题目内容
如图19-4-15所示,宽为a的平行光束从空气斜射到两面平行的玻璃板上表面,入射角为45°.光束中包含两种波长的光,玻璃对这两种波长光的折射率分别为n1=1.5,n2=
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241207429741721.jpg)
图19-4-15
(1)求每种波长的光射入上表面后的折射角r1、r2.
(2)为使光束玻璃下表面出射时能分成不交叠的两束,玻璃板的厚度d至少为多少?并画出光路示意图.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120742958225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241207429741721.jpg)
图19-4-15
(1)求每种波长的光射入上表面后的折射角r1、r2.
(2)为使光束玻璃下表面出射时能分成不交叠的两束,玻璃板的厚度d至少为多少?并画出光路示意图.
(1)r1=arcsin
r2=arcsin
(2)d=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743052472.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120742989267.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743005281.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743052472.gif)
本题考查光的折射定律、有关计算和作图方法,是一道很有特色的新颖试题.
(1)由sini/sinr=n,得sinr1=
=
,sinr2=
.
故r1=arcsin
,r2=arcsin
.
(2)为使光束从玻璃下表面出射时能分成不交叠的两束,设玻璃板的厚度为d,由下图可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241207432232494.jpg)
dtanr1-dtanr2=a/cosi
d=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743239682.gif)
其中tanr1=tan(arcsin
)=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743270283.gif)
tanr2=tan(arcsin
)=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743426284.gif)
解得d=
.
(1)由sini/sinr=n,得sinr1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743052414.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120742989267.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743083549.gif)
故r1=arcsin
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120742989267.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743005281.gif)
(2)为使光束从玻璃下表面出射时能分成不交叠的两束,设玻璃板的厚度为d,由下图可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241207432232494.jpg)
dtanr1-dtanr2=a/cosi
d=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743239682.gif)
其中tanr1=tan(arcsin
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120742989267.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743270283.gif)
tanr2=tan(arcsin
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743005281.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743426284.gif)
解得d=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120743052472.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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