ABERRATION, SPHERICAL. A term used in geometrical optics (see LIGHT) to express the difference in path and effect. of rays of light incident perpendicularly and obliquely upon a mirror or upon a surface separating two portions of transparent matter, e.g., upon a surface of water. If a source of light is very small, it can be called a and can be considered as sending out "rays of light" in all directions, like the radii of a sphere. If one of these rays is perpendicular to the surface of the mirror or to the surface of separation of the two media, the rays near this will form a small cone or "pencil of rays ;" and in optics it is shown that such a perpendicular pencil of rays always gives rise by retleetion or refraction to another peneil of rays which meet in a point called the "image" or "focus" of the point-sou•ce. If, however. a small cone or pencil of rays be chosen around a ray which falls obliquely on the mirror or sep arating surface, it will give rise by reflection or refraction to rays which do not form a cone and therefore do not have a point as a focus, except in the ease of a plain mirror, such as an ordinary looking-gla..s. If the incident pencil is narrow, the reflected or refracted rays will hale two foci, in the form of two short, straight lines, some distance apart and perpendicular to eaeh other. These are called "focal lines;" and in between them the rays come the closest to forming a point focus, produeing what is called the "circle of least confusion." If instead of considering a narrow pencil of rays, we study the whole bundle of rays falling on the entire reflect ing or refracting surface, it is evident that the rays are brought to a focus on a surface which can be thought of as due to the combined effect of the short focal lines produced by the indi vidual pencils of which the bundle of rays is. composed, and which has a cusp or projecting point ending at the point-focus due to the per pendicular pencil. A section of this "caustic surface" is often seen on looking down on a cup of coffee or in glass of milk, if there is a lighted lamp near; because the projecting sides of the cup or glass act as a curved mirror. An imme diate consequence of spherical aberration is that the image formed of any object by a curved, mirror or by a lens or prism is not "sharp," but blurred, unless care be taken to exclude the oblique rays. This is done ordinarily by the
use of diaphragms, such as are seen in opera glasses, photographic lenses, etc. The smaller the opening in the diaphragm, so much the sharper is the image. See CAUSTIC.
The accompanying diagrams will show the effect of spherical aberration in the case of spherical and parabolic mir rors and convex lenses. In fig.
parallel rays are incident on a spherical mirror.
Those falling per pendicularly o r near the centre of the mirror are re flected to the point. Q, which is termed the princi pal focus of the mirror. The rays which strike the surf ace more obliquely do not meet at Q after re fleetion, hut at points which lie on the caustic surface v•hose section is represented by the heavy line with a cusp at Q. In fig.2the elimina tion of spherical aberration by the use of a para bolic mirror is shown, as here, by the peculiar property of a parabola (q.v.), all rays parallel to the axis are brought to a point at F, called the focus. For this reason the parabolic mirror is theoretically the most available for telescopes (q.v.), but in practice the construction of such mirrors presents great difficulties, which are but rarely effectually surmounted. The effect of spherical aberration in the case of a lens is indicated in fig. 3, where the rays passing through the lens near its circumference are brought to a focus at C, while those lying nearer the axis AB meet at or near F. The foci for intermediate rays lie between that point and C. From these diagrams the advantages obtained by the use of diaphragms will be seen. The oblique rays, or those which strike the mirror or lens at a distance from its centre, and which do not come to a focus at the same point as those passing through the central portion, are accordingly cut off and the image rendered more distinct. The spherical aberration of lenses can be reduced by using two or more lenses in com bination, as is done in the case of most photo graphic objectives. Two lenses with equal focal lengths can be combined, and their effect is the same as a lens with one-half the focal length, while the spherical aberration is greatly dimin ished. The books of reference mentioned under ABERRATION, CHROMATIC, \ 11 also supply ample information on this subject.