Bi-refraction by calcite crystal

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SUMMARY

When light passes through a calcite crystal, it undergoes bi-refraction, splitting into two distinct rays: the ordinary ray and the extraordinary ray. The ordinary ray travels straight and is faster, while the extraordinary ray is refracted and travels slower due to the negative birefringence of calcite. This phenomenon is governed by Snell's law, and the extraordinary ray's velocity varies based on its angle relative to the optical axis. The wavefronts in this context are ellipsoidal rather than spherical, as illustrated in the provided PDF resource.

PREREQUISITES
  • Understanding of Snell's law
  • Familiarity with optical properties of materials
  • Knowledge of birefringence and its implications
  • Basic principles of wavefront construction
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  • Study the principles of birefringence in detail
  • Learn about the optical properties of calcite crystals
  • Explore Huyghens' principle and its applications in optics
  • Investigate the implications of negative birefringence in various materials
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Physicists, optical engineers, and students studying optics who seek to understand the behavior of light in birefringent materials like calcite crystals.

Ryoukomaru
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When light passes through calcite crystal it splits into two rays, extra ordinary and an ordinary ray. Ordinary ray travels straight and extra ordinary ray is refracted. This would mean ordinary ray travels faster and e-ordinary ray travels slower because index of refraction is inversely proportional to speed. But somewhere (here) I read that calcite has an negative birefringence therefore ordinary ray travels slower. Can some1 explain this to me ?
 
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Well, the ordinary ray travels straight only at normal incidence. At other angles it is refracted according to Snell's law.

The extraordinary ray is polarized perpendicular to the ordinary ray. Depending on its angle with respect to the optical axis, it travels at different velocities. In a Huyghens construction, the wavefronts are not spherical but ellipsoidal. This one can use to construct the direction of the extraordinary ray. Here is a .pdf with some figures:
http://www.ph.rhul.ac.uk/course_materials/PH231/POLnotes.pdf
 

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