题目内容
( 9分 )如图所示,扇形OAB为透明柱状介质的横截面,其圆柱半径为R,介质的折射率
,圆心角∠AOB=60°,一细束激光平行于角平分线由OA面的P点射入,射入介质后第一次射到界面上的N
点,已知弧长AN是弧长AB的四分之一。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409032883871.jpg)
(1)完成光在透明柱状介质中传播的光路图
(2)求入射点P与圆心O的距离
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903226449.png)
点,已知弧长AN是弧长AB的四分之一。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409032883871.jpg)
(1)完成光在透明柱状介质中传播的光路图
(2)求入射点P与圆心O的距离
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409033664506.jpg)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903382696.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409033664506.jpg)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903382696.png)
(1)光路图如图(3分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409034444515.jpg)
(2)由几何关系可知光从P点射
入时的入射角![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903460313.png)
,(1分)
由折射定律:
(1分)
得折射角为:∠
=
(1分);
由几何关系可知:∠PON=
;∠PNO=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903803370.png)
由正弦定理:
(2分); 得:
(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409034444515.jpg)
(2)由几何关系可知光从P点射
入时的入射角
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903460313.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903491388.png)
由折射定律:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903538807.png)
得折射角为:∠
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903600305.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903678389.png)
由几何关系可知:∠PON=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903756332.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903803370.png)
由正弦定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903881989.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140903382696.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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