Elements of natural philosophy (Volume 2-3) . m to move from thesenew positions without having at any time occupied the first case the image will be real and in the second Real image;virtual. In general, but a part of each wave can be de-viated by the use of spherical deviating surfaces to sat-isfy these conditions, for those portions remote from the Yirtual imacr0iundeviated ray of each pencil cannot, in consequence ofaberration and astigmatism, be brought to accurate ver-gency. §62. To ascertain the relation between an object and To find theits image, let us suppose the deviation to
Elements of natural philosophy (Volume 2-3) . m to move from thesenew positions without having at any time occupied the first case the image will be real and in the second Real image;virtual. In general, but a part of each wave can be de-viated by the use of spherical deviating surfaces to sat-isfy these conditions, for those portions remote from the Yirtual imacr0iundeviated ray of each pencil cannot, in consequence ofaberration and astigmatism, be brought to accurate ver-gency. §62. To ascertain the relation between an object and To find theits image, let us suppose the deviation to be produced relat1ion bet^ ° J x x -L an object and its by a lens, so thin that its thickness may be neglected, image formed bywhich is the usual case in practice. The optical centre alens;<r, may be taken ,i . ,» Fig. 39. as the origin oi co-ordinates. Denot-ing by Z, the dis-tance from thispoint to any as-sumed point P inthe object, and writing this quantity for /, in Equation (33), which wemay do without sensible error, we get. /= F. ii F14- — W^V corresponding toan assumedradiant point. 224: NATURAL PHILOSOPHY. Section of tbe Let the object be a plane, perpendicular to the axis object assumed to Qf ^ ^ ^ section ^jj b(} & . ^ ^ p ^ q^ . be a right line; ° ^ the angle included between the axis of any oblique pen-cil and the axis of the lens. When the pencil becomdirect, & will be zero, and I will equal f. But, generally,we have General relation; I- f ? cosd this in Equation (50), reduces it to Equation of theimage of a rightline; /= F. a 1 j a cos 6 (51) which, is the polar equation of the image referred to theoptical centre as a pole. It is the same in form as thepolar equation of a conic section, which is Is the same inform as that of aconic section; A{l-e2)<r = — *- 1 + e cos v Conclusion; Whence we conclude that the image of a straight lineperpendicular to the axis of the lens which forms it, isa conic section, and comparing the two Equations, wefind, J
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