题目内容
如图,矩形ABCD为一水平放置的玻璃砖的截面,在截面所在平面内有一细束激光照射玻璃砖,入射点距底面的高度为h,反射光线和折射光线的底面所在平面的交点到AB的距离分别为l1和l2。在截面所在平面内,改变激光束在AB面上入射点的高度和入射角的大小,当折射光线与底面的交点到AB的距离为l3时,光线恰好不能从底面射出。求此时入射点距底面的高度H。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500494077315268.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500494077315268.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004940804967.png)
试题分析:设玻璃砖的折射率为n,入射角和反射角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004940820325.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004940835360.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004940866707.png)
根据几何关系,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004940882898.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004940898928.png)
联立以上各式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004940913843.png)
根据题意,折射光线在某一点刚好无法从底面射出,此时发生全反射。设在底面发生全反射时的入射角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004941022364.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004941038648.png)
由几何关系得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004941054886.png)
联立可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004940804967.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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