We used Brewster's Law to examine the mechanism of liquid crystal (LC) alignment on an organic insulation layer when subjected to ion-beam irradiation. Brewster's Law implies that the maximum rate polarized ray on a slanted insulation layers on the substrate and it illustrates the dependence of polarization and the mechanical structure on the ion beam irradiation process. The pretilt angle of nematic LCs on the organic insulation surface was about 1.13 degrees for an ion beam exposure of 45 degrees for 1 minute at 1800 eV. This shows the dependence of LC alignment on the polarization ratio in a slanted organic insulation layer. We also discussed the electro-optical characteristic of twisted nematic (TN) LCD using ion beam irradiation on organic overcoat layer.