题目内容
已知玻璃对某种单色光的折射率n=
,现使一束该单色光沿如图所示方向射到三棱镜的AB面上,最后从棱镜射出.假设光在行进过程中有折射光线存在时不考虑反射问题,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241147410383377.jpg)
(1)在原图中画出该光束在棱镜中的光路图.
(2)求光射出棱镜时的折射角.(结果可用反三角函数表示.已知一组可能使用的三角函数近似值sin 100="0." 17,sin 200="0." 34, sin 400="0." 64, sin 500="0." 77)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741023225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241147410383377.jpg)
(1)在原图中画出该光束在棱镜中的光路图.
(2)求光射出棱镜时的折射角.(结果可用反三角函数表示.已知一组可能使用的三角函数近似值sin 100="0." 17,sin 200="0." 34, sin 400="0." 64, sin 500="0." 77)
(1) (2)
="arcsin" 0. 905.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241147410702325.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741054217.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241147410702325.jpg)
(1)如图所示.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241147410702325.jpg)
(2)由折射定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741101671.gif)
故
=300,
=400.
即该束光在玻璃中折射光线与三棱镜BC边平行,故它在玻璃中的折射光线一定射到AC面,而射到AC面的入射角小于全反射的临界角,故在AC面射出.如图所示.则
sin
="nsin" 400="0." 64
(或0.905),
故
="arcsin" 0. 905.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241147410702325.jpg)
(2)由折射定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741101671.gif)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741116200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741116201.gif)
即该束光在玻璃中折射光线与三棱镜BC边平行,故它在玻璃中的折射光线一定射到AC面,而射到AC面的入射角小于全反射的临界角,故在AC面射出.如图所示.则
sin
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741054217.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741023225.gif)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114741054217.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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