  In the recent times, test of Lorentz Invariance has been used as a means to
probe theories of physics beyond the standard model. We describe a simple way
of utilizing the polarimeters, which are a critical beam instrument at
precision and intensity frontier nuclear physics labs such as the erstwhile
Stanford Linear Accelerator Center (SLAC) and Jefferson Lab (JLab), to
constrain the dependence of vacuum dispersion with the energy of the photons
and its direction of propagation at unprecedented level of precision. We obtain
a limit of minimal Standard Model extension (MSME) parameters:
$\sqrt{\kappa_X^2 + \kappa_Y^2} < 4.6 \times 10^{-10}$ and $\sqrt{\left(
2c_{TX} - (\tilde{\kappa}_{0^+}^{YZ} \right)^2 + \left( 2c_{TY} -
(\tilde{\kappa}_{0^+}^{ZX} \right)^2} < 4.6 \times 10^{-10}$. We also obtain a
leading constraint for the refractive index of free space $n = 1 +
(2.44\times10^{-9} \pm 6.82\times 10^{-9})$.
