Abstract
An alternative way to determine the birefringence for uniaxial crystals with Brillouin scattering experiments equipped with a Fabry-Perot interferometer is presented. The value of the minimum cavity spacing of the interferometer to observe the birefringence was found, and it is shown that the experimental error of the birefringence could be reduced by increasing the cavity spacing. For a single crystal of $\alpha$-LiIO$_3$, the birefringence was found to be 0.14814$\pm$0.0007 at 514.5 nm.