题目内容
(9分)如图,一个三棱镜的截面为等腰直角
ABC,
为直角。一细束光线沿此截面所在平面且平行于BC边的方向射到AB边上的M点,M、A间距为l。光进入棱镜后直接射到AC边上,并刚好能发生全反射。试求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250024301601940.png)
(i)该棱镜材料的折射率n=?
(ii)光从AB边到AC边的传播时间t=?(已知真空中的光速为c。)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430129319.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430144370.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250024301601940.png)
(i)该棱镜材料的折射率n=?
(ii)光从AB边到AC边的传播时间t=?(已知真空中的光速为c。)
(1)
(2) ![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430191611.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430175612.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430191611.png)
试题分析:设光从AB边射入时,折射角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430207319.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430222344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500243023812041.png)
根据(1) 根据折射定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430269740.png)
光在AC边上恰好全反射:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430347591.png)
根据几何关系
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430363635.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430175612.png)
(2) 由图中几何关系可得MN之间的距离为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430456658.png)
由(1)可解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430472695.png)
用v表示光在棱镜内的传播速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430487490.png)
光从AB边到AC变的传播时间为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825002430550858.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目