Polarisation by Double Refraction

Erasmus Bartholinus, a Danish physicist, discovered that when a ray of unpolarised light is incident on a calcite crystal, it splits into two separate refracted rays, so a single object viewed through the crystal appears doubled -- a phenomenon called double refraction, or birefringence, also shown by other crystals such as quartz and mica. Viewing an ink dot through a calcite crystal and rotating the crystal shows one image (the ordinary image, O) staying fixed, while the other (the extraordinary image, E) rotates around it. The O-ray is produced by refraction that obeys the ordinary laws of refraction (Snell's law), travelling with the same speed in every direction inside the crystal (a spherical wavefront); the E-ray does not obey the ordinary laws of refraction, travels with a direction-dependent speed inside the crystal (an elliptical wavefront), and is found, on testing, to be plane polarised. There …