260 Image Formation by Crystalline Media, 



Crystalline Components in a Lens System. 



Whenever a crystalline component, — lens or plane-parallel 

 plate, — which produces two image series is incorporated into 

 a lens system, the system as a whole will of course produce 

 two series of images. For example, for a doublet consisting 

 of a lens of crystal of powers K' and K" and a lens of glass 

 of power K, the combination will have the powers K'-fK 

 and K" + K. It is evident that the relative values of the 

 powers of such a combination may be made almost any- 

 thing one wishes ; one of the values may even be made zero 

 by choosing the glass lens of power equal and opposite to that 

 of the selected crystal power. In this case the other power 

 will be the difference K' — K" of the powers of the crystal 

 lens. 



Again, it will not be possible to produce an achromatic 

 doublet which will at the same time correct the chromatic 

 aberration of both powers of a lens of crystal. If g/, co", co, 

 are the dispersions for the ordinary and extraordinary powers 

 of the crystalline lens and of the glass lens combined with 

 it, and K', K", K the corresponding mean powers, the 

 chromatic aberrations of the powers of the combination are 



o/K'-f o>K, and a>"K" + o>K. 



If the values of co and K are so chosen that one of these 

 is zero in accordance with the ordinary principles of 

 Geometrical Optics, the value of the other will be 



ft)"K // -a)'K / , 



and this will not likely happen to be zero. In the case of a 

 lens of Iceland spar, of which the principal indices are about 

 1*66 and 1*49 and th«e dispersions for the D— F lines *014 

 and *0O88, this outstanding chromatic aberration will be 

 — '0051 (1/r— 1/s), or about '02 of the power of the com- 

 bination if the glass lens has the index 1*62 and the 

 dispersion *02, 



Summary. 



Laws for the image position are developed for a number 

 of typical cases of image formation by the extraordinary 

 rays in uniaxial ciystals. 



It will be noticed that in the examples of light travelling 

 along the axis of the crystal, the thickness of the crystal 

 traversed enters into the expressions for image position as if 

 the index were ?u 2 /n 1 as compared with isotropic substances; 

 n x and n 2 are the principal indices of the crystal. This 

 quantity may be considered a sort of pseudo-index applicable 

 to such cases. 



It is shown that lenses of crystal will in general form two 



