Page:Encyclopædia Britannica, Ninth Edition, v. 17.djvu/869

OPTICS 805 the following rule as in all probability sufficiently exact for use. A double object-glass will be free from aberration, provided the radius of the exterior surface of the crown lens be 6 720 and of the flint 14 20, the focal length of the combin ation being 10 000, and the radii of the interior surface being computed from these data, by the formulae given in all elementary works on optics, so as to make the focal lengths of the two glasses in the direct ratio of their dis persive powers. Numerous experiments have been made with the view of abolishing the secondary spectrum. Theoretically, if three different kinds of glasses are combined it will gen erally be possible to make the focal lengths of the com bination equal for any three selected rays of the spectrum. Or the ingredients of one of the glasses may be mixed in such proportions as to suit the requirements of the problem when combined with crown. In this way Stokes has succeeded in constructing a small object-glass free from secondary colour, but it is doubtful whether the practical difficulties could be overcome in the construction of a large object-glass, where alone the outstanding chro matic aberration is important. The practical optician is not limited to spherical surfaces, and the final adjustment of the aberration of large object- glasses is controlled by the action of the polishing tool. It is understood that some of the best makers apply a local correction, according to the methods developed by Foucault for mirrors. The light from a natural or artificial star is allowed to fall upon the lens, At the focus is placed a small screen, which is gradually advanced so as to cut off the light. The eye is immediately behind the screen and is focused upon the lens. If there are no imperfections the illumination falls off very suddenly, the surface of the mirror passing from light to dark through a nearly uniform grey tint. If, however, from uniform aberration, or from local defects, any of the light goes a little astray, the corre sponding parts of the surface will show irregularities of illumination during the passage of the screen, and in this manner a guide is afforded for the completion of the figuring. Tb ppler l has developed the idea of Foucault into a general method for rendering visible very small optical differences. Instead of a mere point of light, it is advis able to use as source an aperture (backed by a bright flame) of sensible size, and bounded on one side by a straight edge. An image of this source is formed at a considerable distance by a lens of large aperture and free from imper fections, and in the plane of the image is arranged a screen whose edge is parallel to the straight edge of the image, and can be advanced gradually so as to coincide with it. Behind this screen comes a small telescope through which the observer examines the object placed near the lens. When the light is just cut off by the advancing screen, the apparatus is in the most sensitive state, and the slightest disturbance of the course of the rays is rendered evident. To show the delicacy of the arrangement Toppler intro duced into the cone of light a small trough with parallel glass sides containing distilled water. A syphon dipped under the surface and discharged distilled water from another vessel, and it was found almost impossible so to control the temperatures that the issuing jet should remain invisible. Not only were sound-waves in air, generated by electric sparks, rendered visible, but their behaviour when reflected from neighbouring obstacles was beautifully exhibited. An apparatus on this principle may often be employed 1 Pogg. Ann., cxxxi.. 1867. with advantage in physical demonstrations, for instance, for the exhibition of the changes of density in the neigh bourhood of the electrodes of a metallic solution under going electrolysis. The smallest irregularity that could be rendered visible would be such as would retard trans mitted light by a moderate fraction of the Avave-length. 2 In objectives for photographic use the requirements are in many respects different from those most important in the case of telescopes. A flat field, a wide angle of view in some cases as much as 90 freedom from distortion, and a great concentration of light are more important than a high degree of definition. As a rule, photographs are not subjected to the ordeal of a high magnifying power. Usually the picture includes objects at various distances from the camera, which cannot all be in focus at once. That the objects at one particular distance should be de picted with especial sharpness would often be rather a disadvantage than otherwise. A moderate amount of " diffusion of focus " is thus desirable, and implies residual aberration. In some lenses an adjustment is provided by means of which the diffusion of focus may be varied according to the circumstances of the case. For landscapes and general purposes a so-called single lens is usually employed. This, however, for the sake of achromatism, is compounded of a flint and a crown cemented together ; or sometimes three component lenses are used, the flint being encased in two crowns, one on each side. To get tolerable definition and flatness of field a stop must be added, whose proper place is some little distance in front of the lens. For portraiture, especially before the introduction of the modern rapid dry plates, a brilliant image was a necessity. This implies a high ratio of aperture to focal length, which cannot be attained satisfactorily with any form of single lens. To meet the demand, Petzval designed the " portrait-lens, " in which two achromatic lenses, placed at a certain distance apart, combine to form the image. This construction is so successful that the focal length is often no more than three times the available aperture. When stops are employed to increase the sharpness and depth of focus they are placed bdween the lenses. Vision through a Single Lens.- A single lens may be used to improve the vision of a defective eye, or as a magnifying glass. A normal eye is capable of focusing upon objects at any distance greater than about 8 inches. The eyes of a short-sighted person are optically too powerful, and can not be focused upon an object at a moderate distance. The remedy is of course to be found in concave glasses. On the other hand, persons beyond middle life usually lose the power of seeing near objects distinctly, and require convex glasses. A not uncommon defect, distinct from mere short or weak sight, is that known as astigmatism. In such cases the focal length varies in different planes, and at no distance is the definition perfect. Many people, whose sight would not usually be considered inferior, are affected by astig matism to a certain extent. If a set of parallel black lines ruled upon white paper be turned gradually round in its own plane, it will often be seen more distinctly and with greater contrast of the white and black parts in one azimuth than in another. When the focal line on the retina is parallel to the length of the bar, the definition (as in^the case of the spectroscope) is not much prejudiced, but it is 2 Even when the optical differences are not small it is well to re member that transparent bodies are only visible in virtue of a variable illumination. If the light falls equally in all directions, as it miglit approximately do for an observer on a high monument during 1 a thick fog, the edge of (for example) a perfectly transparent prism would be absolutely invisible. If a spherical cloud, composed of absolutely transparent material, surround symmetrically a source of light, the illumination at a distance would not be diminished by its presence.