题目内容
(10分)两束平行的细激光束,垂直于半圆柱玻璃的平面射到半圆柱玻璃上,如图所示。已知其中一条光线沿直线穿过玻璃,它的入射点是O,另一条光线的入射点为A,穿过玻璃后两条光线交于P点。已知玻璃截面的圆半径为R,OA=
,OP=
R。求玻璃材料的折射率。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241245082863594.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124508254244.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124508270225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241245082863594.jpg)
光路如图所示:其中一条光线沿直线穿过玻璃,可知O点为圆心;另一条光线沿直线进入玻璃,在半圆面上的入射点为B,入射角设为θ1,折射角设为θ2,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241245083014435.jpg)
sinθ1=
(2分)
θ1="30° " (2分)
因OP=
R,由几何关系知BP=R,则折射角
θ2="60° " (3分)
由折射定律得玻璃的折射率为
n=
="1.73. " (3分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241245083014435.jpg)
sinθ1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124508317404.gif)
θ1="30° " (2分)
因OP=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124508270225.gif)
θ2="60° " (3分)
由折射定律得玻璃的折射率为
n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124508332870.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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