A divergent lens can give only a virtual, upright, diminished image of a real object, at a position closer to the observer than the object.
This property is utilized in the construction of " brilliant finders." 44. Optical Centre—Nodal Points. In the optical axis of a lens is always a point, called the optical centre,' such that every ray the path of which (or its prolongation) within the lens passes through this point has its paths outside the lens parallel. The interrupted path of this ray of light forms what is called a secondary axis. The centre can be inside the lens (Fig. 16A) or outside (Fig. In the second case, it is not the effective path of the ray passing through the lens without angular deviation which meets this point ; the optical centre is the intersection with the optical axis of the continuation of the internal part of the ray.
The intersections of the optical axis with the external parts of a secondary axis (or their continuation) define two points N and N' (Figs. 16A and i6B). In a perfectly corrected system the positions of these nodal is invariable, whatever the direction of the rays considered. If the optical centre could be realized, it would be found that each of the nodal points is its image formed by one of the surfaces of the lens, but on the assumption that this sur face is bounded by an infinitely thick lens on one hand and by air on the other. Each of the nodal points is the image of the other formed by the lens or lens system considered.
In order to distinguish between the nodal points, the one towards which the secondary axes from different points of the object converge is called the nodal point of incidence; that from which the secondary axes diverge to the different points of the image is the nodal point of emergence.
The intersections PP' of the surfaces with the axis are sometimes called the poles.
45. Foci—Focal Length. The image of an infinitely distant point (e.g. a star) towards which the optical axis of a lens is pointed, is the focus of that lens. From considerations of symmetry this is necessarily situated on the optical axis. As the lens can be turned with either face to the point-object, it possesses two foci F and F' (Fig. 17). In the case of a con vergent lens the foci are the nearest points to the lens at which a real image can be formed of a real object. The word " focus " recalls the use of " burning glasses," the concentration of rays being a maximum in the neighbourhood of the focus so that tinder or other inflammable material can be ignited there when the lens is directed towards the sun.
When the two surfaces of the lens are in free contact with the air, the distance of each of the foci from the corresponding nodal point is the same ; this distance (NF = N'F') is called the focal distance or focal length. For a rough approximation and where a thin lens is con sidered, the nodal points can be ignored and the focal length reckoned from the optical centre C. In many lenses the optical centre is close to the diaphragm. Telephoto lenses are the chief exception.
The focal length of an optical instrument is one of its essential characteristics.
46. Chromatic Aberration. The refraction of a ray of light passing from one medium to another (from air to glass, or vice versa) at non-normal incidence has not the same value for different colours. Therefore, when a beam of white light (§ I) traverses a lens, the sharp images formed by light of different colours do not coincide. The rays which are refracted most, ultra-violet and violet, form their images nearer to the lens than those which are refracted less, green and (Fig. r8.) There is thus an infinite number of images each corresponding with one of the component radiations. In par ticular the position of the foci (images of infi nitely distant points on the axis) and of the nodal points (images of the optical centre) vary with rays of different colours, as does also the focal length.
The practical consequence of this is that whatever be the position of the viewing screen This inconvenience can be minimized by displacing the photographic plate by the correct amount after visual focussing, or by using, both for focussing and photographing, a coloured filter which transmits only a small portion of the spectrum. Generally it is preferable to correct the chromatic aberration more or less completely by the use of at least two glasses of different characteristics, usually a crown and a flint, the use of different material allowing or the photographic plate on which the image is to be recorded, the sharp image corresponding with the apex of one of the cones is surrounded by bright rings corresponding with sections of all the other cones. If the position of the screen has been determined visually, and if the image is photographed with it in the same position, the phenomenon is increased by the fact that the focus chosen is the best for the yellow-green images, which are the brightest visually, and consequently will not all agree with that for the ultra-violet and violet images, usually the most active on a photographic Calling x the mean refractive index of glass and and n" the values of the index for the two rays con sidered, the difference of focal length (fi—f "), expressed in the images formed by two different colours to be united. Lenses for photography are generally corrected for D (yellow) and G (blue-violet) rays of the solar spectrum, and are then called matic (from Greek, meaning colourless). For some work, in particular colour photography, such a correction is insufficient, and coincidence of the nodal points and foci for three different colours is aimed at, generally by the employment of at least three glasses. A lens so corrected is called apochromatic 1 (or with reduced secondary spectrum). Fig. 19 is drawn for a photographic lens of 16 ft. focal length (in order that the aberration can be easily read), and indicates approximately the displacements (distances from the mean focal plane PP') of the images formed by different spectral regions.