基于光的反射与折射定律的表述方法推导及应用

光的反射和光的折射是几何光学应用中最基本的方法。在现代精密光学元件加工过程中，其不同的表述方法可以为光线追迹、棱镜误差分析以及棱镜装调提供不同的解决思路。介绍了光的反射定律和折射定律的传统形式表述方法，并推导了光的反射定律和折射定律的矢量、矩阵及四元数3种表述方法。通过Matlab辅助下的模拟计算，得到施密特棱镜检验光路中2个不同区域入射光线的反射在水平方向上对称分布于前表面反射像两侧，与实际应用相符，实现了矢量、矩阵和四元数表述方法在施密特棱镜检验光路中的应用。3种表述方法可以为光线追迹、棱镜误差分析以及棱镜装调提供科学、实用的解决方法。

Derivation and application of expression methods based on law of reflection and refraction of light

The reflection and refraction of light are the most basic methods for the application of geometric optics. In the processing of modern precision optical elements, the different expression methods can provide different solutions for light tracing, prism error analysis as well as prism assembly and adjustment. The traditional form expression methods of the law of reflection and the law of refraction of light were introduced, and the expression methods of vector, matrix and quaternion were derived. Through the simulation calculation assisted by Matlab, the reflected rays of incident light in two different areas of the Schmidt prism inspection optical path was symmetrically distributed on both sides of the reflected rays on the front surface in the horizontal direction, which was consistent with the practical application. The application of expression methods of vector, matrix and quaternion in Schmidt prism inspection optical path was realized. The three expression methods can provide scientific and practical solutions for light tracing, prism error analysis as well as prism assembly and adjustment.