The advantages of this relatively economical construction, leaving the optician the greatest number of variable factors with the minimum number of lenses, led to the appearance of a number of variants, in most of which, however, one of the single lenses was replaced by a system of two cemented lenses. Such is the case, for example, with the lens designed by Rudolph and E. Wandersleb (1902), of which there are several series. That shown in Fig. 8o, intended especially for portraiture, covers a field of about 35° at F/3-5. Others at F/4-5 and F/6.3 cover respectively 55° and 65° at full aperture, and with a small stop (about F/36).
io6. Symmetrical Anastigmats of Separated Lenses. With a view to simplifying the con at full aperture, " because with small stops harmful reflected images may sometimes be formed." Each of the halves of such a lens can be used separately behind the diaphragm, when the maximum aperture will be F/io to F/11.
107. The Hypergon Wide-angle Lens. Al though such a lens has only a very restricted use, we ought to mention, if only as a curiosity, the wide-angle lens (Fig. 82), calculated by von Hoegh in 1900 to cover a flat anastigmat field of 140°, almost four-tenths of the complete horizon, at an aperture of F/22 (actually the full aperture is used only for focussing, and a smaller aperture used when the photograph is taken). The correction for astigmatism is only obtained by the use of extremely thin lenses spherical and chromatic aberrations are not corrected, but the relative aperture is so small, and thus the depth of focus is so large, that these aberrations do not affect the image in practice, and no correction for focus is necessary. When the field used exceeds 'To° the difference of illumination between the centre and the edge is so great that it is necessary to use a star-shaped diaphragm (§ 54) to reduce the illumination at the centre for a considerable proportion of the exposure.
The large angle between the extreme secon dary axes, and the fact that the focal length is scarcely one-fifth the diagonal of the plate covered, means that the lens can only be used on a specially-made camera ; also it is generally impossible to use a shutter with it.
io8. Lenses of Variable Foci. To the variable power telephotos may be connected the variable focus lenses used in cinematography to obtain a progressive variation in the scale of a given scene. These lenses usually comprise three systems, moved by cams in such a manner that the variation in focal length does not affect the sharpness of the image of distant objects, the focussing on near objects being then obtained by means of supplementary lenses (§ 118). For the separation between the lenses and correcting them specially for this purpose. Such a system, in fact, constitutes an objective the focal length of which can be varied at will between very wide limits by altering the separation between the elements. Such a system has the very
considerable advantage that the nodal points are thrown forward a great distance in front of the lens, so that the distance between the lens and the image is only a small fraction of the focal length, thus rendering unnecessary the use of the cumbrous cameras required for normal lenses of great focal length. It was only in 1891 that this suggestion was exploited by T. R. Dallmeyer, followed closely by A. Miethe and Steinheil, and then by many other opticians.
Consider (Fig. 83) a system formed of a con vergent lens of focal length f, and a divergent instance, in the Vario lens (A. Warmisham, 1932) the focus varies from 40 mm. (aperture F/3-5) to 120 mm. (aperture Provided the varia tion in focal length is restricted, the iris dia phragm can be automatically regulated, so as to keep the relative aperture constant and to keep the image at a constant luminosity.
To facilitate focussing on small and medium size cameras, several opticians have made lenses formed of two systems of which the separation is variable by means of a helical mount graduated in subject distances. The amount of displace ment of the front system can then be much smaller than the movement it would be neces sary to give the lens as a whole.
109. Variable-power Telephotos. A divergent lens had several times been used for enlarging the image given by an astronomical objective (L. Porn), 1851; Warren de la Rue, 186o), or by a microscope (Foucault and Donne, 1845 ; Bork and de Tournemine, 1869) when, in 1873, j. Traill Taylor pointed out the importance to photographers of obtaining large pictures of distant objects directly in the camera, by using an objective constructed on the principle of the Galilean telescope (opera glasses) but increasing lens of focal length so placed that the back focus f', of the convergent lens falls between it and its (virtual) front focus The image of a distant point in the direction R will be formed, in the absence of the divergent lens, at a point r in the focal plane of the front com ponent. This point acting as virtual object to the divergent lens and closer to it than its focus, its image R' is real, and magnified in the ratio The application of the formulae already quoted in § 7o, bearing in mind that the focal length of the divergent lens must have the " minus " sign, gives for the resultant focal length F— calling e the separation of the components, the optical interval, the distance between the foci f1' The formula shows that when 6 tends to zero the focal length becomes infinitely great (adjustment of the Galilean telescope for normal sight). Conversely, if the lens ap proaches the focal plane of L, there can be no possibility of photographing the image. The optical interval 6 can thus take all values between o and the difference between the two focal lengths.