164 . TESTING THE MICROSCOPE. 



this case, however, if produced backwards, they meet the plane of 

 the virtual images so that the red is on the outside, and the violet 

 on the inside, of the field of view. The object has therefore a red 

 or orange-coloured border. Conversely, too great an approximation 

 of the eye-lens to the field -lens causes a blue border, because the 

 divergence of the emergent rays is increased, and the violet pencils 

 meet the field of view at a greater distance on the outside. 



From what we have just stated, it follows that for every eye a 

 particular position of the eye-lens may be found, at which the 

 differently coloured emergent pencils, when produced backwards, 

 will cross each other exactly at the distance for which it is 

 adjusted. They then unite in one point of the retina to form 

 white light, and the resulting image is free from coloured borders. 



So far the conclusions we have drawn have a general validity, 

 since the over-correction or under-correction of the objective does 

 not here come into account. For complete achromatism it is, 

 however, necessary that the virtual images of / and v' t which are 

 last observed, should be situated at the same distance at which 

 the corresponding cones of light intersect ; in other words, the 

 axes of the differently coloured cones of light must converge back- 

 wards to the same points, from which also the single rays of a cone 

 appear to come. This condition cannot be fulfilled for the right 

 and left sides of the figure simultaneously, because the distances 

 of the similarly coloured real images from the eye-piece are not 

 the same. In consequence of the chromatic aberration 1 of the 

 eye-piece it is even indispensable that v f should be brought some- 

 what nearer than r, if the virtual images if and r" are to coincide. 

 The opposite arrangement, which accompanies the under-correction 

 of the objective, is, therefore, incompatible with the conditions of 



1 The following figures may be of service for more exact consideration. A 

 plano-convex crown lens, whose radius of curvature is equal to 15 mm., gives 

 for the focal length of the violet rays 27-77 mm., for the red rays 28-84 mm. ; 

 consequently a longitudinal chromatic aberration of 1 mm. Similarly, with a 

 radius of curvature of 25 mm., the corresponding focal lengths are 46-3 mm. 

 and 48 mm. If the latter lens is used as the field-lens, and the former as the 

 eye-lens, and if the distance of the virtual object from the field-lens is taken 

 as 50 mm., the violet image of the latter appears at a distance of 24 mm., and 

 the red image is ^ mm. higher still. Since the chromatic aberration of the 

 eye-lens requires exactly the opposite arrangement, the objective must be over- 

 corrected to such a degree that the red rays converge to a point about 6 mm. 

 lower. 



