题目内容
(8分)如图所示,一不透明的圆柱形容器内装满折射率n=
的透明液体,容器底部正中央O点处有一点光源S,平面镜MN与底面成450角放置,若容器高为2 dm,底边半径为(1+
)dm,OM=1 dm,在容器中央正上方1 dm 处水平放置一足够长的刻度尺,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008409295944.jpg)
求光源S发出的光线经平面镜反射后,照射到刻度尺的长度.(不考虑容器侧壁和液面的反射)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000840882344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000840898344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008409295944.jpg)
求光源S发出的光线经平面镜反射后,照射到刻度尺的长度.(不考虑容器侧壁和液面的反射)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000840945812.png)
试题分析:作出边界光路.当光线沿OM入射到平面镜时,发生反射,光线照射到刻度尺的最右端.当射到平面镜上的光线经折射照射到刻度尺的最左端时,根据对称性,作出平面镜反射的光路.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008409608575.jpg)
作图找出发光点S在平面镜中的像点S//,连接S/M延长交直尺于H点,由题设知:光线SM的入射角为45°,根据反射定律可知反射角等于45°,MH沿竖直方向,连接S/P,根据对称性得 S/M=OM=1m,在RtΔPRS//中,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000840976789.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000841023652.png)
由几何知识得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000841038500.png)
由折射定律可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000841054655.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000841070632.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825000841085498.png)
故刻度尺上被照亮的范围为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250008411161241.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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