ABERRATION, in Optics, is of two kinds ; ?lbtr ration (of colour, or refrangibility, somethms called Chromatic aberration ; and .•berration of .slthrricity, .Syt /2 erica/ aberration.
Wilco a beam of white light falls upon a spherical lens, the violet, or most refrangible rays, cross the axis at a point nearer the lens, than the red or least refran gible rays. The distance between the point, where the red ray intersects the axis, and the geometrical lbcus, is called the longitudinal chromatic aberration of the red ray ; and its lateral chromatic aberration is measured by a line perpendicular to the axis, and drawn from the fo cus till it. meet the refracted ray.
In consequence of the spherical figure of the lens, the red, or any other kind of rays that pass nearest the centre of the lens, meet the axis in a point nearer the lens than those which pass at a greater distance from the centre. The distance between this point and the geometrical focus, is called the longitudinal spherical aberration ; and the distance of the geometrical focus from the refracted ray, in a line perpendicular to the axis, is called the late mu! spherical aberration. The same kind of aberration is produced by reflection from sphe rical specula. When the speculum is parabolic, and the point from which the rays proceed infinitely distant, there is no aberration, as all the rays meet in the geo metrical focus. There is also no spherical aberration for parallel rays in the meniscus lens AB, Fig. 4. when its convex surface ACI3, is part of a prolate spheroid, and its concave surface A EB, formed with a radius less than FC, the distance between the vertex of the lens and the fatrhcr focus of the spheroid. If the lens be pla noconvex, as in Fig. 5. having its convex surface part of a Vperboloid, whose major axis is to the distance between the foci, as the sine of incidence is to the sine of refraction out of the solid into the ambient medium, the parallel rays RR will be refracted to the farther fo cus 1', without any spherical aberration.
In order to find the lens of least aberration, M. Klin genstierna has given the following general theorem, a in which a is the radius +r ()Idle surface of the lens next the object ; b the radius of the other surface ; m the index of refraction, or the ratio of the angle of incidence to that of refraction ; r the distance of the radiant point, and fthe focal distance of the refracted rays. When m = and r infinite, we a 1 a and when in= 1686, we have infinite, or a piano-convex lens.
The spherical aberration of lenses being very small, when compared with the chromatic aberration, the con fusion of images arising from the latter is a great ob stacle to the perfection of refracting telescopes. The method of removing this confusion to a certain extent, by a combination of lenses of different refractive and dispersive powers, first discovered by Mr Dollond, gave rise to the achromatic telescope, an instrument which has exercised the genius of the most dis tinguished philosophers. See. Hugenii Diopt•ica ; Trims. ‘ols• xxxv. xlviii. p. ; I. p. i ; p. 944 ; Iii. p. 17 ; liii. p. 173 ; Iv. p. 54 ; _Year/. Par. 1757, 1746; 1752 ; 1735 ; 1756, p. 380 ; 1757, p. 524 ; 1762, p. 578 ; 1764, p. 75 ; 1765, p. 53 ; 1767, p. 43, 423 ; 1770, p. 461.-11/cm. ?ead. Berlin, 1716 ; 1761, p. 231 ; 1762, p. 66, 343; 1766 ; 1790 ; 1791, p. 40; 1798, p. 3.— ,S'aratcdi•chen .,lbhandlungen, it. 79, 944.--Altv. COMM( nt. Petrapol.1762.—illem.
vol. iv. p. 171.— Edinb. Trans. vol. iii. part. 2. p. 26— Commen t . G ot /nig . vol. xiii. Boscovichii Opera ; and Klingenstierna de .1berratiombus ',amines. See also Ac nsomAric. TELESCOPES, and OrTics. (Si')