题目内容
如图所示,一直角三棱镜截面ABC,∠ABC=30°,∠ACB=90°斜边长为L,其折射率为
,一束平行光从斜边距A点
处的O点平行于BC边射入该棱镜。(光在真空中的速度c=3.0×108m/s,不考虑光的反射。)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241706221644093.png)
(1)做出光的折射光路图,并求出光射出棱镜时光的偏向角;
(2)求出光在棱镜中传播的时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170621415452.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170621789392.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241706221644093.png)
(1)做出光的折射光路图,并求出光射出棱镜时光的偏向角;
(2)求出光在棱镜中传播的时间。
(1)60°(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170622600841.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170622600841.png)
试题分析:(1)光路图如图所示。设光在AB面和AC面两次折射的入射角分别为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170622975251.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170623318293.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170623739260.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170624098308.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241706254083740.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170625830632.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170626032485.png)
可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170626422474.png)
由几何关系知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170626875489.png)
又
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170627093708.png)
可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170627343502.png)
所以光射出棱镜时光的偏向角为60°
(2)由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170628138494.png)
在介质中传播的位移为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170628669477.png)
时间为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170629043451.png)
联立解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824170622600841.png)
点评:本题考查了几何光学中常见的计算问题,通过折射率判断光路的角度,通过折射率计算光在介质中的传播速度。
![](http://thumb2018.1010pic.com/images/loading.gif)
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