Formation by Crystalline Media. 259 



Keeping these observations in mind, the following con- 

 clusions may be easily deduced : — 



(1)* For an object-point within a crystal at a distance p 

 from a plane refracting surface. 



Distance from surface to : 



(a) focal line parallel to axis . . pjn 2 ; 

 {b) focal line at right angles to axis, pn 2 /n l s ; 

 (c) ordinary image p/ n i* 



(2) For a lens of crystal. 



The powers of the first and second surfaces and of the lens 

 as a whole are : — 



(a) for pencils of ordinary light : 



h 



_ "i 



ko — 



K = ki + Ji' 2 + k^t/ni ; 



(b) for focal lines parallel to the optic axis of the crystal, 

 as governed by the circular section of the wave-surface: 



1 , , 1-7?, 

 s 



*i' = 



h' = 



K'==* 1 '+Jfe/+* 1 , ife 1 , «/"i 



(c) for focal lines at right angles to optic axis, governed 

 by elliptic section of wave-front : 



k ji = "jrzl s if = kill 5 K" = h" + h" + Wtnzlnf. 



Knowing the values of the powers for these cases, the 

 positions of the sets of cardinal points of the lens and the 

 formulae relating object to image positions may be written 

 down in accordance with the standard formulae for these 

 quantities, — it was shown in the discussion of Section 5 that 

 these formulae in a modified form apply to the refraction of 

 the elliptic wave. 



It will be seen that the powers of the individual refracting 

 surfaces are the same for both the principal sections of the 

 wave-front. The powers of the lens as a whole differ, 

 however, in the term which involves the thickness, so that 

 the amount of the astigmatism is governed by the thickness ; 

 if the thickness is negligible the focal lines degenerate into 

 a point and the emerging pencil remains homocentric. The 

 powers for the ordinary and extraordinary waves are, how- 

 ever, essentially different for each surface and for the lens 

 as a whole. There are therefore always two image series 

 for a lens of crystal cut as described in this section. 

 * Included in Stokes's discussion. 



