[UPSC IFoS 2022] Polarisation and Modern Optics (Q339, 15M)

Discuss the phenomenon of birefringence in a crystal. What do you understand by positive and negative crystals ? If the refractive indices of a calcite crystal for E-ray and O-ray are 1\cdot 488 and 1\cdot 658, respectively, then calculate the thickness of the crystal for which it can work as

(i) quarter wave plate,

(ii) half wave plate. (Wavelength of the light is 5890\text{ \AA})