SPECIFYING QUARTZ CRYSTAL ORIENTATION 243 



of this light is X, and as in a vacuum its velocity is V(— 3 X lO^" cms per 



V 

 F 



second) an equation similar to (2.3) would tell us that X = -^ and hence that: 



F = i (2.5) 



With (2.5) we can rewrite (2.4) as 



X \V/ Vs/ 



The ratio of the velocity in a vacuum to the velocity in a medium is called 

 the refractive index of the medium commonly given the symbol n. For 

 most transparent materials n is between 1.3 and 1.8. 



V.'e write these refractive indices as 



V V 



— = fif and — = Hg respectively. 



Vf I's 



Now (2.4) becomes: 



iV = ^ («/ - n,) (2.7) 



After passing through the crystal plate of thickness t, Fig. 2.21, the two 

 light components recombine. They are polarized at right angles each to 

 each ; they are of unequal intensities, and they differ in phase by N wave- 

 lengths as given by equation (2.7). 



If the crystal were vanishingly thin the two components that recombine 

 would be effectively in step or in phase. In Fig. 2.24 we have plotted vibra- 

 tion amplitude against time for these two components. They are sep- 

 arated for clarity. In the upper curve the slow vibration is shown as ver- 

 tical, in the center curve the fast one is shown as horizontal. In the lower 

 curve corresponding points have been added vectorially. From actual con- 

 struction we see that in the resultant curve the vibration is always parallel 

 to the line AA' . Hence it is plane polarized and can be extinguished by 

 means of an analyzer. 



Let us now consider the case of a thicker plate for which the slow wave 

 gets a quarter-wave-length behind the faster one. This case is plotted in 

 Fig. 2.25 in the same way that the previous case was plotted in Fig. 2.24. 

 It turns out to be a space curve like a slightly flattened corkscrew. Viewed 

 along the axis it looks like an ellipse, as shown to the right of the space 

 curve. If the slow ray had lost but a little with respect to the fast ray, we 

 would have gotten a very flat ellipse. If the two components had had the 



