OPTICAL PRINCIPLES OF THE MICROSCOPE. T 



-\vhich pass through lenses whose curvatures are equal over their whole 

 surfaces. If the course 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 

 a by a b, which are nearer the 

 line of its axis. This may 

 be shown experimentally, by 

 * stopping out ' either the cen- 

 tral or the marginal portion of 

 the lens; for it will then be Diagram illustratin s s * herical ^*"- 

 found that the rays which are allowed to pass through the latter alone 

 form a distinct image at F; whilst those which pass through the former 

 alone form a distinct image at /. Hence, if the whole aperture be in 

 use, and 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; whilst, if the screen be 

 carried back into the focus f of the latter, the rays which were most dis- 

 tant 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 indistinctness; 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 the desired effect could be produced by 

 such an increase of the curvature round the centre of the lens, and such 

 a diminution of the curvature towards its circumference, as would make 

 the two foci coincident. And the requisite conditions may be theoreti- 

 cally fulfilled by a single lens, one of whose surfaces, instead of being 

 spherical, is 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 construc- 

 tion is altogether unavailable; besides which, their performance would 

 only be perfectly accurate for parallel rays. 



10. Various means have been devised for reducing the aberration of 

 lenses of spherical curvature. In the first place, it may be kept down by 

 using ordinary lenses in the most advantageous manner. Thus the aber- 

 ration of a Plano-convex lens whose convex side is turned towards paral- 

 lel rays, is only ly^ths of its thickness; whilst, if its plane side be turned 

 towards them, the aberration is 4J- 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 

 liaving the least spherical aberration, is a Double-convex whose radii are 

 as one to six: when the flattest face of this is turned towards parallel 

 rays, the aberration is nearly 3-J times its thickness; but when its most 

 convex side receives or transmits them, the aberration is only lyj^ths of 

 its thickness. Spherical Aberration is further diminished by reducing 



