2017年IAO理论高低年组第3题-镜和板

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本题为高低年组共用。

英文题目

αβ-3. Mirror and plate. There is a system, consisting of a plane mirror (100% reflection) and a plane glass plate that transmits K% Of the light and reflects the other (100-K%) (This characteristics is the same for the light coming from both the directions). The mirror and plate are parallel and infinite on their right side. An observer is placed at the point O (marked by *) and sees a star with a magnitude 2m within a cone around direction «A». What magnitude(s) star(s) (if any) would the observer see in a cone near direction «B» that is symmetrical to «A»? Calculate numerical value for K=50% and K=5% for each such a star (if any visible) or explain why no stars are visible.

IAO2017Tαβ-3

中文题目

αβ-3:镜与板

有一个系统,包括一个平面镜(反射率为100%)和一个半透镜,它透射K%的光并反射其余100-K%的光。 镜子和平板是在右侧无限延伸的。 观察者在点O(用*标记)观察并且看到在A方向有一个2等的恒星。 观察者在与“A”对称的“B”方向看到的恒星的像的星等(如果有的话)是多少? 计算这颗恒星的像的星等(如果有的话)在半透镜透射率为K = 50%和K = 5%的数值,或解释为什么没有恒星可见。

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