In the visible region of the spectrum the rotation of the place of polarization is given by $\mathrm{\theta }=\mathrm{a}+\frac{\mathrm{b}}{{\mathrm{\lambda }}^2}$. The optical rotation produced by a particular material is found to be ${30}^{\circ }\text{ per }\mathrm{mm}\text{ at }\mathrm{\lambda }=5000\text{Å and }{50}^{\circ }\text{ per }\mathrm{mm}\text{ at }\mathrm{\lambda }=4000\text{Å. }$ The value of constant a will be