Correlating the optical rotation of α-quartz with a skew matrix of a dielectric tensor

A beam of polarized light propagating along the helical axis of α-quartz interacts with SiO_4/2 groups consecutively. When a skew matrix of a resultant dielectric tensor is compared to a skew matrix of a rotation matrix, the polarizability components of an SiO_4/2 group, with two sets of results, may be derived since the specific rotation along the helical axis is known for 5892.9 Å light at 293 K. Both sets have the same mean value for the components. The mean is close to an empirical result based on the bond refractivity of Si–O. In comparison with the optical rotation sign (+ or −) along the optic axis, an opposite rotation sign is derived along the directions perpendicular to both the optic axis and any diad axis. In α-quartz, the inactive directions 33.83° from its optic axis are interpreted. The diad-axis directions are predicted to be inactive directions. Bunn's empirical formula is interpreted.