256 



Prof. H. F. Dawes on Image 



is determined in terms of the optical constants of the system 

 and the position of the object. The method corresponds to 

 the standard one of dealing with a thick lens. Thns : 



y - ci = k'ij' + k"y", by addition, from (12, 13), 



= k'y' + k"y' + k"t/3, by (11), 



= k'y' + k"y r + k"tn l 2 8/n 2 2 



= k'ij + k"y , + k"tn 1 k f y'h h 2 



+ k // tn 1 */n 2 2 , by (12). 

 Hence 



y/a=K . PM + (1 + £'W;> 2 2 ), (14), 



where K is the power of the system and is equal to 



k' + k" + k'k' / tn l /n 2 2 , (15). 

 Similarly, 



u/y=-K . TN + fl-f^W), (16). 



(14) and (16) state the fundamental general law for the 

 image-position by expressing the distances from the refracting 

 surfaces to object and image in terms of the ratio 7/a, which 

 may be considered an arbitrary parameter. These formulae 

 are similar to the standard formula? for a lens of isotropic 

 substance *, the modification consisting essentially in that 

 the distance travelled within the crystal is divided by w 2 2 / w i» 

 corresponding to division by the index in ordinary lenses. 

 The positions of the cardinal points of the lens and the lens 

 formulae of standard type may therefore be written down on 

 this basis. 



In addition to the image system formed by the light 

 which traverses the lens as the extraordinary wave-front, 

 there is an image system produced by the ordinary wave- 

 front, and although the light traverses the lens in the 

 neighbourhood of the optic axis the two image-systems are 

 not coincident. The fundamental formulae corresponding to 

 (14, 16, 15) are for this system, 



y/*=K' .TM+{l + k"t/n 1 ), (17), 



a/ry=-K' . TW + pL + Vt/nj), (18), 



where K' the power of the lens is 



k' + k" + k'k"t/n 1 , (19). 



It will be seen that the difference in the two sets of 

 foimulse lies in the terms which involve the thickness of the 

 lens, so that the two images of an object coincide when and 



* See Hermann, ' Geometrical Optics/ p. 57. 



