Lenses.—A lens is a portion of a refracting medium bounded by spherical surfaces. The refracting medium is usually glass ; but other materials, such as quartz, etc., are sometimes used. Various lenses are shown in Fig. 8, and a modern photographic lens consists of various combinations of these simple lenses of various kinds of glass. The older lenses were made with Crown and Flint glass, the crown glass having the lower refractive index and the lower dispersive power. For some time it was believed that unless glass could be made possessing high refractive power, but only low dispersive power or vice versa, no lens could be con structed which would possess a flat field and be anastigmatic.
Accordingly, the glass-makers set to work and produced such glasses, these being put on the market in 1886. The new glasses are known as Anomalous Glasses, and are indicated in the diagrams throughout this book by horizontal shading thus : . Crown glass is indicated , and flint-glass . Light will always be considered to travel from left to right.
Equivalent Lens.—The modern complex lens can be replaced for purposes of calculation by a single thin lens 1, Fig. 8, which is called the Equivalent Lens. This thin lens is, however, ideal, and possesses no aberrations. It may here be mentioned that the image formed by the lens t suffers from various defects known as aberrations ; but our thin lens is considered as being able to form a plane reproduction of an extended plane object at right angles to its axis. If, there fore, the properties of the lens i for narrow axial pencils of light are known, this knowledge can be applied to all pencils, whether oblique centric or oblique excentric.
Formation of Images.—Any one of the lenses I, 2, 3, Fig. 8, is able to form a reproduction ba or image of an object AB, Fig. 9, on the opposite side of the lens, provided that the object AB is more than a certain distance from the lens. Three typical rays from the point A are shown con verging to the point a. Such lenses are known as Positive or Converging, and can be recognised easily, because they are always thicker at the centre than at the periphery. The lenses 4, 5, 6, Fig. 8, appear to form an image, ab, Fig. io, on the same side of the lens, as the object AB. Such an image of course does not exist, and is called Virtual. The lenses 'are known as Negative or Diverging. They are always thinner at the centre than at the periphery. Negative
lenses would appear in themselves' to be of little use to the photographer, since no image can be received on a screen. Such lenses' are,: however, absolutely indispensable to the construction of a good,lens; and also form an essential part of a ,lens ,which is extremely popular—viz. the Telephoto lens.
Before considering the formula connecting the distances of the object and image from a lens, we must have a clear idea how distances are to be measured. Unfortunately the convention adopted in Photographic Optics is not the same as that, adopted in English treatises on general optics. The usual convention in Photographic Optics is adopted here, but the difference must be borne in mind if more advanced is required from the larger works. The con vention is that distances measured from the lens in the same direction as the incident light are positive, and in the opposite direction negative. Thus in Fig. 9 the distance of the image is positive, and the distance of the object negative. In Fig. 10 both distances are negative.
In Fig. i 1 a biconvex lens, LC, is shown in cross-section passing through the centres of curvature CC' of the surfaces LPL', LP'L' respectively. The straight line CC' is called the Principal Axis of the lens. Let the image of an object, AB, at right angles to this axis be formed at ba. Then if the distance of AB from the lens, which is supposed to be infinitely thin, is u, and the distance of the image ba is v, it can be shown that v 1 1 u , 1 — + — = a constant, denoted In this formula the signs of u, v, f have been allowed for, so that it is only necessary to substitute the numerical values of the various distances.
The constant f is called the Focal Length of the lens, and is the distance of the image when the object is infinitely remote. Rays from such an object are shown in Fig. 12. The point F, where the image cuts the Principal Axis, is called the Principal Focus. The focal length of a thin lens can easily be determined by sharply focussing some distant object such as a church spire, and measuring the distance of the focussing screen from the lens.
Now an infinite number of values of u and v can be found to satisfy the above formula, and the value of u corresponding to any value of v is said to be conjugate to it. The corre sponding points where the object and image cut the Principal Axis are called the Conjugate Foci.