This strange splitting happens because some materials have a very uneven internal atomic structure. Scientists call these uneven substances anisotropic materials. In a perfectly even crystal, light travels at the exact same speed in every single direction.
But in a birefringent crystal, the atoms are packed much tighter in one specific direction. When regular unpolarized light enters this uneven crystal, it instantly breaks into two parts. These parts are named the ordinary ray and the extraordinary ray.
The ordinary ray acts normally and follows the standard rules of bending light. The extraordinary ray acts strangely because it feels a totally different level of optical crowding. Because they face different atomic crowding, the two rays bend at different angles and take different paths.
We measure this bending effect using the birefringence coefficient. This value is found by subtracting the lowest refractive index from the highest refractive index. A common student misconception is that the crystal is somehow creating new light energy.
In truth, the crystal is just sorting the existing light waves based on how they wiggle. This natural sorting trick is incredibly useful for building modern liquid crystal displays and polarizing filters.