19 



Another exact method of findin*,' the focal 

 leu^'th of a lens is Fif}. ■>. As before, we find front 

 focus F, and b ick focus F of lens, and 

 mark this distance on a bas"? hoard. This 

 distance F to F is only approximately double 

 the focal length of lens, because the lens, being a 

 corabinatioQ or thick lens, the two principil points 

 PPdo not coincide in one centre. Place an object 

 of definite size at point A B about half the distance 

 F to F beyond F, and then place screen about a 

 similar position a 6 beyond F, and move the screen 

 and object alternately until the image is quite 

 sharp and exactly the same size as the object. 

 Then the distance F to a 6 is the exact focal 

 length uf the lens. 



It is useful for the amateur to test this and find 

 the exact focus, and see if it agrees with that 

 marked on the lens or in the catalogue. I recentl> 

 bought a lantern lens from London for a special 

 purpose, and, although marked 8-inch tocus, its 

 real focus was nearly lOj inches. 



With negative or concive lenses the same 

 general laws hold good n.s with positive lenses, 

 but as negative lenses form no real images, they 

 are useless for photography when used alone. 

 Fig. 7 II. shows how parallel rays of light behave 

 on passing through a negative lens. Let us take 

 a card with two holes as A and B, and allow light 

 from the sun or sky to pass through the holes 

 And strike the lens at A R. If we place a card on 

 the other side of the lens we find that instead of 

 the rays converging to a focus as with a positive 

 lens {Fig. 7 I), they diverge, and if we move the 

 card to and fro, we shall find a position where the 

 spots of light A. B, are double the distance apart 

 that they were before entering the lens at A B. 

 This distance F from the centre C of lens is the 

 focal length, and the rays appear to come from 

 a focus on the other side of the lens at a point 

 F. If we reverse these conditions as Fig. 7 III. 

 we shall find that the converging rays emerge 

 parallel ; but if the rays converge to a point / 

 between the principal focus F and the centre of 

 the lens they will &tiU converge, and come to a 

 focus somewhere between F and infinity, Fig. 7, 

 IV. It is thus that a negative lens is used in 

 Tele-photography . 



We have already seen that by using a convex 

 lens we can thus converge the rays and allow them 

 to pass through a negative lens, and, if we vary 

 the distance between the two lenses, we can alter 

 the position of the focus to anything between 

 infinity and the surface of the negative lens, as in 

 Fig. S, I., II., and III. If the lenses are of the same 

 focal length, when placed closa together as Fig. S, 

 I., the two act as a plain piece of glass. It is as 

 Fig. S, II., that we use the len?es in Tele-photo- 

 graphy, but insteid of using simple lense"* as in 

 the figure we, of course, use achromatic and 

 rectilinear lenses for both the negative and 

 positive combinations. 



In positive lenses we found the rule for 

 magnificition was to divide the distance of the 

 object from the lens by the focal length of the 

 lens and subtract one, but in negative lenses the 

 rule is to add one instead of substracting. 



It will perhaps be useful for reference if I give 

 a few concise rules for Telephoto lenses. 



(I) To find the magnijication, divide the camera 



extension (distance between negative lens and 

 screen) by the focal length of the negative lens 



and add one : 



M = ^ 4- 1. 



(2) To find the camera extension necessary for a 

 certain magnification, multiply the focus of 

 negative lens bv magnification required less one: 

 E =f (M— 1). 



Example. — + lens f —10 inches, — It^us f == 4 

 inches, object 60 inches distant, and we desire the 

 photo half-size. M igni float ion by -j- lens is = 

 l-7th (Fig. 4). hei.ce we must magnify this image 

 '.i^ times (3i — 1) x 4 = 10, hence the camera 

 extension will be 10 inches. Let us take another 

 example. Suppose a 6 feet clock -\ mile distant 

 and we wish a I inch image of this clock with -f 

 lens 10-inch focus and — lens 3-inch focus. We 

 shall find that the camera extension will be about 

 16 inches. 



(3) To find the focal length of the combination 

 used for any camera extension, multiply focus of 

 the positive lens by the magnification. 



(4) To find the exposure, multiply the exposure 

 of the positive lens alone (with the stop used) by 

 the square of the magnification, or divide the F 

 stop number (FH, F6. etc.) by the magnification, 

 and this will give us F number of combination. 



There is a great saving in camera exteu'^ion, the 

 back focus always being much less than the 

 equivalent focu- of the lens ; for instance, a 5-inch 

 C.D.V. Portrait Lens with ii-ineh negative covers 

 a 15 X 12 plate with back focus of 18 inches, but 

 the equivalent focus is 41 inches. A 6-inch 

 C.D.V. Portrait Lens with 2*4-inch negative covers 

 a 1-1 plate with back focus of 12 inches, but the 

 equivalent focus in 50 inches. 



The positive lens should be a rapid rectilinear 

 or portrait lens working at F6, or at least FS, 

 because by Rule 4 we find that the F number 

 rapidly increases with the magnification, and Lord 

 Rayleigh has shown that it is not possible to use 

 a smaller stop than F71 without vitiating the 

 results, owing to the dilfraction of the light 

 through so small an aperture. The lens should be 

 as free as possible from distortion and astigmatism, 

 etc., because any error is mai^nified hy the 

 nfg;itive lens, but it is not always the lens that 

 is at fault. Finding that a friend sometimes 

 obtained sharp pictures and at other times pictures 

 not sharp with a lens I knew to be a good one, it 

 occurred to me to examine his eyes, and 1 found 

 the astigmatism was in the human eye and not in 

 the lent. If my friend focussed on the vertical 

 lines, the picture was sharp, but if the horizontal 

 lines were the prominent ones, the picture was 

 indistinct. This astigmatism of the human eye 

 is a thing often overlooked in the focussing of a 

 picture on the ground g'ass of the camera. 

 Although theTelephoto-lens is not alensto be used 

 on every occasion, as some other lenses, yet in the 

 future it is bound to come into very general use 

 because of the numerous advantages, especially 

 for scientific and natural history purposes. We 

 cannot always walk up to a bird with a camera, 

 but by using this lens we can obtain magnified 

 results at some distance. Its use in time of war 

 from balloons and for astronomy, and many other 

 purposes, will at once occur to the photographer, 



