CHROMATIC ABERRATION 



115 



focus in the same plane : then the images would, though superposed, be of 

 different sizes. And in order to correct as far as possible these defects, an 

 under correction in one couplet is compensated by an over-correction in the 

 next. Abbe's apochromatic oil-immersion objective is made up of ten lenses, 

 as illustrated in the figure. Even then the achromatism is only carried out 

 with regard to the position of the image, not to its size. Without entering 



FIG. 109. Abbe's apochromatic oil-immersion objective. 



upon a discussion of the calculations necessary to determine the curvatures 

 of the different lenses, it may be said that in practice if an objective be 

 over-corrected, that is if the power of the flint glass be too great in pro- 

 portion to that of the crown glass, the error may be rectified by slightly 

 separating the lenses by means of a compensating collar : this has practi- 

 cally the effect of decreasing the power of the flint lens. Now if an object 

 be examined under a microscope with an achromatic objective it will be 

 found that the image has either a bluish outline or a yellowish outline. 

 The former is the more common defect, and is due to over-correction, while 

 the latter is a result of under-correction. Abbe's apochromatic objective 

 being achromatic for three colours, is free from secondary spectra ; since 

 however the achromatism has regard to the position of the images, not 

 to their sizes, the blue image though formed in the same plane as the red 

 image is larger than the latter. This error is subsequently corrected by the 

 compensating ocular, which produces larger red images than blue. More- 

 over the sine condition is attained for two colours so that each of these 

 images is aplanatic, i.e. the image formed by these two colours is free from 

 spherical aberration and coma. It will therefore be seen that no lens is, 

 in the strict sense of the word, achromatic. 



Apochromatic lenses with the necessary compensating eyepieces are very 

 expensive, and are only necessary for special work. Ordinary achromatic 

 objectives are quite sufficient for general purposes. 



9. Flatness of image. 



Even now all the defects of the image formed by a simple lens have not 

 been studied, for it will always be found that the image is curved. To secure 

 flatness. of the image, a condition known as Petzval's condition must be 

 satisfied. 



Petzval's condition for flatness of image. A couplet must satisfy the condition 

 that 



But the essential condition for achromatism is 



