题目内容
如图所示,空气中有一折射率为
的玻璃柱体,其横截面是圆心角为90°、半径为R的扇形OAB.一束平行光平行于横截面,以45°入射角照射到OA上,OB不透光.若只考虑首次入射到圆弧
上的光,则
上有光透出部分的弧长为 ( ).
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036381512496.png)
A.
πR B.
πR C.
πR D.
πR
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638073344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638088437.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638088437.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036381512496.png)
A.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638166336.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638182303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638182327.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638213409.png)
B
由sin C=
可知光在玻璃柱中发生全反射的临界角C=45°.据折射定律可知所有光线从AO进入玻璃柱后的折射角均为30°.从O点入射后的折射光线将沿半径从C点射出.假设从E点入射的光线经折射后到达D点时刚好
发生全反射,则∠ODE=45°.如图所示,由几何关系可知θ=45°,故弧长
=
πR,故B正确.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036382754681.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638213348.png)
发生全反射,则∠ODE=45°.如图所示,由几何关系可知θ=45°,故弧长
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638229458.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638182303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036382754681.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目