Page:Elementary Text-book of Physics (Anthony, 1897).djvu/436

432 pencil. It will intersect the axis of the mirror between $$x$$ and $$y.$$ If a plane be passed through the point of intersection perpendicular to the axis of the pencil, its intersection with the pencil will be like an elongated figure 8, which may be considered as a focal line at right angles to the axis of the pencil, and in the plane of the paper, and therefore at right angles to the focal line through $$F'.$$ Between these two focal lines there is a section of least area, nearly circular, which is the nearest approach to an image of $$F$$ produced by an oblique incidence such as we have been considering.

If refraction instead of reflection had taken place at $$ac,$$ a result very similar would have been obtained for the refracted pencil. This failure of spherical reflecting or refracting surfaces to bring the light exactly to a focus is called spherical aberration. In order to obtain a sharp focus, therefore, if only a single spherical surface be employed, the light must be confined within narrow limits of normal incidence. When reflection or refraction takes place at two or more surfaces in succession, the aberration of one may be made to partially correct the aberration of the other. For instance, when the waves incident upon a double convex lens are plane, the emerging waves are most nearly spherical when the radius of the second surface is six times that of the first. Two or more lenses may be so constructed and combined as to give, for sources of light at a certain distance, almost perfectly spherical emerging waves. Such combinations are called aplanatic. The same term is applied to single surfaces so formed as to give by reflection or refraction truly spherical waves.

344. The Camera Obscura.—If a converging lens be placed in an opening in the window-shutter of a darkened room, well-defined images of external objects will be formed upon a screen placed at a suitable distance. This constitutes a camera obscura. The photographer's camera is a box in one side of which is a lens so adjusted as to form an image of external objects on a plate on the opposite side. The relation deduced in § 339 serves to determine the size of