2016年泛珠三角物理竞赛综合试卷二答.pdf
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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
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