题目内容
一个圆柱形筒,直径12 cm,高16 cm,人眼在筒侧上方某处观察,所见筒侧的深度为9 cm,当筒中装满液体时,则恰能看到筒侧的最低点,求:
(1)此液体的折射率;
(2)光在此液体中的传播速度.
(1)此液体的折射率;
(2)光在此液体中的传播速度.
(1)
(2)2.25×108 m/s
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003640959373.png)
题中的“恰能看到”表明人眼看到的是筒侧最低点发出的光线经界面折射后进入人眼的边界光线.由此可作出符合题意的光路图(如右图所示).
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036409744144.jpg)
在作图或分析计算时还可以由光路的可逆性,认为“由人眼发出的光线”折射后恰好到达筒侧最低点.
(1)由图可知:sin θ2=
,
sin θ1=
,所以折射率n=
=
=
=
.
(2)光在此液体中的传播速度为
v=
=
m/s=2.25×108 m/s.
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036409744144.jpg)
在作图或分析计算时还可以由光路的可逆性,认为“由人眼发出的光线”折射后恰好到达筒侧最低点.
(1)由图可知:sin θ2=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003640990662.png)
sin θ1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003641005660.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003641005630.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003641193835.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003641239834.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003640959373.png)
(2)光在此液体中的传播速度为
v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003641271377.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003641286709.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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