题目内容
如图所示acb是一块用折射率n=2的玻璃制成的透明体的横截面,ab是半径为R的圆弧,ac边与bc边垂直,∠aOc=60°.当一束平行黄色光垂直照到ac上时,ab部分的外表面只有一部分是黄亮的,其余是暗的.那么黄亮部分的弧长为.( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241350103673667.jpg)
A
B
C
D
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241350103673667.jpg)
A
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135010398482.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135010476505.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135010508492.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135010554511.png)
C
由题意作光路图如图所示,该介质的临界角是C.则 (见图)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135010586690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241350106327835.jpg)
则C=30° 如图,在
时,均发生全反射,图中d点为入射角等于临界角的临界点,所以只有b d部分有黄光透射出,
黄亮部分弧长
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135010586690.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241350106327835.jpg)
则C=30° 如图,在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135010648526.png)
黄亮部分弧长
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824135010679879.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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