题目内容
光从液面到空气时的临界角C为45°,如图3-16所示,液面上有一点光源S发出一束光垂直入射到水平放置于液体中且到液面的距离为d的平面镜M上,当平面镜M绕垂直过中心O的轴以角速度
做逆时针匀速转动时,观察者发现水面上有一光斑掠过,则观察者们观察到的光斑的光斑在水面上掠过的最大速度为多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137366315351.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736584201.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137366315351.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736662728.gif)
本题涉及平面镜的反射及全反射现象,需综合运用反射定律、速度的合成与分解、线速度与角速度的关系等知识求解,确定光斑掠移速度的极值点及其与平面镜转动角速度间的关系,是求解本例的关键。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137366784077.gif)
设平面镜转过
角时,光线反射到水面上的P点,光斑速度为
,如图3-17可知:
,而:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736740724.gif)
故:
,
,而光从液体到空气的临界角为C,所以当
时达到最大值
,即:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736662728.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137366784077.gif)
设平面镜转过
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736678200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736709185.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736725493.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736740724.gif)
故:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736756584.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736771646.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736787456.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736787328.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113736662728.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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