10 OPTICAL PRINCIPLES OF THE MICROSCOPE. 



of the rays passing through an ordinary Convex Lens be carefully 

 laid down (Fig. 8), it will be found that they do not all meet 

 exactly in the foci already stated ; but that the focus f of the rays 

 ab, ab, which have passed through the marginal portion of the 

 lens, is much closer to it than that of the rays ab, ab, which are 

 nearer the line of its axis. Hence, if a screen be held in the 

 focus F of the marginal portion of the lens, the rays which have 

 passed through its central portion will be stopped by it before they 

 have come to a focus ; and if the screen be carried back into the 

 focus / of the latter, 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, and will pass to c and d. In either 

 case, therefore, the image will have a certain degree of indistinct- 

 ness; and there is no one point to which all the rays can be 

 brought by a single Lens of Spherical curvature. The distance f/, 

 between the focal points of the central and of the peripheral rays 

 of any lens, is termed its Spherical Aberration. It is obvious 

 that, to produce the desired effect, the curvature requires 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 con- 

 ditions may be theoretically fulfilled by a single lens, one of whose 

 surfaces, instead of being spherical, should be a portion of an 

 ellipsoid or hyperboloid of certain proportions ; but the difficulties 

 in the way of the mechanical execution of lenses of this description 

 are such, that for practical purposes this plan of construction is 

 altogether unavailable ; and their performance would only be per- 

 fectly accurate for parallel rays. 



10. Various means have been devised for reducing the Aberra- 

 tion of lenses of Spherical curvature. It may be considerably dimin- 

 ished, by making the most advantageous use of ordinary lenses. 

 Thus, the aberration of a Plano-convex Lens whose convex side is 

 turned towards parallel rays, is only 1 Tooths of its thickness ; 

 whilst, if its plane side be turned towards them, the aberration is 

 44 times the thickness of the lens. Hence, when a plano-convex 

 lens is used to form an image by bringing to a focus parallel or 

 slightly-diverging rays from a distant object, its convex surface 

 should be turned towards the object ; but, when it is used to render 

 parallel the rays which are diverging from a very near object, its 

 plane surface should be turned towards the object. The single 

 lens having the least spherical aberration, is a Double-convex whose 

 radii are as one to six : when its flattest face is turned towards 

 parallel rays, the aberration is nearly 3^ times its thickness ; but 

 when its most convex side receives or transmits them, the aberra- 

 tion is only ljlgths of its thickness. Spherical Aberration is 

 further diminished by reducing the aperture or working-surface 

 of the lens, so as to employ only the rays that pass through its 



