back depth 
 
 =5.7 inches. 
 
 It will be observed that our process is to ascribe a smaller limit of 
 indistinctness to the image produced by the positive lens proportionate 
 to the amount it will be subsequently magnified. 
 
 We will now prove that of two lenses of the same focal length, one 
 Toeing of ordinary construction and the other of Telephotographic con- 
 struction, that the latter has the greater depth of focus. 
 
 Example. Let the focal length of both lenses be 30 inches, the 
 Telephotographic combination being formed of a positive lens (c. de v. 
 for instance) of 6 inches focal length and a negative lens of 3 inches 
 
 104 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 focal length. Let both have the same effective aperture of 2 inches,, 
 or I in each case be T 1 5- To find front and back depths for a " magni- 
 fication " of J, or #=4 
 
 (i) For the ordinary lens : 
 
 Distance of object 
 
 = 150 inches. 
 
 Distance of image 
 
 = 30 + 7% = 37! inches. 
 Front depth 
 
 4 x 30 x 5 _ 
 
 IOO 
 
 30 + 5 
 
 = 3" (nearly). 
 
 15 
 
 Back depth 
 
 = 4 x 30 x 5 = 
 
 IOO 
 
 x 30 - 5 
 
 i5 
 (2) For Telephotographic lens : 
 
 Distance of object 
 
 = 1 86 inches. 
 
 Distance of image 
 
 = 1 2 + 7 J = 1 9 J- inches. 
 
 (12 inches extension are required to make the 6 -inch positive lens- 
 equivalent to 30 inches focal length, by means of the 3-inch negative ; 
 the increased conjugate 7^ inches is the same as in the case of the lens- 
 of ordinary construction.) 
 
 Here n i =30 ; and for M = 7|-, ^^ becomes -7^, and 1 = 
 6 
 
 Front depth 
 
 30x6x31 * \, 
 i- =3.64 inches. 
 
 750 
 
 x 6 + 31 
 
 3 
 
 105 
 
TELEPHOTOGRAPHY 
 
 Back depth 
 
 30 x 6 x 31 _ 
 
 750 
 
 x 6 - 31 
 
 = 3.8 inches 
 
 The following tables apply to measurements based upon an admissible 
 circle of indistinctness of xir/' m tne image formed by the positive lens 
 alone. For this degree of definition in the final image the distances 
 given in the first table must be multiplied by the magnification given 
 to the image. 
 
 TABLE I. 
 
 TABLE OF DISTANCES at and beyond which all objects are in focus and may 
 be considered as situated in one plane. 
 
 
 * Intensities of Diaphragm Apertures. 
 
 Focal length of 
 
 I KTrTBBHnBHB 
 
 lens 
 
 H^BBJBE-^B * Bm VJV ' ByB B^B Ri5 Ksi ^^H 
 
 in inches. 
 
 4 56 6 rj 8 ITJ M I 11 6 ^'12213214416411 
 
 
 ^M ^^^^M ^^^a ^^M ^M ^^^ 
 
 Number of feet distant after which all is in focus. 
 
 4 
 
 33 
 
 24 
 
 22 
 
 19 
 
 17 
 
 13 
 
 12 
 
 9 
 
 8 
 
 7 
 
 6 
 
 4 
 
 3 
 
 2 
 
 4i 
 
 38 
 
 27 
 
 25 
 
 21 
 
 19 
 
 15 
 
 M 
 
 10 
 
 10 
 
 8 
 
 7 
 
 5 
 
 34 
 
 24 
 
 44 
 
 42 
 
 30 
 
 28 
 
 24 
 
 21 
 
 17 
 
 15 
 
 ii 
 
 ii 
 
 84 
 
 74 
 
 54 
 
 4 
 
 3 
 
 4l 
 
 47 
 
 34 
 
 31 
 
 27 
 
 24 
 
 19 
 
 17 
 
 12 
 
 12 
 
 94 
 
 84 
 
 6 
 
 5 
 
 3 
 
 5 
 
 52 
 
 36 
 
 35 
 
 30 
 
 26 
 
 21 
 
 19 
 
 14 
 
 13 
 
 104 
 
 94 
 
 64 
 
 54 
 
 34 
 
 8 
 
 57 
 63 
 68 
 
 40 
 45 
 50 
 
 38 
 43 
 46 
 
 33 
 36 
 38 
 
 28 
 31 
 34 
 
 23 
 
 25 
 27 
 
 21 
 23 
 25 
 
 15 
 17 
 
 18 
 
 14 
 15 
 
 17 
 
 "4 
 
 134 
 
 104 
 
 "4 
 
 7 
 
 74 
 
 84 
 
 54 
 6 
 
 64 
 
 34 
 4 
 4 
 
 6 
 
 75 
 
 54 
 
 50 
 
 42 
 
 38 
 
 30 
 
 28 
 
 20 
 
 19 
 
 15 
 
 M 
 
 9 
 
 7 
 
 4* 
 
 6^ 
 
 81 
 
 58 
 
 54 
 
 46 
 
 40 
 
 32 
 
 29 
 
 22 
 
 20 
 
 16 
 
 15 
 
 10 
 
 74 
 
 5 
 
 64 
 
 87 
 
 62 
 
 58 
 
 50 
 
 44 
 
 35 
 
 32 
 
 23 
 
 22 
 
 174 
 
 16 
 
 ii 
 
 8 
 
 54 
 
 M 
 
 94 
 
 67 
 
 63 
 
 54 
 
 47 
 
 38 
 
 34 
 
 25 
 
 24 
 
 19 
 
 17 
 
 12 
 
 84 
 
 6 
 
 7 
 
 IOI 
 
 72 
 
 68 
 
 58 
 
 51 
 
 40 
 
 37 
 
 27 
 
 25 
 
 20 
 
 18 
 
 124 
 
 9 
 
 6 
 
 7i 
 
 109 
 
 78 
 
 73 
 
 62 
 
 54 
 
 44 
 
 39 
 
 29 
 
 27 
 
 22 
 
 20 
 
 134 
 
 10 
 
 64 
 
 74 
 
 117 
 
 83 
 
 78 
 
 64 
 
 58 
 
 47 
 
 42 
 
 31 
 
 29 
 
 24 
 
 21 
 
 144 
 
 104 
 
 7 
 
 7i 
 
 124 
 
 90 
 
 83 
 
 71 
 
 62 
 
 5 
 
 45 
 
 33 
 
 31 
 
 25 
 
 22 
 
 154 
 
 ii 
 
 74 
 
 8 
 
 132 
 
 96 
 
 88 
 
 76 
 
 68 
 
 52 
 
 48 
 
 36 
 
 32 
 
 28 
 
 24 
 
 16 
 
 12 
 
 8 
 
 8i 
 
 141 
 
 100 
 
 94 
 
 80 
 
 71 
 
 56 
 
 
 37 
 
 35 
 
 29 
 
 25 
 
 174 
 
 124 
 
 84 
 
 84 
 
 
 104 
 
 100 
 
 84 
 
 76 
 
 60 
 
 56 
 
 40 
 
 38 
 
 30 
 
 27 
 
 19 
 
 134 
 
 9 
 
 8| 
 
 156 
 
 in 
 
 104 
 
 89 
 
 78 
 
 63 
 
 57 
 
 42 
 
 39 
 
 32 
 
 29 
 
 20 
 
 14 
 
 10 
 
 9 
 
 168 
 
 1 20 
 
 112 
 
 96 
 
 84 
 
 67 
 
 61 
 
 45 
 
 42 
 
 34 
 
 31 
 
 21 
 
 15 
 
 104 
 
 
 180 
 
 127 
 
 116 
 
 IOI 
 
 90 
 
 71 
 
 65 
 
 47 
 
 45 
 
 35 
 
 32 
 
 22 
 
 16 
 
 ii 
 
 94 
 
 190 
 
 133 
 
 125 
 
 107 
 
 95 
 
 74 
 
 68 
 
 50 
 
 47 
 
 37 
 
 34 
 
 24 
 
 17 
 
 12 
 
 9 
 
 197 
 
 141 
 
 
 "3 
 
 99 
 
 79 
 
 72 
 
 52 
 
 50 
 
 39 
 
 36 
 
 25 
 
 IS 
 
 "4 
 
 10 
 
 208 
 
 148 
 
 140 
 
 1 20 
 
 104 
 
 83 
 
 75 
 
 55 
 
 52 
 
 42 
 
 38 
 
 26 
 
 19 
 
 13 
 
 Intensities marked white on black ground are illustrated in Fig. 48. 
 
 106 
 
In the annexed table the front and back depth must be divided by the 
 magnification given to the positive lens, if the same degree of definition 
 is required in the final image. 
 
 As the Telephotographic lens may be used with advantage in the 
 production of direct enlarged images of objects which are situated 
 approximately (or entirely) in one plane, we have included quite small 
 multiples of the focal lengths of the positive lenses in the above table. 
 These of course correspond to distances which are far too small for 
 rendering good perspective, or the pictorial representation of objects 
 lying in different planes. 
 
 The application of Table I. is obvious. 
 
 The application of Table II. is as follows: First select the stand- 
 point from which the amount of subject to be included upon the plate 
 appears in good perspective to the eye. Suppose the distance between 
 lens and subject, in a particular case, to be 10 ft. Now the focal length 
 of the positive element of the Telephotographic lens determines the 
 scale of the primary image at this particular distance, and its intensity 
 controls the front and back depth. Say the positive element is a 
 "Cabinet lens" of 12 inches focal length; the scale is then ^, or 18 
 inches in the length of the subject will occupy 2 inches in the primary 
 image. Beneath the column " 10 feet " in the table, and opposite the 
 lens of 12 inches focal length, we find both the scale of reproduction 
 and the front and back depth for a limit of indistinctness of -^-$ of an 
 inch. We must regulate the intensity by the amount of depth required. 
 Say this is 10 inches ; we find that at an intensity of f/6, that the com- 
 bined front and back depth is rather more than this. Hence at a 
 distance of 10 ft. the positive element of our combination, which has a 
 focal length of 1 2 inches, gives an image ^ the size of the object and 
 that a diaphragm of intensity //6 must be used for the required definition 
 throughout the image. 
 
 We may now proceed to consider the magnification to be given by 
 the negative element with which it is combined to form the Telepho- 
 tographic system. Let the negative element have a focal length of 
 6 inches, and suppose we wish to reproduce the object finally as half 
 
 107 
 
TELEPHOTOGRAPHY 
 
 size, or in the scale J. We must magnify the primary image 4J- times ; 
 to do this we set the screen 3^ times the focal length of the negative 
 lens from it, or at a distance of 2 1 inches. An adjustment between the 
 separation of the two elements will enable us to focus accurately upon 
 the screen in this position. 
 
 Any departure from the finest possible definition given by the 
 positive lens (not exceeding T ^Q of an inch) will be magnified 3J times 
 in the final image. This final degree of definition may or may not 
 suffice, according to the requirements of the case. For a large portrait 
 it will probably be sufficiently well defined, as the image will not be 
 viewed too closely. On the other hand, if an absolute degree of 
 definition is required through the depth of the image, equal to that in 
 the primary image for example, it will be necessary to select an 
 intensity which gives 4^- times the depth necessary for the positive 
 element. This is roughly given by dividing the intensity //6 by the 
 magnification to which the primary image has been subjected. 
 
 NOTES. 
 
 On the "Pupils" of a Lens-system. Let us first see how to 
 construct the images of a diaphragm which are formed by the 
 separate portions of a lens-system. In Fig. 55 the upper diagram 
 consists of a lens-system composed of two positive lenses, L lf L 2 re- 
 spectively, the stop s being situated midway between them. In order 
 to find the image of the stop formed by the lens L we draw a line 
 parallel to the axis meeting the lens L W which after refraction must pass 
 through its focal point /[ ; again a ray from the edge of the stop s 
 passing through the centre of the lens L X continues in a straight line ; 
 it will be seen that they meet in a point s x ; we thus find the image of 
 any stop s formed by the lens L x at s r Similarly we determine the 
 position of the image of the stop s formed by the component element 
 of the system L 3 situated behind the stop, and find its image in s,. 
 
 In the lower figure the front element of the system is a positive 
 lens, and the back element is a negative lens ; we construct the image 
 
 icS 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 of the stop s formed by the lens L X and find it at s x ; and using the 
 same construction as before for determining the image of the stop s 
 by the negative lens L 2 , we find its image at s 3 . 
 
 It will be observed that in all cases the stop images in these con- 
 structions are virtual images. It is evident that s 2 is the image of Sj 
 formed by the whole lens-system, and s, and S 2 are therefore conjugate 
 to one another ; so that any ray which passes through the image S 2 
 must before refraction necessarily have passed through s lt and hence a 
 
 FIG. 55 
 s 
 
 + L 
 
 +L. 
 
 + L. 
 
 1 -L. 
 
 stop or diaphragm in the position and of the size s 1 will have the same 
 practical effect in limiting the pencils which form the image as a stop 
 in the position and of the size of S 3 . Both have the same effect as the 
 actual stop s.* 
 
 When we have determined the position of these stop images we 
 are enabled to trace the actual course of the rays which pass through 
 any lens-system by an accurate and pretty geometrical construction, 
 and thus determine the image of any object. Referring to Fig. 55A, if 
 
 * Dr. S. Czapski, "Theorie der optischen instrumente nach Abbe," pp. 155, 156. 
 
 109 H 
 
TELEPHOTOGRAPHY 
 
 TABLE 
 
 TABLE OF FRONT AND 
 
 FOR AN OBJECT AT 
 
 DISTANCE OF OBJECT. 
 
 3 FEET. 
 
 4 FEET. 
 
 5 FEET. 
 
 6 FEET. 
 
 8 FEET. 
 
 - 
 
 
 
 X 
 
 
 
 j3 
 
 
 
 ^ 
 
 
 
 ^ 
 
 
 
 
 
 If" 5 
 
 7, 
 
 H 1 8 
 
 g-s! 
 
 g-S 
 
 H 1 8 
 
 
 "a g 
 
 i a 
 
 CX w 
 
 3.8 
 
 i a 
 
 s-j 
 
 e-SJ 
 
 n i a 
 
 O. <g 
 
 o.'S 
 
 01 g <U 
 
 MJ 
 
 
 
 0-g 
 
 0-5 
 
 
 
 " "o 
 
 "5 
 
 
 
 e| 
 
 S| 
 
 o 
 
 
 a-c 
 
 o 
 
 ^"S 
 
 ^ J= 
 
 THS 
 
 C 
 
 jiT 
 
 c 2 
 
 
 a 
 
 c.S 
 
 
 V 
 
 c.S 
 
 
 iT 
 
 " = 
 
 ^.S 
 
 r 
 
 C S 
 
 .5 
 
 o 1 *""" 
 
 c 
 
 , 
 
 2 n 
 
 rt C 
 
 5 
 
 Q n 
 
 a c 
 
 1 
 
 .B 
 
 a c 
 
 "rt 
 
 gs 
 
 a 
 
 rt 
 
 r 2. s 
 
 rt c 
 
 fa 
 
 
 to 
 
 fa'~ 
 
 pq - 
 
 to 
 
 fa"" 
 
 pq- 
 
 
 fa 
 
 " 
 
 t/5 
 
 fa'" 
 
 8 
 
 W 
 
 fa 
 
 M 
 
 *6" 
 
 F 
 
 I 
 "5 
 
 9 
 
 93 
 
 I 
 
 7 
 
 1.67 
 
 i.75 
 
 I 
 8 
 
 2.05 
 
 2.26 
 
 i 
 ii 
 
 3-73 
 
 4.21 
 
 I 
 
 64 
 
 71 
 
 
 F 
 
 
 
 
 I-I5 
 
 1.25 
 
 
 2.13 
 
 2.36 
 
 
 2.71 
 
 3.06 
 
 
 4.8 
 
 54 
 
 
 84 
 
 i of 
 
 
 F 
 IF 
 
 
 i-43 
 
 1.6 
 
 
 2.62 
 
 3 
 
 
 3-35 
 
 3.89 
 
 
 6 
 
 71 
 
 
 xoj 
 
 I3l 
 
 
 F 
 
 
 1-1 
 
 1-9 
 
 
 3-i 
 
 3-65 
 
 
 3-96 
 
 4.76 
 
 
 7 
 
 9 
 
 
 I2i 
 
 171 
 
 
 F 
 
 
 
 
 2.22 
 
 2.6 
 
 
 4-05 
 
 5.01 
 
 
 51 
 
 64 
 
 
 9 
 
 124 
 
 
 iSf 
 
 242 
 
 
 F 
 TO 
 
 
 2.7 
 
 3-33 
 
 
 4-94 
 
 6* 
 
 
 6| 
 
 84 
 
 
 ii 
 
 164 
 
 
 19 
 
 321 
 
 *8i 
 
 * 
 
 I 
 373 
 
 .42 
 
 43 
 
 i 
 478 
 
 .81 
 
 85 
 
 i 
 
 1-34 
 
 1.42 
 
 i 
 8 
 
 2.09 
 
 2.23 
 
 I 
 II 
 
 3-79 
 
 4.14 
 
 
 F 
 
 
 
 55 
 
 58 
 
 
 i. 08 
 
 1.14 
 
 
 1.77 
 
 1.9 
 
 
 275 
 
 3.01 
 
 
 4-99 
 
 54 
 
 
 J? 
 
 
 .69 
 
 73 
 
 
 1-34 
 
 1.44 
 
 
 2.2 
 
 2.4 
 
 
 3-41 
 
 3-8 
 
 
 61 
 
 7 
 
 
 F 
 
 
 .82 
 
 .87 
 
 
 1.6 
 
 1.74 
 
 
 2.62 
 
 2.91 
 
 
 4-05 
 
 4.62 
 
 
 71 
 
 82 
 
 
 F 
 
 
 1.09 
 
 1.24 
 
 
 2.1 
 
 2.4 
 
 
 3-43 
 
 3-96 
 
 
 51 
 
 61 
 
 
 94 
 
 12 
 
 
 F 
 TT7 
 
 
 r -35 
 
 1.49 
 
 
 2.6 
 
 2.99 
 
 
 4.22 
 
 5.04 
 
 
 64 
 
 8 
 
 
 4 
 
 I5i 
 
 *IO" 
 
 F 
 
 i 
 
 .28 
 
 .29 
 
 i 
 3-8 
 
 54 
 
 55 
 
 i 
 
 s" 
 
 .88 
 
 .91 
 
 i 
 
 672 
 
 31 
 
 i-37 
 
 I 
 
 876 
 
 2.41 
 
 2-55 
 
 
 F 
 4 
 
 
 36 
 
 38 
 
 
 71 
 
 74 
 
 
 1.17 
 
 1.22 
 
 
 1-73 
 
 1.83 
 
 
 3-18 
 
 3-43 
 
 
 F 
 5 
 
 
 45 
 
 47 
 
 
 .89 
 
 93 
 
 
 1-45 
 
 1-54 
 
 
 2.15 
 
 2.31 
 
 
 3-94 
 
 4-33 
 
 
 F 
 
 
 55 
 
 57 
 
 
 1.06 
 
 1. 12 
 
 
 i-73 
 
 1.86 
 
 
 2.56 
 
 2.8 
 
 
 4.68 
 
 5.26 
 
 
 F 
 
 
 .72 
 
 77 
 
 
 1.4 
 
 LSI 
 
 
 2.28 
 
 2.52 
 
 
 3-37 
 
 3-79 
 
 
 61 
 
 7i 
 
 
 F 
 
 TO" 
 
 
 9 
 
 97 
 
 
 1.74 
 
 I.9I 
 
 
 2.83 
 
 3-19 
 
 
 4.16 
 
 4.81 
 
 
 74 
 
 91 
 
 *I2" 
 
 F^ 
 
 i 
 
 2 
 
 17 
 
 .18 
 
 i 
 1 
 
 35 
 
 36 
 
 i 
 4 
 
 59 
 
 .6 
 
 i 
 5 
 
 .88 
 
 9i 
 
 i 
 7 
 
 1.64 
 
 1.71 
 
 
 F 
 
 
 
 23 
 
 .24 
 
 
 47 
 
 .48 
 
 
 78 
 
 .81 
 
 
 1.17 
 
 1.22 
 
 
 2.18 
 
 2.3 
 
 
 F 
 5 
 
 
 29 
 
 3 
 
 
 59 
 
 .6 
 
 
 .98 
 
 ..02 
 
 
 1.46 
 
 1-54 
 
 
 2.71 
 
 2.85 
 
 
 F 
 
 
 35 
 
 36 
 
 
 7 
 
 73 
 
 
 17 
 
 1.23 
 
 
 1.74 
 
 1.8 5 
 
 
 3-23 
 
 3-5 
 
 
 F 
 
 
 47 
 
 49 
 
 
 93 
 
 .98 
 
 
 55 
 
 .65 
 
 
 2.31 
 
 2-5 
 
 
 4.26 
 
 4-73 
 
 
 F 
 TIF 
 
 
 58 
 
 .61 
 
 
 .16 
 
 1.24 
 
 
 92 
 
 2.08 
 
 
 2.85 
 
 3-15 
 
 
 Si 
 
 6 
 
 These particular focal lengths are chosen as they 
 no 
 
 correspond to those of well known 
 into Telephotographic instruments 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 II 
 
 10 FEET. 
 
 12 FEET. 
 
 14 FEET. 
 
 16 FEET. 
 
 18 FEET. 
 
 20 FEET. 
 
 2t FEET. 
 
 Ml 
 
 s 
 
 r 
 
 3 
 
 Front depth 
 in inches. 
 
 Back depth 
 in inches. 
 
 MI 
 
 k 
 O 
 
 jT 
 
 1 
 
 j= 
 
 Is 
 -g 
 
 B.S 
 
 a 
 f* 
 
 Back depth 
 in inches. 
 
 "IS 
 o 
 oT 
 
 a 
 
 w 
 
 Front d-pth 
 in inches. 
 
 Back depth 
 in inches. 
 
 Ml 
 
 
 V 
 
 ~a 
 m 
 
 j= 
 
 &8 
 
 ^g 
 
 'a 
 
 u< - - 
 
 Back depth 
 in inches. 
 
 o 
 T 
 
 1 
 w 
 
 Front depth 
 in inches. 
 
 Back depth 
 in inches. 
 
 MI'S 
 
 b 
 
 O 
 
 T 
 
 1 
 
 OT 
 
 Front depth 
 in inches. 
 
 Back depth 
 in inches. 
 
 M|' 
 k 
 O 
 
 jT 
 
 OT 
 
 Front depth 
 in inches. 
 
 Back depth 
 in inches. 
 
 i 
 19" 
 
 104 
 
 I2f 
 
 I 
 23 
 
 Hf 
 
 i8i 
 
 I 
 
 27 
 
 2O 
 
 26| 
 
 I 
 TI 
 
 251 
 
 354 
 
 i 
 35 
 
 32 
 
 4 6 
 
 I 
 
 39 
 
 39 
 
 584 
 
 I 
 47 
 
 544 
 
 89 
 
 
 134 
 
 174 
 
 
 19 
 
 26^ 
 
 
 254 
 
 37i 
 
 
 32| 
 
 54 
 
 
 40| 
 
 66J 
 
 
 49i 
 
 85 
 
 
 684 
 
 I32| 
 
 
 16! 
 
 22| 
 
 
 23 
 
 344 
 
 
 3<f 
 
 49i 
 
 
 39i 
 
 674 
 
 
 484 
 
 90 
 
 
 584 
 
 117 
 
 
 804 
 
 1 88 
 
 
 19 
 
 284 
 
 
 26| 
 
 43* 
 
 
 354 
 
 63 
 
 
 45i 
 
 874 
 
 
 554 
 
 18 
 
 
 67 
 
 156 
 
 
 9i4 
 
 260^ 
 
 
 24 
 
 414 
 
 
 334 
 
 65 
 
 
 44 
 
 964 
 
 
 554 
 
 1384 
 
 
 68 
 
 194 
 
 
 814 
 
 2674 
 
 
 no 
 
 5 OI i 
 
 
 284 
 
 5' 
 
 
 394 
 
 92 
 
 
 su 
 
 141! 
 
 
 641 
 
 2124 
 
 
 78| 
 
 315 
 
 
 934 
 
 468 
 
 
 I2 5s 
 
 1128 
 
 i 
 14 
 
 6 
 
 6| 
 
 I 
 17 
 
 84 
 
 9i 
 
 I 
 20 
 
 iif 
 
 i3f 
 
 I 
 23 
 
 iSl 
 
 18 
 
 i 
 26 
 
 i9l 
 
 234 
 
 i 
 29 
 
 234 
 
 29i 
 
 i 
 35 
 
 334 
 
 434 
 
 
 7f 
 
 9 
 
 
 "i 
 
 134 
 
 
 i Si 
 
 i8| 
 
 
 i9i 
 
 25 
 
 
 2 4 | 
 
 32J 
 
 
 3oi 
 
 4Qf 
 
 
 43 
 
 61 
 
 
 9l 
 
 "4 
 
 
 US 
 
 174 
 
 
 i8| 
 
 24 
 
 
 24 
 
 32| 
 
 
 3oi 
 
 42 
 
 
 36| 
 
 53i 
 
 
 5if 
 
 804 
 
 
 "1 
 
 Hi 
 
 
 i6i 
 
 21 
 
 
 2l| 
 
 30 
 
 
 28| 
 
 4fc 
 
 
 35i 
 
 524 
 
 
 42| 
 
 66| 
 
 
 60 
 
 1024 
 
 
 144 
 
 194 
 
 
 2Of 
 
 291 
 
 
 28 
 
 4 2i 
 
 
 351 
 
 574 
 
 
 444 
 
 76 
 
 
 54 
 
 9 8i 
 
 
 74S 
 
 i54l 
 
 
 1 7| 
 
 251 
 
 
 25 
 
 39 
 
 
 334 
 
 564 
 
 
 42| 
 
 78 
 
 
 53 
 
 i4i 
 
 
 6 3 f 
 
 I36S 
 
 
 871 
 
 2234 
 
 i 
 ii 
 
 3-82 
 
 4.11 
 
 I 
 13^4 
 
 Si 
 
 6 
 
 I 
 
 15 
 
 7 
 
 74 
 
 I 
 18" 
 
 9i 
 
 ii 
 
 i 
 205 
 
 124 
 
 Hi 
 
 i 
 23 
 
 154 
 
 i7l 
 
 i 
 29 
 
 24 
 
 28| 
 
 
 5-4 
 
 5-54 
 
 
 71 
 
 81 
 
 
 9 
 
 IOJ 
 
 
 I2| 
 
 I4f 
 
 
 i61 
 
 I9i 
 
 
 20 
 
 244 
 
 
 3i 
 
 394 
 
 
 6J 
 
 7 
 
 
 9 
 
 IOJ 
 
 
 ii 
 
 13 
 
 
 154 
 
 19 
 
 
 20 
 
 24f 
 
 
 2 4 f 
 
 3ii 
 
 
 38 
 
 Sii 
 
 
 74 
 
 84 
 
 
 lOf 
 
 I2| 
 
 
 13 
 
 16 
 
 
 184 
 
 23i 
 
 
 234 
 
 3oi 
 
 
 29 
 
 38| 
 
 
 44i 
 
 634 
 
 
 94 
 
 iif 
 
 
 i3f 
 
 174 
 
 
 17 
 
 22 
 
 
 231 
 
 32i 
 
 
 30 
 
 424 
 
 
 37 
 
 544 
 
 
 56 
 
 9i4 
 
 
 nf 
 
 15 
 
 
 i6f 
 
 224 
 
 
 20| 
 
 284 
 
 
 28| 
 
 42i 
 
 
 36i 
 
 56 
 
 
 444 
 
 724 
 
 
 67 
 
 "44 
 
 i 
 
 9 
 
 2.63 
 
 2.77 
 
 i 
 II 
 
 3-84 
 
 4.08 
 
 I 
 J 3 
 
 51 
 
 54 
 
 i 
 IS 
 
 7 
 
 74 
 
 i 
 i? 
 
 8| 
 
 94 
 
 i 
 19 
 
 ii 
 
 12 
 
 i 
 2 3 
 
 154 
 
 174 
 
 
 3-48 
 
 3-72 
 
 
 5 
 
 *54 
 
 
 6| 
 
 74 
 
 
 9 
 
 IO 
 
 
 "4 
 
 13 
 
 
 Hi 
 
 i61 
 
 
 204 
 
 24 
 
 
 4-32 
 
 4-79 
 
 
 6i 
 
 7 
 
 
 84 
 
 94 
 
 
 ill 
 
 I2| 
 
 
 Hi 
 
 164 
 
 
 174 
 
 20f 
 
 
 25 
 
 304 
 
 
 5.14 
 
 5-69 
 
 
 74 
 
 84 
 
 
 iol 
 
 "4 
 
 
 i3l 
 
 '51 
 
 
 i6| 
 
 20 
 
 
 20f 
 
 25i 
 
 
 294 
 
 374 
 
 
 6| 
 
 71 
 
 
 91 
 
 114 
 
 
 13 
 
 15] 
 
 
 1 7| 
 
 211 
 
 
 2l| 
 
 271 
 
 
 26| 
 
 35 
 
 
 38 
 
 524 
 
 
 81 
 
 91 
 
 
 12 
 
 144 
 
 
 16 
 
 2O 
 
 
 211 
 
 2 7 | 
 
 
 264 
 
 36 
 
 
 324 
 
 454 
 
 
 46 
 
 69 
 
 Carte de Visile and Cabinet lenses of high intensity, and are well suited for conversion 
 for taking large portraits in the studio. 
 
 Ill 
 
TELEPHOTOGRAPHY 
 
 112 
 
USE AND EFFECTS OF DIAPHRAGM 
 
 from a point o in the object plane o x oo 3 we draw a pencil of rays to 
 the edge of the image of the stop s formed by the front lens at s v it 
 will be found to cut the lens L : at the points A A ; the actual course of 
 the rays, after passing this lens, will be through the edge of the stop s 
 itself, in the direction A B, A B meeting the lens L 3 at B B. These rays 
 emerge from the lens L 2 as though they had proceeded from the image 
 of the stop s formed by the back lens at S 2 , and meet in the point i of 
 the image. Professor Abbe defines the image of the stop s formed at 
 Sj which appears from o under the smallest angle (2 u) as the "entrance 
 pupil " (eintritts pupille) of the system ; similarly the stop whose image 
 s 2 appears from i under the smallest angle (2 u) he terms the (austritts 
 pupille) "exit pupil." 
 
 In a similar manner to that employed for tracing the course of the 
 pencil of rays from o through the entire system, we may construct the 
 image formed by any points o : O 3 in the plane of the object forming 
 images at i : i 3 respectively ; the dotted lines in the figure indicate the 
 construction. It is evident that o : and O 2 may occupy positions such 
 that rays proceeding from objects further from the axis cannot emerge 
 from the lens at all ; when o : and o 2 are situated in such positions that 
 rays proceeding from them can only just emerge through the entire 
 system, o 1 O 2 will appear from the centre of the "entrance pupil" s x 
 under an angle 2 w ; 2 w determines the angle of the field included by the 
 lens. The image i^i 2 forms an angle 2 w x from the centre of the " exit 
 pupil " s 2 , and appears from it under the smallest angle. 
 
 We thus find that all the pencils of a system are of two kinds : 
 
 (1) those which have their common base in one of the "pupils" and 
 their apices in either the field of the object or the field of the image ; 
 
 (2) those which have their common bases in either the object or the 
 image, and their apices in the corresponding " pupil." 
 
CHAPTER VII 
 PRACTICAL APPLICATIONS OF THE TELEPHOTOGRAPHIC LENS 
 
 I. IN PORTRAITURE 
 
 IT is probably a matter of common observation that the finest portraits 
 are produced by photographers having the advantage of a long studio. 
 
 Where the studio is sufficiently long, the photographer is always 
 able to take up a standpoint from which a study of a head, head and 
 shoulders, and so on to full length of the figure, is seen to the best 
 advantage. In general, the distance must be increased as the amount 
 and depth of subject which he intends to portray increases. 
 
 In order to do himself and his subject justice, these distances should 
 never be departed from, whatever the scale of the image is to be. The 
 lens should be placed at the correct viewing distance, and the focal 
 length of the lens chosen to give the scale required, determining the 
 size of the final image. 
 
 No one positive lens of ordinary construction and definite focal 
 length can answer all purposes satisfactorily. If the focal length be 
 great, suitable for a "life-size" head for example, the lens would be 
 quite unsuitable for taking a " Cabinet " standing figure, because it would 
 have to be removed so far from the subject that the image would appear 
 flat. Conversely, if a lens of shorter focal length, suitable for the 
 " Cabinet " standing figure, were employed to take a " life-size " head, 
 it would have to be brought so close to the sitter that the drawing of 
 the head would be altogether unsatisfactory. 
 
 The general tendency in ordinary photographic practice is to 
 
 114 
 
PRACTICAL APPLICATIONS OF LENS 
 
 commit the latter error viz., to aim at too large an image with a lens 
 which is too short in focal length to allow an adequate distance to 
 intervene between the subject and lens for good perspective rendering. 
 
 The Telephotographic lens affords the great advantage of always 
 enabling the larger sizes of portraits to be taken under favourable 
 conditions for proper perspective rendering. Again, its perspective is 
 always better than that given by an ordinary positive system of the 
 same focal length due to the greater distance that may intervene 
 between subject and lens. 
 
 Let us now illustrate some comparative examples of the employ- 
 ment of ordinary and Telephotographic constructions. 
 
 The production of a "life-size" head : We know that to accomplish 
 this with an ordinary lens the sitter must be at a distance equal to 
 twice the focal length of the lens from it. Suppose we take a lens of 
 
 Tf 
 
 5 inches diameter and 40 inches focal length (intensity -) ; the distance 
 
 o 
 
 of the sitter from the lens must be 80 inches, and the camera extension 
 also 80 inches. A distance of 80 inches is none too far for good per- 
 spective rendering, and yet it is seldom that even this distance intervenes 
 between lens and sitter for a " life-size" head, because the focal lengths 
 of most large portrait combinations are less than half this distance, or 
 40 inches. 
 
 Let us now form a Telephotographic lens by combining a rapid 
 cabinet lens of 3^- inches diameter and 10 inches focal length with a 
 negative lens of 4 inches focal length, as illustrated in Fig. 56. 
 
 If we place the combination at the same distance (80 inches) from 
 the sitter, the positive element alone gives an image ^ the size of the 
 original. In order that the final image may be of the same size as the 
 original, we must magnify it seven times. To do so, the focusing 
 screen must be placed at a distance E from the negative lens, where 
 E=/^ (M i)=4 (7 1) = 24 inches, as compared with 80 inches above, 
 see (13). On adjusting the separation between the lenses by means of 
 the rack and pinion mount, the image will now be found to be of the 
 same size as the original. To compare our present conditions for 
 
 "5 
 
TELEPHOTOGRAPHY 
 
 rapidity with those above, we must determine the focal length of the 
 combination when thus employed. Substituting in (18) p. 75 where 
 
 10 
 
 1 = 24, m = 2^,/ 1 = 10 and N (for equal size) = 
 Focal length 
 
 m E 
 
 N 
 
 60 + 10 
 
 * + 
 
 I 
 
 = 20 inches only, 
 
 and hence this combination will work at the same initial intensity as the 
 former with an aperture of only 2 j- inches. 
 
 FIG. 56. 
 
 m small m high 
 
 Observe that as the lens produces the image of equal size with the 
 object, the position of the screen must be 20 inches distant from its 
 focal point, or focus for parallel rays. In other words, the combination 
 focused for a very distant object would form an image at a distance of 
 24 20, or 4 inches from the negative lens. For parallel rays we see 
 from (13) F = m E-f/j= 10 + 10=20 inches, and our conclusion is con- 
 firmed. 
 
 From this result we can proceed to emphasise the valuable and 
 important fact that a greater distance must intervene between a 
 Telephotographic lens and the subject than is required for an ordinary 
 
 116 
 
PLATE XXI 
 
 Facade, San Michele, Lucca. Taken with an ordinary lens 12-in. focal 
 length. (Copyright of and kindly lent by J. W. Cruichshanh, Esq.) 
 
PLATE XXII 
 
 South-West Corner, Second and Third Stories of Fa?ade, San 
 Michele, Lucca. Taken with 6-in. Ross Universal Symmetrical with 3-in. 
 negative, i8J in. in draw from back of lens to plate. Stopped down to T ^, 
 56 seconds exposure. (Copyright of and kindly lent by J. W. Cruichshank, Esq.) 
 
PRACTICAL APPLICATIONS OF LENS 
 
 lens of the same focal length. With the former we have found 80 
 inches is required, while with the latter it must be twice 20, or 40 
 inches. These results also exemplify in a striking manner the fallacy 
 of the usual tenet that the correct viewing distance of the photograph 
 should be determined by the focal length of the lens with which it was 
 taken. The result by the 2O-inch Telephotographic lens and the 40- 
 inch lens of ordinary construction should of course be viewed from the 
 same standpoint when the result is "life-size " ; and, again, we see that 
 if both lenses have the same focal length the result produced by a lens 
 of ordinary construction should be viewed at a distance of 40 inches 
 only as against 80 inches by the Telephotographic system. The latter 
 is the more likely distance from which a " life-size " head w r ould be 
 viewed, and the result by the Telephotographic lens will appear in 
 better drawing and be a more truthful representation. 
 
 Although there is a considerable gain in using the Telephoto- 
 graphic lens, both as regards improved perspective and greater depth 
 of focus, as compared with the lens of ordinary construction, there is a 
 loss in rapidity when two lenses of the same focal length are compared. 
 The comparative rapidities are now influenced by the " law of inverse 
 squares " and their exposures are proportional to the squares of their 
 respective distances from the subject. We have seen, however, that a 
 Telephotographic lens of considerably shorter focal length than an 
 ordinary lens can produce the same size of image at an equal distance, 
 and hence the diameter of the positive element in the Telephoto- 
 graphic system may be smaller and yet give the same rapidity ; this 
 will be found both an advantage and an economy. 
 
 Reverting to the case of a ''life-size " representation of a head, it 
 is obvious that the distance of 80 inches is not by any means binding 
 in the case of one and the same Telephotographic combination. Both 
 theoretically and practically this lens may be placed at any greater 
 distance we choose from the sitter. If a greater distance be chosen 
 the scale of the image produced by its positive element becomes smaller 
 and therefore requires greater magnification by its negative element in 
 order to yield the same size of image finally. 
 
TELEPHOTOGRAPHY 
 
 It is probable that a distance of 10 or 12 ft. will be chosen tor the 
 representation of a "life-size" head. At 10 ft., employing a Tele- 
 photographic lens composed of a cabinet lens of say 1 2 inches focal 
 length and 4 inches aperture as positive element, and a negative lens 
 of 6 inches focal length as negative element (to vary the numerical 
 examples), the primary image will be ^ of the original, and we must 
 magnify it nine times for equal size. This requires a camera extension 
 of 6 (91) = 48 inches, which shows from (i 8) that the lens has a focal 
 length of 36 inches, and therefore an initial intensity of fjg. 
 
 If we wish to produce the image in the scale of half natural size, 
 it is evident that all we have to do is to magnify the image 4^- times. 
 In this case we must take the camera extension 6 (4^- i) or 21 inches. 
 The focal length of the system is now 26 inches, and the intensity 
 
 = JL 
 
 26 " 6.5' 
 
 It is hardly possible to give any hard and fast rules for the method 
 of procedure in the various requirements of large portraiture, but it 
 may safely be said that if a certain carte de viste or cabinet lens pro- 
 duces the size of image for which it was constructed at a given distance 
 from the sitter, in really satisfactory perspective, these images may be 
 taken as the basis of subsequent magnification by the negative elements 
 with which they are combined to form Telephotographic systems. It 
 is hoped that Table II. (p. no) may be of considerable assistance in 
 this respect. 
 
 The magnification of the primary image produced by the positive 
 element can be accomplished in either of two ways : (i) By using a 
 negative element of very short focal length in comparison to the 
 positive element, or, in other words, making -^. 1 , or m, great, and using 
 
 J 2 
 
 only a very small camera extension ; or (2) by using a negative lens 
 of longer focal length, or making m small, and obtaining the same 
 magnification by the necessarily greater camera extension. The latter 
 method is far preferable in portraiture, and, in fact, in almost all cases, 
 as the conditions favour greater covering power, more even illumina- 
 tion, and freedom from distortion of the lines near the margin. For 
 
 i*8 
 
PRACTICAL APPLICATIONS OF LENS 
 
 portraiture the focal length of the positive element should not be more 
 than 2 to 2\ times as great as that of the negative lens, or m should 
 not exceed 2^. 
 
 Plates I. and II. show a nearly full-length portrait of a child ; 
 Plate I. was taken at a distance of 10 ft. with an ordinary cabinet lens 
 constructed for a short studio; Plate II. was taken by a c. de v. lens 
 of 83- inches focal length, combined with a negative lens of about half 
 its focal length, at a distance of 24 ft. The difference in the drawing 
 is apparent ; in Plate I. the hand and flower are too large, the back- 
 ground falls away too rapidly and appears too small, and the pedestal 
 is out of drawing; in Plate II. the relative planes of the picture take 
 their proper proportions. Plate III. illustrates a cabinet head, taken 
 by the same Telephotographic combination at a distance of 15 ft. 
 Again Plate IV. was also taken by the same Telephotographic com- 
 bination at a distance of 10 ft. (N.B. It could have been as sharp as 
 desired ; the method of producing the soft effect is referred to later), 
 and Plate V. was taken by a skilful professional photographer, 
 Mr. Habgood of Boscombe, who was asked to produce a head of the 
 same size by his ordinary methods. He naturally selected the lens of 
 the greatest focal length in his possession (a rapid rectilinear of 16 inches 
 focal length) for the purpose. The distortion of the features in this 
 presentment, as the lens had to be brought within 4 ft. of the sitter, is 
 apparent ; the face appearing " bulged " and the size of the mouth 
 distinctly exaggerated. Both negatives were purposely left untouched. 
 
 In addition to the precautions necessary for giving good perspective 
 rendering in the image, the ill-effects of distortion in the lens itself 
 must be carefully guarded against. For this reason the author gives 
 preference to a non-distorting, well-corrected compound positive element, 
 as against a single cemented lens of high intensity. Messrs. Zeiss 
 have recently introduced a very interesting single cemented lens, 
 illustrated in Fig. 57, which has the same high intensity as a portrait 
 combination fj$. This is designed for combination with a single 
 cemented negative lens illustrated in the same figure, in which m is 
 advisedly kept small (as in such a combination, where the diaphragm is 
 
 119 
 
TELEPHOTOGRAPHY 
 
 placed between the combinations, the distortion increases as m increases), 
 and the photographer is warned not to utilise its covering power to the 
 limits on account of the unavoidable distortion produced at and near 
 the margins. Messrs. Zeiss describe the practical working of this lens, 
 as they do that of all their Telephotographic lenses, in accordance with 
 the method of treating the system under heading A., Chapter V. 
 Dr. Rudolph, in his " Monograph " already referred to, furnishes a 
 
 FIG. 57. 
 
 number of tables applied to particular constructions manufactured by 
 the^firm. 
 
 Dr. Miethe, of Messrs. Voigtlancler, Brunswick, adopts the method 
 of employing a portrait combination of high intensity as positive 
 element, added to a triple cemented negative, in his constructions 
 destined for large portraiture in the studio. 
 
 There is a theoretical advantage as regards the brilliancy of the 
 image, by keeping the number of reflecting surfaces in any optical 
 combination as small as possible ; and the construction of Messrs. Zeiss 
 fulfils this condition in reducing them to the minimum. 
 
 The degree of brilliancy due to a greater or less number of reflect- 
 
 120 
 
PRACTICAL APPLICATIONS OF LENS 
 
 ing surfaces is at least difficult to trace in practical photographic work,, 
 particularly in the studio. 
 
 Soft Effects in large Portraititre. Since the early sixties a con- 
 siderable number of photographers, aiming at artistic effects, have 
 sought a softer degree of definition than is given by a perfectly 
 corrected photographic lens. The latter defines too well for their 
 purpose, and, in fact, shows up facial defects which are not even visible 
 to the eye, some, indeed, being beneath the skin. In this case the 
 retoucher's skill must be requisitioned, and upon this, if artistically 
 
 Fie. 58. 
 
 applied, will the true likeness largely depend, even more perhaps than 
 upon the drawing originally given by the lens. 
 
 In the portrait lens designed by the late J. H. Dallmeyer, a 
 mechanical means of adjustment was given in order that the image 
 might gradually depart from keen definition to an increasing softness 
 in the image. This device introduces what is technically known as 
 " Spherical Aberration." Fig. 58 roughly indicates how the effect is 
 produced, (i) and (2) represent the posterior portion of the portrait 
 combination. In (i) the lenses are very close together, and the rays 
 leaving the combination converge accurately to a point, the focus. In 
 
 121 
 
TELEPHOTOGRAPHY 
 
 (2) the lenses are separated from their normal position by unscrewing 
 the hindermost lens, and the rays no longer converge accurately to one 
 point ; those refracted from the margin of the lens cross the axis nearer 
 to the lens than those near the centre. The position where the image 
 of any point in object is now best defined is no longer a point, but a 
 small bundle of rays. Now points in the object situated on either side 
 of the chief point or plane focused upon are represented in (i) by 
 circles of indistinctness which contrast strongly with the finest defini- 
 tion in the chief plane focused for ; in (2) by circles of indistinctness 
 which have far less contrast with the definition in the chief plane 
 focused for. The result by (i) may be compared to a drawing in 
 which one plane is drawn by a finely pointed hard pencil and the rest 
 by blunter points of the same pencil : the result by (2) may be com- 
 pared to a drawing produced throughout by a blunt-pointed soft pencil. 
 So that by sacrificing fine definition in one plane, we produce a softer 
 but more uniform type of definition, which gives the appearance of 
 greater "depth of focus." This softening, due to the introduction of 
 spherical aberration, does not destroy the modelling of the subject, nor 
 detract from the massing of light and shade, but greatly reduces and 
 frequently eliminates the necessity for retouching. 
 
 If a portrait lens of this type forms the positive element of a Tele- 
 photographic system we can produce a soft primary image and enlarge 
 it by the negative element. The results will seldom require the 
 retoucher's aid, and yet faithfully portray the leading characteristics 
 in the features of the subject. Plate V. was produced in this manner 
 but should not be viewed from too near a standpoint. 
 
 In 1893 Mr- J. S. Bergheim carried out some interesting and 
 original experiments by combining single uncorrected positive and 
 negative lenses with a view of suppressing unnecessary detail and 
 aiming at a "quality" in definition he deemed better than that given 
 by corrected lenses. His "Cinderella," for example, shown at the 
 Royal Photographic Society's Exhibition in 1894, showed what his 
 lens was capable of doing in the hands of an artist. 
 
 Mr. Bergheim placed the results of his investigations at the author's 
 
 122 
 
PRACTICAL APPLICATIONS OF LENS 
 
 disposal for development. Fig. 59 illustrates the lens in its present 
 form, showing the single uncorrected lenses of which it is composed. 
 By placing the diaphragm in front of the front lens, distortion is 
 eliminated. In this construction m is very low, and hence it has been 
 possible to make the back single lens of rather larger diameter than the 
 front, enabling a large amount of subject to be included upon the plate 
 when the camera extension is considerable. 
 
 Rigidity and considerable variation in the camera extension are 
 essential in a camera for studio work ; Fig. 60 illustrates the type of 
 
 camera and stand suitable for the purpose when large plates are to be 
 covered. The ordinary studio camera, in which there is the usual 
 amount of extension, will answer for the purpose of producing large 
 heads such as those to which reference has been made. 
 
 II. MEDICAL AND SURGICAL PHOTOGRAPHY 
 
 Hitherto the application of photography to the sciences of medicine 
 and surgery has been somewhat limited on account of the necessity of 
 bringing the lens very near to the subject in order to obtain images 
 sufficiently large to show the necessary details. When a lens is brought 
 in close proximity to the subject, it has been found that inconveniences, 
 
 123 
 
TELEPHOTOGRAPHY 
 
 such as breathing upon the lens, nervousness in the subject, the 
 obstruction of light caused by the instrument itself, the lack of depth of 
 definition, &c., have interfered with an otherwise valuable practice. 
 The increased distance between object and lens rendered possible by 
 use of the Telephotographic combination enables the surgeon to obtain 
 
 FIG. 60. 
 
 Studio Camera suitably mounted on heavy square table stand, for 
 use in telephotographic portraiture. 
 
 records of operations, skin diseases, and various phases of changed 
 conditions in disease, &c., which were formerly practically impossible. 
 The author has only indicated the application to this branch of 
 photography in photographs of the human eye taken under quite 
 ordinary conditions. Plate VI. shows two eyes of children, natural 
 size, and an adult eye enlarged, but taken direct. In each case the 
 
 124 
 
PRACTICAL APPLICATIONS OF LENS 
 
 lens was 4 ft. from the subject. For a reduced scale in the image it is 
 obvious that a considerable distance may intervene between the lens 
 and the subject to be photographed. High intensity in the positive 
 element of the system is of course essential. 
 
 III. GROUPS AND HAND-CAMERA WORK BY MEANS OF THE 
 TELEPHOTOGRAPHIC LENS 
 
 It will have been observed from the premisses that if we include a 
 foreground subject, such as a figure, under a large angle, we must, in 
 order to obtain a sufficiently large image from a given standpoint, 
 necessarily include a large angle of subject in the receding planes, which 
 become dwarfed and insignificant in value. The further we remove the 
 lens from the foreground of our subject, the smaller is the angle under 
 which it is seen or photographed, and the receding planes have now 
 greater importance than in the former case, although the whole is in a 
 diminished scale. If by the Telephotographic lens we make the 
 subject in the foreground of the same size as before at this greater 
 distance, it is obvious that very much less subject will be included in 
 the receding planes, and that they will be rendered in a larger scale 
 than before, possessing due importance. 
 
 One frequently notices in a group of figures produced by ordinary 
 photographic means, the rapid diminution in the scale of the images of 
 persons in the receding planes of the group. This is easily obviated 
 with the Telephotographic combination, by taking up a position in 
 which the individuals forming the group are represented more nearly 
 equal in size, and producing the required scale in the final image by the 
 magnification obtained by the negative element of the system in con- 
 junction with the requisite camera extension. 
 
 Ordinary common-sense considerations will enable the photographer 
 readily to grasp the bearing of this subject. If we observe from a 
 distance a moving object, such as a railway train, travelling directly in 
 a line towards us, an advance in our direction of a hundred yards or so 
 seems to make but very little difference in the size of the object itself ; 
 
 125 i 
 
TELEPHOTOGRAPHY 
 
 but as it continues to approach, equal increments of distance have 
 a greater and greater effect upon its appearance in perspective drawing 
 until, when it is so near that its distance from us is some small multiple 
 only of its entire length, the perspective in which it is seen alters 
 rapidly. The problem which the photographer has to solve in every 
 case where there is considerable depth in his subject is : how far from 
 the foreground his standpoint should be in order to maintain the 
 perspective rendering in a degree which is not overdone in either of the 
 two directions possible. On the one hand, by loss of perspective in 
 taking the subject from too distant a standpoint, and thus diminishing 
 the due effect of distance ; or, on the other, by choosing too near a 
 standpoint and so causing the receding planes of his picture to 
 diminish too rapidly in scale, and thereby unduly extending the effect 
 of distance. For the purpose of picture making, irrespective of truthful 
 representation of the subject, the former error is the less objectionable. 
 It must be noted that the perspective effect can be readily observed in 
 the image formed by the positive lens alone, a small portion of the 
 image near the centre of the plate only being considered. When the 
 perspective effect of this small central portion is found satisfactory, the 
 photographer will then increase its scale by means of the negative 
 element of his Telephotographic system, and thus cause that small 
 portion to fill the entire plate on the enlarged scale. 
 
 The Telephotographic lens applied to the hand-camera enables the 
 photographer not only to obtain a larger scale in the image than is 
 possible with a lens of ordinary construction, using the same camera 
 extension, but also to produce the same scale given by the latter at a 
 greater distance, with the accompanying improved perspective rendering. 
 To give an example : suppose we take as our positive element a small 
 portrait combination working at //3 of 5 inches focal length, and com- 
 bine it with a negative element of 2 J inches focal length, and set the 
 screen at a distance of 5 inches from the negative element, we shall 
 produce an image three times as large as that given by the 5-inch lens 
 alone. In the case of ordinary studies of figure subjects we shall now 
 be able to take up a standpoint three times as far as would be neces- 
 
 126 
 
PRACTICAL APPLICATIONS OF LENS 
 
 sary to produce the same size of image with the 5-inch lens. The 
 drawing will be vastly better, even in the foreground of the subject, 
 and the receding planes will have much more importance and will not 
 diminish in size so rapidly, while the amount of subject included in the 
 background will of course be considerably less, and generally contribute 
 to a more pictorial effect. With the lens we have described, the size 
 of the image will correspond to that given by an ordinary lens of 1 5 
 
 FIG. 61. 
 
 Telephotographic Hand-camera, which may be used with positive 
 lens alone, by placing dark slide in the opening nearest the lens, or two 
 degrees of magnification may be obtained when using the telephoto 
 attachment by placing the slide in one of the other openings. 
 
 inches focal length, and as the positive element works at an initial 
 intensity of ff$, and its image has been subjected to a magnification of 
 three times, the combination will work at an intensity of fig, which is 
 sufficiently rapid for the ordinary requirements of "instantaneous" 
 hand-camera work. Many useful developments in this branch of 
 photography suggest themselves. Fig. 61 represents a hand-camera 
 in which the positive element is a stigmatic portrait lens of 6 inches 
 focal length combined with a negative element of 3 inches focal length. 
 The box of the camera admits of a separation of 9 inches between the 
 negative lens and the screen, thus giving a magnification of four times 
 
 127 
 
TELEPHOTOGRAPHY 
 
 to the image produced by the positive lens alone. We thus have 
 an image equal in size to that produced by an ordinary lens of 24 
 inches focal length which works at an intensity of //i6. A camera of 
 this kind is a veritable "detective" camera, and is valuable for render- 
 ing large images on small plates in studies of animal and bird life, 
 ships at sea, distant mountain scenery, &c., and generally in all cases 
 where the rendering of distance is inadequate with the ordinary hand- 
 camera. 
 
 IV. Telephotography for distant Subjects. The application of the 
 Telephotographic lens for photographing distant objects has been that 
 most generally employed. In this connection the Telephotographic 
 lens does not differ in its performance from a lens of ordinary construc- 
 tion of the same focal length, but its advantage over the latter lies in 
 the fact that we may produce very large images corresponding to those 
 given by lenses of very great focal length without the necessity for the 
 accompanying great camera extension which the latter involve. The 
 fact that almost any positive system may be converted into a Tele- 
 photographic combination by combining it with a negative element 
 whose function is simply to magnify the primary image has made the 
 practice of Telephotography both wide-spread and popular. 
 
 It is preferable that the positive element composing the system 
 should have at any rate an intensity not less than// 8 for the reason 
 given in Chapter VI., viz., that the limit of magnification which may 
 be given to the image produced by it is comparatively small, without 
 introducing the deleterious effect of diffraction. This, as we have said, 
 commences to assert itself when the intensity of the compound system 
 is below//7i. 
 
 It is obvious, then, that the effective aperture of the positive 
 element controls the limit of magnification, corresponding to a certain 
 equivalent focal length, which must not be exceeded. The equivalent 
 lens must not be more than 71 times the effective aperture of the 
 positive system ; so that if very high magnification is desired, our 
 positive element must be large in diameter. A positive lens of i-inch 
 aperture must never be converted into a Telephotographic system in 
 
 128 
 
PRACTICAL APPLICATIONS OF LENS 
 
 which an equivalent focal length of more than 6 ft. should be brought 
 about ; with a 2-inch positive lens, 12 ft, and so on. 
 
 The particular constructions which have been designed for the 
 purpose include as positive elements : portrait lenses, any non-distort- 
 ing doublet, such as a rapid rectilinear, the antiplanat, anastigmatic, 
 stigmatic, &c. We will now shortly describe the various Telephoto- 
 graphic constructions which are in use. 
 
 The author's original construction (1891) consisted of a single 
 cemented positive element of high intensity combined with a single 
 
 FIG. 62. 
 
 Stigmatic lens converted into Telephotographic lens of 
 moderate power by the addition of a negative lens of | its focal 
 length, y- = m = 2. 
 
 cemented negative element, with a diaphragm placed between the 
 combinations, The inherent defect of pincushion distortion led him to 
 abandon this form of combination. The chief aim, when the Tele- 
 photographic construction was first made, was to dwell on the 
 astounding results produced by high magnification ; and, as already 
 pointed out, if the ratio of the focal lengths of the elements composing 
 the system, or m t is high, the distortion is so palpable as to render its 
 employment highly undesirable. He therefore substituted either a 
 portrait combination of high intensity, fj$ t or any other non-distorting 
 combination as positive element, of an intensity not less than//8, com- 
 
 129 
 
TELEPHOTOGRAPHY 
 
 bining it with a double combination negative element as illustrated in 
 Fig. 62. This form of negative element was constructed to give the 
 greatest freedom from distortion, and was found preferable to the single 
 cemented (triple) combination formerly employed. By employing the 
 portrait lens already referred to, in which the spherical correction is 
 adjustable, the author was enabled to produce a Telephotographic 
 system which is perfectly corrected or able to produce sharp images of 
 either near or distant objects. When the positive element of the 
 system is combined with a negative lens for the purpose of attaining 
 high magnification, the spherical correction cannot be perfect for both 
 
 FIG. 62A. 
 
 near and distant objects, unless some means be given to regulate the 
 spherical correction. When this is not possible, it is obvious that the 
 only means of attaining a high degree of definition is by use of the 
 diaphragm, involving a loss in rapidity. In the author's combination, 
 the system is corrected to give the finest definition on a moderately 
 near object ; but if it be employed for photographing a very distant 
 object, a slight unscrewing of the back element of the portrait combina- 
 tion will adjust the spherical correction. The necessity for this is most 
 apparent when a high power is employed. The stigmatic lens of 
 intensity y/4 also has this means of adjustment, rendering it eminently 
 suitable for the positive element of a Telephotographic system. 
 
 130 
 
PRACTICAL APPLICATIONS OF LENS 
 
 Messrs. Steinheil of Munich have given considerable attention to 
 various types of instrument in which the negative enlarging lens is 
 employed. They have produced interesting telescopes of great com- 
 pactness and yet possessing high power, the magnification being 
 arrived at by the employment of a negative enlarging system which 
 increases the focal length of the object glass without necessitating a 
 long telescope tube. Messrs. Steinheil also construct telescopes for 
 
 FIG. 63. 
 
 photographic purposes on the same principle, which are designed for 
 high magnification, but to include only a very small angle. For 
 ordinary Telephotographic work, they combine their Group Antiplanat 
 as positive element with a triple cemented negative as shown in Fig. 62A. 
 
 Messrs. Zeiss of Jena construct two types of a Telephotographic lens. 
 We have already referred to the form designed for portraiture illus- 
 trated in Fig. 57. They recommend their double anastigmat combined 
 with a triple cemented negative lens for all cases in which distortion is 
 inadmissible. This combination is illustrated in Fig. 63. 
 
 It will be observed that the same negative lens is used in both 
 
TELEPHOTOGRAPHY 
 
 cases ; if combined with the single cemented positive lens the curved 
 surface faces the ground glass, but when used in conjunction with a 
 double combination the flat surface is directed to the ground glass. 
 The mounting of this lens has an engraved scale in millimetres which 
 can be read off showing the interval (d of the formula) from which the 
 equivalent focal length of the system can be calculated for any given 
 separation. It is obtained by multiplying the focal lengths of the 
 component lenses together and dividing by the interval which can be 
 read off on the one hand, or set to produce a desired focal length on 
 the other. 
 
 FIG. 64. 
 
 Dr. Miethe in his Telephotographic construction for all ordinary 
 purposes in which distortion is inadmissible, employs a Collinear lens as 
 the positive element, combining it with a triple cemented negative lens 
 as illustrated in Fig. 64. 
 
 We will now call attention to some of the many other applications 
 of the Telephotographic lens in distant photography. 
 
 (i) In astronomical work the method of direct enlargement by a 
 negative lens corrected for photographic purposes has of late years 
 superseded the former method of secondary magnification by means of 
 a second positive lens. Plates VII. and VIII. illustrate the applica- 
 tion of the negative lens to large telescopes, increasing their focal 
 length in order to produce a larger direct image. In solar photography 
 
 132 
 
PRACTICAL APPLICATIONS OF LENS 
 
 generally, the exposures are so short that good results may be obtained 
 with an ordinary camera which is not mounted equatorially, and valu- 
 able records of important sun spots and partial or total eclipses of the 
 sun may be readily obtained in ordinary photographic practice. The 
 diameter of the image given of the sun or moon is approximately T V of 
 an inch for every 10 inches of focal length, and it is readily seen that 
 almost any Telephotographic system will enable us to produce an 
 image of sufficient size to be of interest. 
 
 In lunar photography, however, it is not possible to attain a very 
 high degree of definition, owing to the apparent complex movement 
 of the moon during the period of exposure which is necessary for 
 obtaining a good negative ; but, nevertheless, records of partial and 
 total eclipses of the moon in progress are sufficiently well defined to 
 be in themselves interesting. A few years ago the author exhibited 
 some lunar photographs at the Camera Club, which have been referred 
 to as warranting further efforts in this direction. 
 
 (2) The value of the instrument in photographing distant mountain 
 scenery is already well known and much practised. The author has 
 reproduced as the frontispiece a reduced copy of the historical photo- 
 graph by M. Boissonas of Geneva, taken at a distance of 44 miles 
 direct in a camera of 5 ft. extension on a 20 x 16 plate. In order 
 that the same size of image could be produced by a lens of ordinary 
 construction a camera 25 ft. in length would have had to be employed. 
 Plates IX. and X. show more modest results with a quarter-plate 
 camera, which can be carried by any enthusiastic mountain climber. 
 
 (3) Plates XI. and XII. exhibit the application to long-distance 
 photography generally, and are purposely included as examples of 
 what can be accomplished across the water, even in this climate, where 
 atmospheric conditions are seldom favourable. This leads us to say 
 that the application of the Telephotographic lens in distant photography, 
 even when atmospheric conditions are unfavourable, enables us fre- 
 quently to obtain results which are far more distinct than the impression 
 given to the eye. 
 
 (4) The geologist will appreciate the results shown in the compara- 
 
TELEPHOTOGRAPHY 
 
 tive work illustrated in Plates XIII. and XIV. In this case the cliff 
 is at a distance of more than five hundred yards from the camera, and 
 the details shown will point to the application of the Telephotographic 
 lens to studies of geological formations which are inaccessible. 
 
 (5) The application of the lens to balloon photography is illustrated 
 in Plate XV., XVI., and XVII. In this application it is needless to 
 say that the positive element of the combination must have a very high 
 intensity. The instrument designed by the author for this purpose 
 consists of a portrait combination of large diameter and high intensity 
 combined with a negative lens which is also of large diameter in rela- 
 tion to its focal length. The value of this instrument to military 
 departments is evident. 
 
 (6) Plate XVI 1 1. illustrates the possibility of obtaining naval records 
 in warfare, and suggests the use of the instrument for becoming fully 
 acquainted with details of foreign naval equipments even in times of peace. 
 
 (7) The architect and student of archaeology will find a wide field 
 in the application of the lens in recalling details of ancient and historical 
 buildings. Portions of carving and sculpture in quite inaccessible 
 positions may be photographed on a large scale on the one hand ; or, 
 on the other, large buildings may be photographed from such a distance 
 that they will be rendered without perspective effect, showing the true 
 relative proportions, and being practically a plan in elevation. This 
 branch of the subject has been most clearly exemplified by the work 
 of Mr. E. Marriage, who gained the medal of the Royal Photographic 
 Society in 1895. Fine specimens of the work on a large scale, kindly 
 lent by Mr. Cruickshank, are illustrated in Plates XIX., XX., XXL, 
 and XXII. In this particular branch of work special arrangements in 
 the camera and stand are almost essential. We illustrate in Fig. 65 
 an arrangement for tilting the camera recommended by Mr. Marriage, 
 and also a strut connecting the tripod and camera for the purpose of 
 greater steadiness. Although the camera may have to be pointed 
 upwards at a considerable angle, the camera back must always be plumB* 
 In these subjects where the duration of exposure is not of great 
 moment, we can afford to employ almost the limit diaphragm for the 
 
PRACTICAL APPLICATIONS OF LENS 
 combination, and in this case the pencils which form the image are so 
 
 FIG. 65. 
 
 attenuated that it is possible to obtain fine definition even when the 
 
 '35 
 
TELEPHOTOGRAPHY 
 
 camera back has been considerably swung to obtain the true 
 plumb. 
 
 In Fig. 65 we illustrate a useful device for employment when 
 photographing interiors of cathedrals, churches, &c., in order to pre- 
 vent the legs of the camera from slipping during exposure. The 
 underside of the three arms is lined with rubber, the three arms them- 
 selves being made of soft wood to support the points of the tripod 
 legs. 
 
 (8) Plates XXIII., XXIV., and XXV. serve to illustrate a branch 
 of photography referred to in the previous section, as also many 
 similar conditions. The whale illustrated in Plate XXIII. can only 
 be represented by an ordinary lens in painful fore-shortened perspective 
 upon the plate, as, owing to the cramped conditions, it is impossible 
 to obtain a broadside image of it from a view-point on the pier, or one 
 which properly shows the relative proportions of the animal. To 
 obtain these it was necessary to take the camera along the shore to a 
 position where a broadside view could be obtained, necessitating a 
 distance of upwards of three hundred yards from the whale itself. 
 Plate XXIV. shows the result obtained by the same lens that was 
 employed for the near view. The size of the image is now too 
 insignificant to be of value in itself, or to bear enlargement from the 
 photographic negative without loss of detail. By employing a nega- 
 tive lens in conjunction with the same positive element, we produce 
 the result shown in Plate XXV. from the same standpoint. 
 
 (9) The application of the Telephotographic lens to animal and 
 bird life has already been roughly hinted at. For some years 
 Mr. R. B. Lodge of Enfield has devoted much patient care to this 
 subject. His methods have been published in several photographic 
 periodicals and he has lectured on the subject before the Royal 
 Photographic Society, who awarded him a medal in 1895 for his work 
 in this branch. Plate XXVI. is indicative of results that may be 
 obtained in this field of work. 
 
 136 
 
CHAPTER VIII 
 
 WORKING DATA 
 
 THE camera and stand must be perfectly rigid. A large tripod head 
 and a bigger clamping screw than usual are advantageous. When 
 long extensions of camera are employed, either a strut attached to the 
 tripod, or an independent support should be given to the back end of 
 the camera to prevent vibration during exposure. The importance of 
 guarding against vibration cannot be insisted upon too strongly. Any 
 slight movement of the camera corresponds to a displacement of the 
 short end of a lever, and the definition is impaired by a corresponding 
 movement of the long end. 
 
 When it is possible to choose atmospheric conditions, the clearer 
 and quieter the atmosphere the better. The clearest appearance of the 
 atmosphere is not always to be relied upon in photographing distant 
 objects ; tremor due to differences in the temperature of air currents, 
 evaporation of moisture, &c., may frequently interfere with the defini- 
 tion given. If these effects are not visible to the eye, a careful examina- 
 tion of the image on the ground glass may reveal them, showing a 
 slight appearance of " dancing." These drawbacks are most likely to 
 occur in hot weather, when the atmosphere is seldom homogeneous. 
 
 Focusing must be performed with the greatest care and patience. 
 When a considerable magnification is given, focusing is best carried 
 out by means of the rack and pinion on the lens mount, which adjusts 
 the separation of the elements of the system. A very slight movement 
 of this will rapidly throw the image in or out of focus, and it is best to 
 use a magnifier upon the ground glass. Focusing should always be 
 
TELEPHOTOGRAPHY 
 
 performed with the largest aperture in the positive lens consistent with 
 good definition, even if a smaller stop is finally employed. 
 
 The greater the magnification given, the less crisp in itself will the 
 image appear on the ground glass, as compared to images given by 
 ordinary positive lenses, but details which are invisible in the smaller 
 image are now clearly visible in the magnified image, and can be 
 photographed. The separate bricks, or blocks of stone, for example, 
 in a building may each not be visible in a small image given by a 
 lens of short focal length, yet when the primary magnification has 
 taken place, we are able to obtain an image of sufficient size to render 
 this separation possible. It is evident that calculation of the requisite 
 magnification (or the equivalent focal length of the system necessary) 
 is always possible when we know the size of certain details in the 
 object, and its distance, in order to render the necessary details visible 
 in the image. The scale of the image is determined by the focal 
 length of the lens, and if we ascribe a limit to the actual size of the 
 image for distinctness, the calculation is simple. As a numerical 
 example, say a church clock 6 ft. in diameter is 500 yards distant, 
 To determine the focal length of the lens necessary to give an image ^ 
 
 of an inch in diameter, the scale is -A. or - ; so that the focal length of 
 
 72 288 
 
 the combination must be yards, or roughly, 60 inches. Hence, if 
 
 288 
 
 our positive element has a focal length of 10 inches, the image must be 
 magnified 6 times by the negative element, or the screen must be placed 
 at a distance of 5 times the focal length of the negative lens from it. 
 
 A focusing cloth of sufficient size should be employed to allow the 
 corners of the plate to be examined, after the stop with which the 
 photograph is to be taken has been inserted. If the corners are not 
 fully illuminated, a greater extension of camera must be employed, and 
 the operation of focusing repeated. When considerable extension of 
 camera is employed, it may be found necessary to use a " Hooks 
 Joint " handle in order to focus by an adjustment of the separation 
 between the lenses. 
 
 138 
 
If the positive lens has a high intensity, and only moderate magnifi- 
 cation is given, the position of sharp focus may be roughly arrived at 
 by means of the rack and pinion as before, the final focusing being 
 carried out by the camera rack, which will now act as a " fine adjust- 
 ment " in determining the plane of the sharpest focus. In the previous 
 case the pencils will probably be too attenuated to permit of this method 
 
 FIG. 66. 
 
 Focusing by means of Hook's universal joint ; the handle may 
 be made of any length. 
 
 of focusing, as the screen may be moved a considerable distance 
 without much alteration in the definition being traceable. 
 
 In focusing, attention must be paid to the varying " curvature of 
 field " caused at different camera extensions ; the plane of the image 
 being adjusted to equalise any difference between the planes of best 
 definition for centre and edge of plate, when uniformity throughout is 
 desired. If emphasis is required for any particular plane in the object, 
 naturally the sharpest possible definition is given to this plane. 
 
 139 
 
TELEPHOTOGRAPHY 
 
 Where orthochromatic methods are advantageous in ordinary 
 photography, they will be pronouncedly so in Telephotography. The 
 utility of proper light filters (yellow screens, &c.) in the lens used in 
 conjunction with orthochromatic plates is of the highest importance for 
 distant work. When an object is very far off and brightly illuminated, 
 the exposure will be found to be considerably shorter than is necessary 
 for a comparatively near object : The author has found that the 
 increase of exposure presumed to be necessary when using an ortho- 
 chromatic screen (when the theoretical increase is not more than 2 to 
 2^- times), may be ignored ; that is to say, normal exposure, as indicated 
 by the exposure meter without the screen, may be given. 
 
 Generally speaking, shorter exposures are necessary in photo- 
 graphing distant objects than would be expected ; while longer ex- 
 posures are necessary with the Telephotographic lens than for lenses of 
 ordinary construction of the same focal length, when near objects are 
 photographed, the increase of exposure being proportional to the 
 square of the distance between lens and object. 
 
 The chief difficulty in distant Telephotographic work is the adequate 
 rendering of contrast in the negative. At great distances we have not 
 only to contend with the lack of homogeneity in the atmosphere already 
 referred to, but with dust and other impurities in the air which reflect 
 light, and contribute to a general haziness. Backed plates should 
 always be used and slow emulsions are to be preferred. 
 
 It is advisable to develop slowly (the plate being carefully pro- 
 tected from light), adding the accelerator very gradually, but develop- 
 ment should be carried a little farther than is necessary for a negative 
 taken under ordinary conditions. As the tendency in using all Tele- 
 photographic lenses is towards inequality of illumination, or a falling 
 off in the intensity of the image towards the edges of the plate, it is 
 always advisable after first flooding the plate, to develop from the 
 edges towards the centre, by allowing the developer to continually 
 move round the edges in a circular manner in the developing dish. 
 
 The requirement of emphasising contrasts will suggest many kinds 
 of developer to the photographer. The following formula given by 
 
 140 
 
PLATE XX 
 
 Wheel Window, San Zeno, from same point of view as in Plate XIX., 
 
 taken with 6-in. Ross Universal Symmetrical with 3-in. negative attachment, 
 
 15 in. from back of lens to plate, stopped down to -^tr. 38 seconds exposure. 
 
 (Copyright of and kindly lent by J. W. Cniickshank, Esq.) 
 
WORKING DATA 
 
 Mr. Marriage has been found to produce admirable results in architec- 
 tural work : 
 
 No. i. Pyrogallic acid . . . . . . i ounce . 
 
 Sodium sulphite . . . . 3 
 
 Citric acid . . ... . . -\ 
 
 Water to make ...... 10 
 
 No. 2. Washing soda . . . . . 8 
 
 Sodium sulphite . . . .10,, 
 
 Water to make ...... 80 
 
 No. 3. Bromide of potassium .... i 
 Water to make . . . .- . .10,, 
 
 No. 4. Carbonate of ammonia . . '. . i 
 Water to make . .10., 
 
 For use take 30 minims No. i, |- ounce No. 2, and 10 minims No. 3 
 make up to one ounce with water. If the plate is over exposed, add 
 equal parts of 3 and 4 to the developer (say 15 minims of each per 
 ounce of developer). 
 
 Comparative results by an ordinary and a Telephotographic lens 
 of all ancient and interesting buildings, landmarks, &c., printed in a 
 permanent process, stating the standpoint from which the photographs 
 are taken, date, &c., should be sent to Sir Benjamin Stone, M.P., for the 
 National Photographic Record collection. The ordinary photograph 
 will show the intervening country, or buildings as the case may be, 
 when taken from a distance, between the standpoint and the chief 
 object of interest. These records in pairs will have an added interest 
 in years to come. 
 
 141 
 
TELEPHOTOGRAPHY 
 
 ABRIDGED FORMULA FOR REFERENCE 
 
 POSITIVE LENS 
 
 IF f represents the focal length of an ordinary positive lens, nf any 
 multiple of it, 
 
 By the law of conjugate foci : 
 
 r =*y (i) 
 
 where xnf, a.ndy=-f. 
 
 If o be the distance of any object from the lens, and i the distance 
 of the image from it : 
 
 o = (n + 
 
 TELEPHOTOGRAPHIC LENS (A) 
 
 If F represents the focal length of the combination, f^ and f z the 
 focal lengths of the positive and negative lenses composing it, d an 
 interval of separation greater than the difference of their focal lengths, 
 and a their entire separation : 
 
 and the back focal length 
 
 BF = 
 
 d 
 
 Calling m the ratio of the focal lengths of positive and negative 
 elements composing the system, or its power : 
 
 (5) 
 
 or /! -mf % } (6) 
 
 142 
 
WORKING DATA 
 
 If o be the distance of any object from the Telephotographic lens, 
 and i the distance of the image from it : 
 
 = F + #F+/j ....... (7) 
 
 1 =1 F + -F -/ 3 ....... (8) 
 
 n m 
 
 where n, as above, is any multiple of the focal length of the entire 
 system, and m the focal length of the positive element divided by the 
 focal length of the negative element. 
 
 To compare the distance between object and lens, and image and 
 lens in the case of an ordinary positive lens, and in the case of the 
 Telephotographic lens ; by equations (2) (7) and (8), we see : 
 
 O = o + {F(* - i) + /iJ ...... (9) 
 
 Calling d the interval of separation between the positive and nega- 
 tive elements greater than the difference of their focal lengths : 
 Separation of principal points 
 
 TELEPHOTOGRAPHIC LENS (B) 
 
 Calling M the magnification to which the image formed by the 
 positive element f l is subjected by the negative element /~ 2 , and E the 
 camera extension from the negative element to the screen : 
 
 M = ^ + i ......... (12) 
 
 E =/ 2 ( M -- i) . . . . '. . Y . (13) 
 
 If F represents the focal length of the entire system, and m,-&, as 
 before, 
 
 F = ME +/j . .. , . . , , (15) 
 
 143 
 
TELEPHOTOGRAPHY 
 
 If / is the correct exposure to give to the positive element/, if used 
 alone, and T that for the entire system : 
 
 T = M 2 t ......... (l6) 
 
 If - represent the scale of the image given by the entire system, 
 and - that given by the positive lens alone 
 
 11 / \ 
 
 - = - M .......... (17) 
 
 N n x ' 
 
 To find the focal length of the entire system when a near object is 
 rendered in a given scale of -, 
 
 N 
 
 F = 
 
 (18) 
 
 N 
 
 It is evident that when N is oo, this equation is identical with (15). 
 If we wish to reproduce an object in a given scale - by the entire 
 
 system of definite focal length F,/ and/ being known, and we propose 
 to magnify the primary image M times (for convenience), in order to do 
 so, we see from (17) that n M N, and hence, distance of object from 
 
 lens 
 
 = (MN + i)/ ........ (19) 
 
 THE DIAPHRAGM 
 
 If a represents the effective aperture of the lens,/ its focal length, 
 and i its intensity, 
 
 1 = 7 ; M 
 
 Calling E the camera extension, / and/ the focal lengths of positive 
 
 144 
 
WORKING DATA 
 
 and negative lenses, and d l and d z their diameters respectively, and D 
 the circle of illumination covered by the system : 
 
 D 
 
 /2 J\ ~ JZ 
 
 Using the same notation as before, and taking T o of an inch as 
 limit of indistinctness : 
 
 Distance beyond which all objects are in focus 
 
 = looaf + f ........ (22) 
 
 or 
 
 = 100 i/ 2 +/ (22a) 
 
 For a near object accurately focused : 
 
 Front depth, 
 
 */( + (23) 
 
 100 i/+ (n + i) 
 
 Back depth, 
 
 */(* + (24) 
 
 100 if (n + i) 
 
 UNIVERSITY 
 
 or 
 s*UFORii> 
 
BIBLIOGRAPHY 
 
 " Concave Achromatic Glass Lens, &c." Proceedings of ttie Royal Society. Peter 
 Barlow, F.R.S., and G. Dollond, F.R.S., February and May 1834. 
 
 "Eclipse du 28 Juillet 1851, Relevee Heliographiquement," par MM. Vaillat et 
 Thompson, avec un objectif sthenallatique de M. Porro. Compt. Rend. 1851. 
 
 Bulletin Soc. Franc., pp. 114-117, 1856. J. Porro. 
 
 " Enlarged Views by One Operation." British Journal of Photography, September 19, 
 1873. Editor, J. T. Taylor (The Use of the Opera Glass). 
 
 " A Novel Enlarging Lens " (Opera Glass). By J. T. Taylor, British Journal 
 Almanac, 1877. 
 
 " Telescopic Photography Without a Telescope." Editorial comment on the author's 
 lens. By J. T. Taylor, in the British Journal of Photography, October 16, 1891. 
 
 Dr. A. Meithe's independent work set forth in letter to British Journal of Photography, 
 October 30, 1891. 
 
 " A New Telescopic Photographic Lens." A Paper read at the Camera Club, London, 
 by the Author, December 10, 1891. 
 
 "A Compound Telephotographic Lens." A Paper read at the Camera Club by the 
 Author, March 10, 1892. 
 
 Description of "A New Form of Telephotographic Lens." By the Author at the 
 Photographic Society, April 30, 1892. ("The Progress Medal" of the now Royal 
 Photographic Society was awarded in 1896.) 
 
 "The Telephotographic Lens." An illustrated pamphlet by the Author, August 1892. 
 (Out of print.) 
 
 "Traite Encyclopedique de Photographic." Ch. Fabre. Prem. Supplem. 1892. 
 
 " Ueber Fernphotographie." By A. Steinheil. Photo. Correspond. 1892. 
 
 147 
 
TELEPHOTOGRAPHY 
 
 "Telephotography." A Paper delivered at the Society of Arts by the Author. 
 Published in the Journal, March 3, 1893. (Awarded the Society's Silver Medal.) 
 
 " Telephotographic Systems of Moderate Amplification." A pamphlet by the Author, 
 1893. (Out of print.) 
 
 " Teleobjective " Eder's Jahrbuch, 1893, p. 348. (Reference is here made to 
 A. Duboscq's lens.) 
 
 " Gebrauchsanleitung fur Teleobjective." Von Dr. P. Rudolph (of the firm of Carl 
 Zeiss, Jena), May 1896. 
 
 " Geschichte und Theorie des Photographischen Teleobjectivs." Dr. Von Rohr (of the 
 firm of Carl Zeiss, Jena), April 1897. 
 
 "Das Fernobjective." Hans Schmidt, Berlin, April 1898. 
 
 PRACTICAL APPLICATIONS OF THE LENS 
 
 " Stalking with the Camera." A series of illustrated articles in the Photogram. By 
 R. B. Lodge. 1897. 
 
 "Telephotography Applied to Architecture." By E. Marriage, in the Photogram, 
 January 1898. 
 
 " Des Services que peut rendre le Tele-Objective au point de vue Pictorial." By 
 M. Demachy, Photo Club de Paris, in November 1898. An abstract appears in the 
 Amateur Photographer, January 13, 1899. 
 
 "Telephotography." Illustrated. By Dr. E. J. Spitta, F.R.A.S., in Photography 
 March 23, 1899. 
 
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