题目内容
如图所示,为一玻璃圆柱体的截面图,其半径为
,
为圆柱截面的圆心,AB为截面圆的直径。在B点放一个能发某种单色光的点光源,照射到直径AB上方,只有圆弧AMN段有光线折射出来,其中从M点折射出的光线恰好平行AB,已知∠ABM=
。求:直线BN的长度。(用R、
表示)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250001141133240.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000114066303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000114082292.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000114098297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000114098297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250001141133240.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250001141291165.png)
试题分析:设光线BM在M点发生折射对应的入射角为i,折射角为r,
由几何知识可知,i=θ,r=2θ, (1分)
根据折射定律得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000114144646.png)
代入数据得:n=2cosθ (1分)
光线BN恰好在N点发生全反射,则∠BNO为临界角C,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000114160610.png)
由几何知识可知,等腰三角形NOB中,BN的距离:
BN="2RcosC" (1分)
联立求得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250001141291165.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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