Bi-refraction by calcite crystal

[Ryoukomaru]

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 ?

 

[Pieter Kuiper]

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

 

[Graeme Robinson]

Bi-refraction by calcite crystal, also known as double refraction, occurs when light passes through a calcite crystal and splits into two rays. One ray, known as the ordinary ray, travels straight through the crystal, while the other ray, known as the extraordinary ray, is refracted. This phenomenon is caused by the unique crystal structure of calcite, which has two different refractive indices in different directions.

The ordinary ray travels faster than the extraordinary ray because the speed of light is inversely proportional to the refractive index. However, in the case of calcite, the ordinary ray actually travels slower than the extraordinary ray. This is because calcite has a negative birefringence, meaning that its ordinary refractive index is lower than its extraordinary refractive index.

This phenomenon can be explained by the crystal structure of calcite. In calcite, the atoms are arranged in layers that are perpendicular to the direction of light propagation. When light enters the crystal, it is split into two rays, one of which travels along the layers of atoms (the ordinary ray) and the other travels between the layers (the extraordinary ray). The layers of atoms act as a barrier for the ordinary ray, slowing it down and causing it to travel slower than the extraordinary ray.

In conclusion, the negative birefringence of calcite results in the ordinary ray traveling slower than the extraordinary ray, even though the ordinary refractive index is usually higher. This unique property of calcite makes it a valuable material in various optical applications, such as polarizers and waveplates.