Understanding Double Refraction & Its Impact on Refractive Indices

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Double refraction occurs in certain materials, like crystals, due to the presence of an optical axis that affects light propagation. The ordinary ray travels parallel to this axis, while the extraordinary ray travels perpendicular, resulting in different velocities for each. This difference in velocity is caused by the orientation of the electric field components relative to the optical axis. Consequently, the ordinary and extraordinary rays exhibit distinct refractive indices, leading to the splitting of light into two separate rays. Understanding these principles is crucial for grasping the implications of double refraction in optics.
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Im trying to understand double refraction, but have certain doubts.

One question is, that why does the direction of oscillation of the ordinary and extraordinary ray change their refractive indices?

Why is it that when one component of the electric field is perpendicular to the optic axis, it has a different velocity and the one parallel to the axis has another velocity? I understand that their different velocities lead to their different refractive indices, but don't know why the velocities are different.

Here are some notes : http://edafologia.ugr.es/OptMine/intro/doblerew.htm
 
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Double refraction occurs when light passes through certain types of materials, such as crystals. This phenomenon occurs because the material has an optical axis, which is a direction in which the light waves propagate more slowly than in other directions. For example, in a calcite crystal, the ordinary ray of light (the one that does not experience double refraction) will be parallel to the optical axis, while the extraordinary ray (the one that experiences double refraction) will be perpendicular to the optical axis. The different velocities of the two rays are due to the fact that they are oscillating in different directions: the ordinary ray is oscillating along the optical axis, while the extraordinary ray is oscillating perpendicular to the optical axis. Thus, the material has different refractive indices for the two rays, and this leads to the splitting of the beam into two separate rays.
 
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