How did calcite crystals produce double refraction in Erasmus Bartholin’s experiments?

Erasmus Bartholin did not explain the mechanism behind double refraction in his experiments; rather, he was the first to observe and document the phenomenon. While he correctly identified that the calcite crystal split a single ray of light into two distinct beams—which he termed the "ordinary beam" (which remained stationary) and the "extraordinary beam" (which rotated with the crystal)—the underlying physical cause remained unknown to him at the time.1

In modern physics, we understand that double refraction occurs because calcite is an anisotropic medium. When unpolarized light enters the crystal, it is split into two rays that are polarized in planes vibrating at right angles to each other. The ordinary ray travels through the medium with a constant refractive index in all directions, while the extraordinary ray experiences a varying refractive index, causing it to bend at an angle and travel at a different speed. This difference in velocity and direction is what creates the two visible images.23