Measuring the refraction index of a triangular prism by spectrometer is one of the typical college physics experiments．Based on the formulas of exit angle and deviation angle，we analyzed the distribution law of critical angleand deduced the formula of minimum deviation angle，and illustrated the measurement method of refractive index by rotating a triangular prism．Then，the curves (curve family)and curved surface were plotted by MATLAB．The MATLAB program in the appendix is relatively complete，which can intuitively demonstrate and solve this above problems for readers’reference．