题目内容
半径为R的半圆柱形玻璃,横截面如图13-7-12所示,O为圆心,已知玻璃的折射率为
,当光由玻璃射向空气时,发生全反射的临界角为45°,一束光以与MN平面成45°角的方向射向半圆柱形玻璃,求能从MN射出的光束的宽度为多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200325531816.jpg)
图13-7-12
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120032538225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200325531816.jpg)
图13-7-12
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120032678272.gif)
如图所示,进入玻璃中的光线①垂直半球面,沿半径方向直达球心位置O,且入射角等于临界角,恰好在O点发生全反射.光线①左侧的光线(如:光线②)经球面折射后,射在MN上发生全反射,不能射出.光线①右侧的光线经半球面折射后,射到MN面上的入射角均小于临界角,能从MN面上射出.最右边射向半球的光线③与球面相切,入射角i=90°,由折射定律知:sinr=
=
,则r=45°.故光线③将垂直MN射出.所以在MN面上射出的光束宽度应是OE=Rsinr=
R.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200330212978.jpg)
图13-7-13
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120032881405.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120032678272.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120032678272.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241200330212978.jpg)
图13-7-13
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目