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If ordinary and extraordinary rays emerge out of calcite crystal at different points(double refraction) then why do we consider perpendicular electromagnetic wave components shifted by a phase in case of wave plates emerge at the same point?

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This is because of how wave plate is made and used. The crystal is cut so that the optic axis is parallel to the long faces. Incident rays are normal to the plate and the optic axis so there is no refraction, only retardation. Wave plates are typically very thin (about 0.1mm) so even if the angle of incidence is not zero the deviation is very small compared with the diameter of the beam.

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  • $\begingroup$ Then whats the thing that is different in crystal in case of double refraction? Even though the incident ray is normal it undergoes refraction, right? $\endgroup$ – Akhil Nov 30 '17 at 13:14
  • $\begingroup$ Yes that is correct, but it depends on the orientation of the optic axis. I have updated my answer. $\endgroup$ – sammy gerbil Nov 30 '17 at 13:21
  • $\begingroup$ But how can we add those two perpendicular components of EM wave given that microscopic deviation? $\endgroup$ – Akhil Nov 30 '17 at 13:25
  • $\begingroup$ The beam is usually from a laser, so it has good spatial coherence across the beam. Two parts of the beam will interfere if they are coherent. $\endgroup$ – sammy gerbil Nov 30 '17 at 16:10

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