题目内容
某透明物体的横截面如图所示,其中ABC为直角三角形,AB为直角边,长度为2L,
=45
, ADC为一圆弧,其圆心在AC边的中点,此透明物体的折射率为n=2.0.若一束宽度与AB边长度相等的平行光从AB边垂直射入透明物体,试由光路图画出光线从ADC圆弧射出的区域,并求此区域的圆弧长度s.(不考虑经ADC圆弧反射后的光线)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241326403903838.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132640296531.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132640343214.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241326403903838.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132640406558.png)
如右图,作出两条边缘光线,所求光线射出的区域为EDF.………………………(1分)
从圆弧ADC射出的边缘光线对应的入射角等于材料的临界角
,因
………(1分)
故
=30°.由几何关系得:
圆弧EDF长度为s=2
……………………………………………………………………(1分)
故所求
………………………………………………………………………………(1分)
从圆弧ADC射出的边缘光线对应的入射角等于材料的临界角
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132640437300.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132640484591.png)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132640437300.png)
圆弧EDF长度为s=2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132640515355.png)
故所求
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824132640406558.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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