题目内容
一台激光器,它的功率为P,如果它发射出的单色光在空气中的波长为λ.
(1)它在时间t内辐射的光能为__________,如果已知这束单色光在某介质中的传播速度为v,那么这束单色光从该介质射向真空发生全反射的临界角为__________.
(2)由于激光是亮度高、平行度好、单色性好的相干光,所以光导纤维中用激光作为信息高速传输的载体.要使射到粗细均匀的圆形光导纤维一个端面上的激光束都能从另一个端面射出,而不会从侧壁“泄漏”出来,光导纤维所用材料的折射率至少应为多大?![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241415421652368.jpg)
(1)它在时间t内辐射的光能为__________,如果已知这束单色光在某介质中的传播速度为v,那么这束单色光从该介质射向真空发生全反射的临界角为__________.
(2)由于激光是亮度高、平行度好、单色性好的相干光,所以光导纤维中用激光作为信息高速传输的载体.要使射到粗细均匀的圆形光导纤维一个端面上的激光束都能从另一个端面射出,而不会从侧壁“泄漏”出来,光导纤维所用材料的折射率至少应为多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241415421652368.jpg)
(1)Pt arcsin
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542243344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542181346.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542243344.png)
(1)激光器t时间内发出的光能W=Pt
由n=
,sinC=
,则C=arcsin
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241415424302363.jpg)
2)设激光束在光导纤维端面的入射角为i,折射角为r,折射光线射向侧面时的入射角为i′,折射角为r′,如图所示.
由折射定律:n=
,
由几何关系:r+i′=90°,sinr=cosi′.
由全反射临界角的公式:
sini′=
,
cosi′=
,
要保证从端面射入的任何光线都能发生全反射,应有i=r′=90°,sini=1.故
n=
=
=
,
解得n=
,故光导纤维的折射率至少应为
.
由n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542290346.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542337348.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542181346.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241415424302363.jpg)
2)设激光束在光导纤维端面的入射角为i,折射角为r,折射光线射向侧面时的入射角为i′,折射角为r′,如图所示.
由折射定律:n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542430534.png)
由几何关系:r+i′=90°,sinr=cosi′.
由全反射临界角的公式:
sini′=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542337348.png)
cosi′=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542524548.png)
要保证从端面射入的任何光线都能发生全反射,应有i=r′=90°,sini=1.故
n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542430534.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542805578.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542867578.png)
解得n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542243344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824141542243344.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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