Final answer:
The ordinary and extraordinary rays along the optic axis of a birefringent crystal like calcite travel with different velocities. The ordinary ray follows Snell's law, whereas the extraordinary ray does not, and its speed depends on its direction of propagation and its angle with the optic axis.
Step-by-step explanation:
Along the optic axis of a crystal, the velocities of the ordinary and extraordinary rays are different due to the phenomenon of birefringence. Birefringent materials, such as calcite, have two distinct indices of refraction. The ordinary ray follows Snell's law and is polarized with its electric field oscillating perpendicular to the optic axis, propagating at the speed of light divided by the ordinary index of refraction of the crystal.
Meanwhile, the extraordinary ray does not obey Snell's law and is polarized with its electric field oscillating in a plane containing the optic axis, with its velocity depending on the direction of propagation and the angle with the optic axis.
Directly along the optic axis, the extraordinary ray travels at the speed of light divided by the ordinary index of refraction, the same as the ordinary ray. However, at any other angle, its velocity can differ and is generally described using the extraordinary index of refraction, which varies with the direction in comparison to the optic axis.