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LENSES 117
must be such that rays starting from the various points of the object are able to converge to a series of points in the plane of the plate, these points being arranged in a similar manner to the points of the object, so that a perfectly flat image is formed. This problem was investigated by Gauss, who showed how the action of the lens system could be predicted when its focal and other chief points are known, and he further showed how these points could be determined in quantities depending on the form, material, and distances apart of the lenses. Of course no system of lenses absolutely fulfils all these conditions : the object is to devise such a system that the deviations from the theoretical ideal shall be as small as possible.
Such work as this was of the utmost importance, for the early lenses were mainly the outcome of a large amount of experimental work combined with little if any mathematical work.
For some time the Petzval combination lens was the only example of a theoretical lens (see p. 15).
When, later on, Abbe and Schott undertook to construct a lens suitable for this work, they had the very great advantage of having a definite aim in view.
Photographic Lenses. — The various kinds of doublet lenses used in photographic work may be classed as follows : —
I. The Rapid Rectilinear. — So called since it is so corrected that spherical aberration is reduced to a minimum, and straight lines in the object are represented by straight lines in the image.
II. The Portrait Lens. — Originally due to Petzval. A lens so constructed as to work at a very large aperture and to give a soft definition over a very small area.
III. The Wide-angle Lens. — A system by means of which it is possible to take a photograph of an extended object when the distance which the camera can be placed from the object is limited. Such lenses are of short focus