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changed. All rays from 5 in the horizontal plane emerge plane polarized 

 and can be extinguished by an analyzer set for vertical extinction. The 

 ray po is in both these planes so it can be similarly extinguished. 



With the ray ps the situation is different. Here the vibration is not in the 

 z p3 plane so the ray breaks up inside the crystal into two components which 

 travel with different velocities and recombine in or out of phase to give the 

 various degrees of elliptical polarization (including plane and circular). 

 Hence, an eye looking back along ps, through an analyzer set for vertical 

 extinction, will see light or dark depending on the phase shift N. Now this 

 phase shift for a given thickness of plate is zero along po but increases as 

 6 increases (without changing <^; see Fig. 2.28), passing through one integral 



<1) = I 80° 



Fig. 2.29 — A plot of phase as a function of <f> and d 



value after another. Therefore, as we allow 6 to increase, the eye should 

 see alternate dark and bright regions. Moreover, since the crystal is op- 

 tically symmetric about z, if </> is changed without changing d, the apparent 

 brightness will not change (except that if </> = 0, 90°, 180° or 270° the field 

 is dark as we previously explained). Consequently, if we could see along 

 all directions at once we would see a pattern of concentric dark rings on a 

 dark cross as shown in Fig. 2.29. 



But we can see along all these directions at once if we employ a properly 

 placed lens for a lens can converge all these rays to one point where an eye 

 can be placed for viewing. 



Thus an eye at e, Fig. 2.30, will see, in the direction e po, the ray that 



