2016年泛珠三角物理竞赛综合试卷二答.pdf

Pan Pearl River Delta Physics Olympiad 2016 2016 年泛珠三角及中华名校物理奥林匹克邀请赛 Sponsored by Institute for Advanced Study, HKUST 香港科技大学高等研究院赞助 Simplified Chinese Part-2 (Total 3 Problems) 简体版卷-2 （共3题） 2:00 pm – 5:00 pm, 18 February, 2016 1. Gravitational Lens Simulator (9 marks) 引力透镜仿真镜(9 分) The gravitational field of a massive body exercises a lenslike condensing action upon radiation passing through it. A simulated gravitational lens was constructed of Plexiglas for use in demonstrating the lens phenomenon. 大质量物体附近的引力场会对经过的光线产生类似透镜的作用, 称为引力透镜效应。 这里 我们考虑以有机玻璃制造一个光学透镜以仿真引力透镜现象。 According to general relativity, a light ray passing at a distance of closest approach to the center of a spherically symmetric body of mass , will be deflected toward the body through an angle which, for small deflections, is given by 根据广义相对论, 当一束光线经过一个拥有球对称、质量为 的物体时,会产生屈折。当屈 折角度很小，而光线与物体中心最靠近距离为r 时,该角度可由下面的公式得出 where is the gravitational constant and is the speed of light. We, therefore, require of our simulator that it deflects transmitted light through an angle 在上式中 为引力常数， 为光速。因此我们要求仿真镜以下式中的角度屈折光线 where is a constant. 在上式中 是某个常数。 The lens, illustrated in cross section in Fig. 1, is designed to be hand held within the range between roughly one foot and arm’s length from the observer. The object for viewing is assumed to be at a distance much larger than one meter on the