Based on the measurement principle of refractive index of triangular prism, the relative uncertainty is theoretically analyzed by using minimum deviation angle method, glancing incidence method and vertical bottom edge incidence method respectively. The results show that the relative uncertainty of the refractive index decreases with the increasing of the vertex angle of the triangular prism. The effect of the beams with different wavelengths on the relative uncertainty of the refractive index is small. And the relative uncertainty of the refractive index increases with the increasing of the uncertainty of the angulation. Moreover, when minimum deviation angle method is used, the effect of the deviation angle near the minimum deviation angle position on the incident angle is not obvious. But the unapparent variation range of the deviation angle decreases with the increasing of the vertex angle of the triangular prism. Finally, the optimal scheme is provided for obtaining the minimum relative uncertainty of refractive index, which provides a theoretical basis for the accurate measurement of the refractive index of the triangular prism.