334 



MICROSCOPE. 



Fig. 155. 



Formation of images by convex lenses. 



lance on the other side of the lens, will be of 

 the same dimensions with the object : whilst, 

 on the other hand, if the object be nearer the 

 lens, the image will be farther from it, and of 

 larger dimensions ; and if the object be farther 

 from the lens, the image will be nearer to it, and 

 smaller than itself. Further, it is to be re- 

 marked, that the larger the image in proportion 

 to the object, the less bright it will be, because 

 the same amount of light has to be spread over 

 a greater surface ; whilst a smaller image will 

 be much more brilliant, in the same proportion. 

 The knowledge of these general facts will 

 enable us readily to understand the ordinary 

 operation of the microscope ; but the instru- 

 ment is subject to imperfections of various 

 kinds, the mode of remedying which cannot be 

 comprehended without an acquaintance with 

 their nature. One of these imperfections re- 

 sults from the spherical aberration of the rays 

 which have passed through lenses, whose curva- 

 tures are equal over their whole surfaces. If 

 the course of the rays be carefully laid down, it 

 will be found that they do not all meet exactly 



Fig. 156. 



A B, rays falling on the periphery of the lens; F, 

 focus of these ; a, b, rays falling nearer the 

 centre ; /, more distant focus of these. 



in the foci already stated, but that the focus of 

 the rays which have passed through the peri- 

 pheral- portion of the lens is much closer to it 

 than that of the rays which are nearer the line 

 of its axis ; so that, if a screen be held in the 

 former, the rays which have passed through the 

 central portion of the lens will be stopped by 

 it before they have come to a focus ; and if the 

 screen be carried back into the focus of these, 

 the rays which were most distant from the axis 

 will have previously met and crossed, so that 

 they will come to it in a state of divergence. 

 In either case, therefore, the image will have a 

 certain degree of indistinctness ; and there is 

 no one point to which all the rays can be 

 brought by a lens of spherical curvature. The 

 difference between the focal points of the cen- 

 tral and of the peripheral rays is termed the 

 spherical aberration. It is obvious that, to 



produce the desired effect, the curvature is re- 

 quired to be increased around the centre of 

 the lens, so as to bring the rays which pass 

 through it more speedily to a focus, and to be 

 diminished towards the circumference, so as to 

 throw the focus of the rays influenced by it to 

 a greater distance. The requisite conditions 

 may be exactly fulfilled by a lens one of whose 

 surfaces, instead of being spherical, is a portion 

 of an ellipsoid or hyperboloid of certain pro- 

 portions ; but the difficulties in the way of the 

 mechanical execution of lenses of this descrip- 

 tion are such, that, for all practical purposes, 

 they have been entirely abandoned in favour of 

 lenses with spherical surfaces. Various means 

 have been devised for diminishing the aber- 

 ration of these. In microscopes of ordinary 

 construction, the method employed is to dimi- 

 nish the aperture or working surface of the lens, 

 so as to employ only the rays that pass through 

 the central part, which, if sufficiently small in 

 proportion to the whole sphere, will bring them 

 all to nearly the same focus. The use of this 

 may be particularly noticed in the object-glasses 

 of common microscopes ; where, although the 

 lens itself be large, the greater portion of its 

 surface is rendered inoperative by a stop, which 

 is a plate with a circular aperture interposed 

 between the lens and the rest of the instrument. 

 If this aperture be gradually enlarged, it will 

 be seen that, although the image becomes more 

 and more illuminated, it is at the same time 

 becoming more and more indistinct; and that, 

 in order to gain defining power, the aperture 

 must be reduced again. Now this reduction is 

 attended with two great inconveniences ; in the 

 first place, the loss of intensity of light, the de- 

 gree of which will depend upon the quantity 

 transmitted by the lens, and will vary therefore 

 with its aperture ; and, secondly, the diminu- 

 tion of the number or quantity of rays, which 

 will prevent the surfaces of objects from being 

 properly seen. Thus, for example, we shall 

 suppose the observer to be looking at the scales 

 of a butterfly's wing with a microscope fur- 

 nished with two object-glasses of the same 

 focal length, one corrected, the other not so. 

 If, with the same illumination of the object, he 

 apply to it the uncorrected objective, the aper- 

 ture of which is necessarily small, after having 

 looked at it with the corrected lens, he will, in 

 the first place, perceive that the whole field is 

 much darker; but if, by increasing his illumi- 

 nation, he give the image an equal brightness, 

 and see its outline with equal distinctness, he 

 will be completely unable to see with the un- 

 corrected lens a series of delicate lines upon 

 the surface of the scale, which the other makes 

 evident. The power of exhibiting these and 

 similar objects is termed penetration ; it de- 

 pends upon the size of the conical pencils of 

 light admitted by the lens, and therefore upon 

 its aperture. 



The spherical aberration may be considerably 

 diminished by making the most advantageous 

 use of single lenses. Thus the aberration of a 

 plano-convex lens, whose convex side is turned 

 towards parallel rays, is only -i^s 1 ' 15 f * ts 

 thickness, whilst, if the plane side be turned 



