题目内容
为了测定某种材料制成的长方体的折射率,用一束光线从AB面以60°入射角射入长方体时,光线刚好不能从BD面射出,如图所示,求该材料的折射率.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036385091301.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036385091301.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638525438.png)
如下图所示,根据折射定律
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036385411865.png)
n=
①
由题意可知sin C=
②
而C=90°-r ③
由②③得cos r=
④
而cos r=
代入④得
=
⑤
联立①和④得n=
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036385411865.png)
n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638556705.png)
由题意可知sin C=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638587348.png)
而C=90°-r ③
由②③得cos r=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638587348.png)
而cos r=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638619618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638619618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638587348.png)
联立①和④得n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003638525438.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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