Q.Inside the calcite crystal, along the optic axis, the ratio of velocities of extraordinary ray to ordinary ray is :

Certain crystals, such as calcite and quartz, show double refraction (birefringence): a single unpolarised ray entering the crystal splits into two refracted rays, so a single object viewed through the crystal appears doubled. One image, the ordinary image (O), is produced by rays that obey the ordinary laws of refraction (Snell's law) and travel with the same speed in every direction inside the crystal (a spherical wavefront); the other, the extraordinary image (E), is produced by rays that do not obey the ordinary laws of refraction, travel with a direction-dependent speed (an elliptical wavefront), and are found to be plane polarised. There exists one special direction inside such a crystal, called the optic axis, along which the O-ray and E-ray travel with the same speed and no double refraction occurs; crystals with just one such axis (calcite, quartz, tourmaline, ice) are called uniaxial, while those with two (mica, topaz, selenite, aragonite) are called biaxial. William Nicol (1828) exploited this double refraction to build the Nicol prism: a calcite crystal is cut along a diagonal and the two halves rejoined with a thin layer of Canada balsam cement, chosen because its refractive index (1.523) lies between that of calcite for the ordinary ray (1.658) and for the extraordinary ray (1.486); the ordinary ray strikes the balsam layer at an angle exceeding its critical angle there and undergoes total internal reflec …