题目内容
图丙是北京奥运会期间安置在游泳池底部的照相机拍摄的一张照片,照相机的镜头竖直向上。照片中,水立方运动馆的景象呈现在半径
的圆型范围内,水面上的运动员手到脚的长度
,若已知水的折射率为
,请根据运动员的实际身高估算该游泳池的水深
,(结果保留两位有效数字)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082411370371512061.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703559402.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703574418.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703606392.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703652200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082411370371512061.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703762457.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703824441.gif)
根据题意能画出光路图,正确使用物象比解决本题的关键。
设照片圆形区域的实际半径为
,运动员的实际长为
,光路如图:
折射定律![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113704042532.gif)
几何关系
得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113704354550.gif)
取
,解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703762457.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137044013491.jpg)
(本题为估算题,在取运动员实际长度时可以有一个范围,但要符合实际,故求得h值可以不同
均可)
设照片圆形区域的实际半径为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703840204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703855197.gif)
折射定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113704042532.gif)
几何关系
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113704339945.gif)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113704354550.gif)
取
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113704370406.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703762457.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137044013491.jpg)
(本题为估算题,在取运动员实际长度时可以有一个范围,但要符合实际,故求得h值可以不同
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113703824441.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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