当前位置:首页 >> 学科竞赛 >>

IPhO2013


Speed of light (solution)
In this document decimal comma is used instead of decimal point in graphs and tables

E1

1.1

Use the LDM to measure the distance

from the top of the table to the floor. Write 0.4 down the uncertainty . Show with a sketch how you perform this measurement.

. See the sketch in the figure corresponding to 1.3b. It must appear how the height is measured with the LDM in the rear mode.

1.2a

Measure corresponding values of and . Set up a table with your measurements. Draw 1.8 a graph showing as a function of .

Here, a 2 m cable is used, but 1 m is sufficient. There should be about 8 lengths evenly distributed in the interval from 0 m to 1 m.
x m 0,103 0,176 0,348 0,546 0,617 0,839 1,025 1,107 1,750 2,000 y m 0,177 0,232 0,396 0,517 0,570 0,748 0,885 0,950 1,459 1,642

Display y as function of cable length x
y = 0,7710x + 0,1014 R? = 0,9996 1,8 1,6 1,4 Display y [m] 1,2 1,0 0,8 0,6 0,4 0,2 0,0 0,0 0,5 1,0 cable length x [m] 1,5 2,0

Page 1 of 5

Speed of light (solution)
Use the graph to find the refractive index for the material from which the core of 1.2b the fiber optic cable is made. Calculate the speed of light in the core of the fiber 1.2 optic cable. The refractive index is twice the gradient of the linear graph, The reason for that is that the travel time for a light pulse .

E1

The display will therefore show The speed of light in the core of the cable is

.

Measure with the LDM the distance to the laser dot where the laser beam hits the table top. Then move the box with the LDM horizontally until the laser beam hits the 1.3a 0.2 floor. Measure the distance to the laser dot where the laser beam hits the floor. State the uncertainties. , Calculate the angle using only these measurements Determine the uncertainty . and (from problem 1.1).

1.3b

0.4

( ( (see the figure)

) )











Page 2 of 5

Speed of light (solution)
Measuring the horizontal part of some triangle is very inaccurate because of the size of the laser dot. No marks will be awarded for that. Using as the uncertainty of , and , the uncertainty of can be calculated as follows: ( Using simple derivatives yields )

E1

(

)

(

)

Otherwise, using min/max method ( Alternatively, calculate using ( ) ) √( √( ) Also, accept and . ) ( ( ( ) ) ) √ ( and then )

1.4a

Measure corresponding values of a graph of as a function of .

and . Set up a table with your measurements. Draw

1.6

x [mm] 4 17 27 32 39 51 58 66 76 82 90 96

y [mm] 450 454 457 459 461 466 467 471 473 476 478 480

Page 3 of 5

Speed of light (solution)
1.4b Use equations to explain theoretically what the graph is expected to look like. The time it takes the light to reach the water surface is ( 1.2

E1

)

From the water surface to the bottom the light uses the time

Total travel time forth and back (

) ) ( )

Hence, the display will show (we simply write

which is a linear function of . Then, using a trigonometric identity and Snell’s law, √ From this the gradient is found to be √ √ √ .

1.4c Use the graph to determine the refractive index Knowing the gradient Introducing a practical parameter,

for water.

1.2

from the graph, the index of refraction

is found by solving this equation.

the above equation becomes √ with the solution √ From the graph is found All solutions with √ √ √ √ ( and hence . are omitted. Page 4 of 5 )

, which leads to

Speed of light (solution)

E1

Another and more elegant way of finding

is to use Snell’s law in the equation

This yields

From here the angle

can be calculated leading to , and measurement of is not involved).

. This method also only uses the graph and

The table value for pure water at normal conditions is The following approximations can be used: For small angles √

at the wavelength

.



(

)



(

)

(

(

) )

For very small angles, we get It is much simpler, but not recommendable, to do the experiment with very small Reflections in the water surface will ruin the signal from the bottom. .

Page 5 of 5


相关文章:
昆虫名录
双翅目 Diptera 环裂亚目 Cyclorrhapha 丽蝇科 Calliphoridae 绿蝇属 Lucilia ...文档贡献者 liuhe654606 贡献于2013-08-30 1/2 相关文档推荐 贵州省药用昆虫...
签证用户口簿翻译模板
cherishme0812贡献于2013-06-25 0.0分 (0人评价)暂无用户评价 我要评价...Baipho 哈尼 Hani / Ha Nhi 哈萨克 Kazakh / Kazak 黎 Li / Hlai 傣 Dai...
新手必读 一文说破有关破解iphone的很多概念
分享一下自己使用 iPho新手必读 一文说破有关破解的很多概念入手 iPhone 3GS ...文档贡献者 li676338210 贡献于2013-01-23 专题推荐 2014教师资格材料分析辅.....
春节是啥
jsyzw2010贡献于2013-02-20 0.0分 (0人评价)暂无用户评价 我要评价... 赶集网春节营销活动送ipho... 1页 2财富值 春节 12页 2财富值 盼春节 1...
全国中学生物理竞赛介绍
鉴于 Ipho 在促进物理教育进步和推动国际交流上所取得的成绩,国际物理教育委员会...文档贡献者 vidadhara 贡献于2013-03-27 专题推荐 2014教师资格材料分析辅......
供应商会议发言稿(质量部)
大家都知道,质量是具有时效性的,就拿手机来说吧,去年我们买部 IPHOP4,觉得...文档贡献者 penghuihandian 贡献于2013-12-05 1/2 相关文档推荐 ...
咸阳市教育教学研究室
2013年注会经济法统考真题 2013年注会设计统考真题及答案68份文档 新市场营销...文档贡献者 eibaipho 贡献于2010-09-18 1/2 相关文档推荐 咸阳市中小学有效...
iPhone_5正常资费
举报文档 amagomy贡献于2013-02-07 0.0分 (0人评价)暂无用户评价 我要评价... 1页 免费 解密:联通版及电信版iPho... 4页 免费喜欢此文档的还喜欢...
如何鉴别非法期刊
2013年注会经济法统考真题 2013年注会设计统考真题及答案81份文档 笑话大全集...文档贡献者 eibaipho 贡献于2010-09-17 1/2 相关文档推荐 如何鉴别非法期刊...
都是制度的过?
至今没有iPho ne,几乎什么时髦都不跟。这在她的同学里即使不是 绝无仅有,也...2013年美国出版一本题目为《被洗脑》的书,检 讨脑神经科学和心理学的一些成果...
更多相关标签: