题目内容
如图所示,扇形AOB为透明柱状介质的横截面,半径为R,介质折射率为
,圆心角为45°,一束平行于OB的单色光由OA面射入介质,要使柱体AB面上没有光线射出,至少要在O点上方竖直放置多高的遮光板?(不考虑OB面的反射)。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051435142941.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005143467344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051435142941.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005143545431.png)
试题分析:设在OA面上的一点P入射的光线恰好不能从AB面射出,经过折射在AB面的N点发生全反射.由几何关系可知光从P点射入时的入射角i=45°,由折射定律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005143561729.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051435761277.png)
设临界角为C,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005143592647.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005143623731.png)
要使光不能从AB面射出,在N点的入射角等于45°
由正弦定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051436701166.png)
得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005143685744.png)
遮光板的长度至少为L=OPsin45°=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825005143545431.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250051437323256.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目