In the recent times, test of Lorentz Invariance has been used as a means to probe theories of physics beyond the standard model, especially those such as extensions to String Theory and Quantum Gravity. Tests of Lorentz invariance could go a long way in setting the stage for possible quantum gravity theories which are 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 Stanford Linear Accelerator Center (SLAC) and Jefferson Lab (JLab), to limit the dependence of speed of light with the energy of the photons. Furthermore, we also describe a way of limiting directional dependence of speed of light at previously unprecedented levels of precision by studying the sidereal variations. We obtain a limit of MSME parameters: √K²_X + K²_Y < 4.6 x 10^-10 and √(2c_TX - (K^~YZ₀₊)² + (2c_TY - (K^~ZX₀₊)² < 4.6 x 10^-10. We also obtain a leading value for the refractive index of free space n = 1 + (2.44 × 10^-9 ± 6.82 × 10^-9).