题目内容
一半圆柱形透明物体横截面如图所示,地面AOB镀银,(图中粗线),O表示半圆截面的圆心,一束光线在横截面内从M点的入射,经过AB面反射后从N点射出,已知光线在M点的入射角为30
,
MOA=60
,
NOB=30
。求
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250034473443560.jpg)
(i)光线在M点的折射角
(ii)透明物体的折射率
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447032214.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447047258.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447032214.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447047258.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447032214.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250034473443560.jpg)
(i)光线在M点的折射角
(ii)透明物体的折射率
试题分析:如图,透明物体内部的光路为折线MPN,Q、M点相对于氏面EF对称,Q、P和N
三点共线。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250034474223951.jpg)
设在M点处,光的和射角为i,折射角为r,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250034474371039.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447453487.png)
由几何关系得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447468772.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447484609.png)
且
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447515531.png)
由①②③式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447531428.png)
(ii)解:根据折射率公式有
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447546591.png)
由④⑤式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003447578722.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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