The optic axis of a calcite crystal is the direction in which mixed-polarization light does not split into two beams, due to the uniform atomic structure in that direction. Calcite is birefringent, causing light to refract differently based on polarization, resulting in double images when viewed through the crystal. When polarized light is used, it does not split because it can only refract in one way. The discussion also touches on the concept of the principal plane and principal axis, which relate to the crystal's optical properties and how light interacts with its structure. Understanding these concepts can be explored through hands-on experimentation with calcite crystals.