题目内容
用折射率为
的透明物质做成内、外径分别为
、
的球壳,球壳的内表面涂有能完全吸收光的物质,如图所示,当一束平行光从左侧射向该球壳时,被吸收掉的光束在射进球壳左侧外表面前的横截面积有多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250046179264719.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004617863297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004617879283.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004617910299.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250046179264719.png)
若
时,S=πn2a2; 若
时,进入球壳的光线全部被吸收,此时,S=πb2。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004617941540.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004617957552.png)
试题分析:如图,若光线经球壳折射后恰与球壳的内表面相切,则被吸收的光束进入球壳前的横截面积S=πR2, ①
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250046179888512.png)
由折射定律sini=nsinr ②
sini=R/b ③
sinr=a/b ④
将③④代入②得:R=na,
若
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004618004536.png)
若
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004617957552.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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