题目内容
(10分)如图所示,半径为R的半圆柱形玻璃砖某一截面的圆心为O点。有两条光线垂直于水平柱面射入玻璃砖中,其中一条光线通过圆心O,另一条光线通过A点,且OA=
。这两条光线射出玻璃砖后相交于一点,该点到O点的距离为
,求玻璃砖的折射率。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025459911899.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002545945414.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002545960442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025459911899.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250025460073733.png)
试题分析:做出光路图OBD为法线,则
sin∠ABO=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002546023512.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002546147338.png)
设两条出射光线交点为S,根据几何关系有:
OC=Rcos30O, (2分)
所以,CS=OS-OC=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002546163344.png)
∠BSC=30O ,∠SBD=60O (2分)
由折射定律:n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002546179616.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002546210853.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002546163344.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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