430 C. Trams — Behavior of Crystals in Light 



„. A ^ AD 2 (Ztan^) 2 

 A (tftan^) 2 



2DA 



For other pairs of rays in the plane of the axes, the relative 

 lengths of SA and SD are changed, but the phase difference A 

 at the point of interference is constant if the rays are so nearly 

 parallel to the axis that their front velocity in the crystal may 

 be considered constant. The reason for this is evident upon 

 reference to iig. 1 and the accompanying discussion. 



When the section is not cut normal to the optic axis (as in 

 figure 1), it can be shown that the above results hold if t', the 

 thickness parallel to the axis, be substituted for t. 



For equally thick sections, with the source of light at a con- 

 stant distance, the maximum phase difference A, due to the 

 cause considered above, depends upon tan <j> L . The value of 

 (£i for aragonite is 1° 50', which is exceeded in very few other 

 substances ; the greatest known value is that for sulphur, for 

 which 0j = 7° approximately. Approximate values of A for 

 sections of sulphur and aragonite, with D assumed as one meter, 

 and X as 0'0005 mrh , are as follows : 



Sulphur Aragonite 



t (mm.) A t (mm.) A 



10 1-0 10 0-1 



5 0*25 5 0-025 



1 0-01 1 0-001 



We may conclude from this, that with the source of light at 

 distances commonly used when working with the polarizing 

 microscope, A becomes practically zero in the very great majority 

 of cases. (This assumes that the condensing system is removed 

 from the polarizer.) Any illumination that is observed between 

 crossed nicols is, therefore, due to the fact that the direction 

 of the light is so inclined to the optic axis that one ray is appre- 

 ciably retarded with respect to the other, in traversing the 

 crystal. In other words, the behavior of the crystal in light 

 that is approximately 'parallel to an optic axis, must be 

 referred to interference effects of exactly the same nature as 

 those observed in any general section, with the light falling at 

 any inclination to the axis. 



§ 3. The relative amount of light that a crystal section will 

 transmit, when examined between crossed nicols, may be 

 determined by means of the interference figure given by the 

 same section in convergent light. This figure is virtually a 

 spherical projection, in which each point represents a ray direc- 

 tion : if a is the angle between a given direction and the line 



