相对论反射定律的圆锥截面法
A Conic Section Approach to the Relativistic Reflection Law
摘要：
我们考虑光从一个固定的光源的光的反射，离开一个均匀移动的平面镜，并推导出相对论反射定律使用众所周知的性质的圆锥部分。有效反射面（ESR）被定义为在给定时间从光源发出的所有光束与移动反射镜相交的轨迹。然后将费马最小时间原理应用于ESR，证明了在假定与光速无关的情况下，结果与相对论反射定律一致。对于匀速运动的反射镜，ESR是二次曲线，反射定律变成二次曲线的双角方程的情况，入射和反射光束与二次曲线的聚焦光线重合。一个简短的微积分为基础的证明加速镜也给出了。
英文摘要：
We consider the reflection of light, from a stationary source, off of a uniformly moving flat mirror, and derive the relativistic reflection law using well-known properties of conic sections. The effective surface of reflection (ESR) is defined as the loci of intersection of all beams, emanating from the source at a given time, with the moving mirror. Fermat principle of least time is then applied to ESR and it is shown that, assuming the independence of speed of light, the result is identical with the relativistic reflection law. For a uniformly moving mirror ESR is a conic and the reflection law becomes a case of bi-angular equation of the conic, with the incident and reflected beams coinciding with the focal rays of the conic. A short calculus-based proof for accelerating mirrors is also given.
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