题目内容
(9分)一个半圆形玻璃砖,某横截面半径为R的半圆,AB为半圆的直径。O为圆心,如图所示,玻璃的折射率为![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925095472.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049251425412.png)
(i)一束平行光垂直射向玻璃砖的下表面,若光线到达上表面后,都能从该表面射出,则入射光束在AB上的最大宽度为多少?
(ii)一细束光线在O点左侧与O相距
处垂直于AB从下方入射,求此光线从玻璃砖射出点的位置
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925095472.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049251425412.png)
(i)一束平行光垂直射向玻璃砖的下表面,若光线到达上表面后,都能从该表面射出,则入射光束在AB上的最大宽度为多少?
(ii)一细束光线在O点左侧与O相距
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925157565.png)
(i)
(ii)右侧与O相距![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925157565.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925173553.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925157565.png)
试题分析:(i)光线垂直AB面入射后传播方向不变,在圆弧面发生折射,射入射角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925220297.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049252353127.png)
出射时发生全反射的临界角
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925266590.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925282471.png)
根据对称性可得入射光的宽度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925298834.png)
(ii)由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925329908.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925157565.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049253601040.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925376486.png)
在圆弧面反射后根据几何关系入射角仍为
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925376486.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925407885.png)
所以出射点在O点右侧
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825004925157565.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250049254386556.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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