Formation by Crystalline Media. 257 



only when the thickness is negligible. In consequence of 

 this it will not be possible with thick lenses of crystal to 

 focus sharply either on a photographic plate or in the focal 

 plane of an eyepiece. The two most important cases in 

 which this may affect the efficiency of the lens are in its use 

 as objective of telescope or collimator. In these cases it is 

 the separation of the one set of principal foci which is 

 important. This separation may be estimated as follows : — 

 The distances from the lens to the second principal foci 

 are determined by setting the arbitrary parameter equal to 

 zero in (16) and (18). giving 



0=-K .FN + (l + ^,/V), 



0=-K' . Jf'N+CL + #*/»!), 



from which the distance between the foci is equal to 



k / H(n 1 2 -n 2 2 )/n 2 2 n l KK\ 



In a quartz lens of say about 20 cm. focal length and 

 surfaces of equal curvature, this amounts to about "00 J of 

 the thickness, and in a calcite lens of the same power to 

 about '0o7 of the thickness. The separation is thus un- 

 important in quartz lenses of less than about "5 cm. thickness 

 except for the highest magnifications. 



This separation of the second principal foci disappears 

 when the first surface of the lens is plane, so that plane 

 waves are unchanged in shape until the second surface is 

 passed, but in this case the separation of the first principal 

 foci is proportionately greater on account of the fact that the 

 whole of the dioptric power is produced at the one surface. 

 Similar considerations would show that the separation of the 

 first principal foci would be zero for a lens with the second 

 surface plane. The fact of double refraction requires, 

 therefore, that the objectives of collimator and telescope be 

 plano-convex and that the lenses be placed with plane 

 faces out. 



6. linage-formation by direct refraction by uniaxial crystals 

 cut so that the optic axis is at right angles to the geometrical 

 axis of the refracting system. — For such examples of refraction 

 of the extraordinary wave, the part of the spheroid presented 

 to the refracting surface lies in the neighbourhood of zero 

 latitude. The curvatures in normal sections in this part of 

 the wave-front are unequal, so that on refraction by a 

 symmetrical system an astigmatic image will be formed. 

 Since the principal curvatures lie in and at right angles to 



Phil. Mag. S. 6. Vol. 32. No. 188. Aug. 1916. S 





