利用旋转液体特性测量液体折射率(全面版)资料

1、利用旋转液体特性测量液体折射率（全面版）资料第27卷第7期2007年7月物 理实验 P H YSICS EXPERIM EN TA TIONVol.27 No.7J ul.,2007圆柱容器XYJ旋转液体物件仪转盘电动机ft细唱收稿日期：2006212215修改日期：2007203219 作者简介:高 严（1986-,男山东日照人，中国石油大学（北京资源与信息地质工程专业2004级本科生.指导教师:王爱军（1968-，男，河北沽源人,中国石油大学（北 京数理系副教授，硕士,从事凝聚态物理研究.利用旋转液体特性测量液体折射率高 严 1, 范 凯 1, 王爱军 2, 唐军杰 2(1.中国石油大学

2、(北京资源与信息学院 ,北京 102249;2.中国石油大学 (北京数理系 ,北京 102249摘 要:在XY 21型旋转液体实验仪的圆柱形容器底部加装了圆形平面镜，利用旋转液体的几何特性和折射定律 ,即可测量液体的折射率 .关键词:旋转液体;旋转抛物面;折射率中图分类号 :O351;O552.423 文献标识码 :A 文章编 号:100524642(200707200422031引言盛有液体的圆柱形容器绕其圆柱面的对称轴匀速转动时 ,旋转液体的表面将成为抛物面 .抛物面的参数与重力加速度有关 ,利 用此性质可以测重力加速度 ;旋转液体的上凹面可作为光学系统加以研究,还可测定液体折射率等 ;因

3、此旋转液体实验是一个内容十分丰富的综合性实验12.但是,在旋转液体特性研究实验中测量测液体折射率采用的是光栅衍射的方法,比较繁琐 ,没有充分运用旋转液体的特性 .本文对旋转液体实验装置的圆柱形容器稍作改进,根据旋转液体的几何特性和折射定律 ,提出一种利用旋转液体特性测量液体折射率的方法 .2 实验原理及仪器改进2.1 匀速旋转液体的几何性质半径为R盛有液体的圆柱形容器，当圆柱体绕对称轴以角速度 匀速稳定转动 时，液体的表面将成为抛物面.设x轴为水平方向,y轴为垂直水平面向上方向，抛物面 的方程为 1,3y = 3 2x 22g +h-Qo 2R24gJ(1其中|x | < R ,1是圆柱

4、形容器内液体静止时液面高度,g是重力加速度.当x =x0=R2时,由(1式得y (x 0=h 0,即液面在x 0处的高度是恒定的，它不随旋转圆柱体的转动角速 度改变而改变 ,图1为旋转液体特性实验装置示意图 .透明屏幕上有毫米坐标 ,用于实验中读取 入射光点与反射光点的距离 ,屏幕可在竖直方向上下移动 .圆筒侧壁有毫米刻度线 ,用 于读取液面高度 ,也可以用直尺测量 .圆筒底部正中央有小标识 ,用以确定光轴 .圆形转 盘由直流电动机驱动，可通过调节直流电源的电压改变液体转动的角速度.用XY 21旋转液体物性仪测量液体旋转周期 .仪器底座有气泡式水平仪 ,圆柱形容器的内径用游标卡尺测量 .图 1

5、 旋转液体特性实验装置示意图为了便于测量液体折射率 ,在原仪器的圆形容器底面加装圆形平面镜 ,用以加强容器底面反射光线的强度.2.3利用旋转液体特性测液体折射率实验原理如图2所示，设圆柱形容器内液体静止时液面高度为h 0当液体旋转起来后，根据旋转液体性质，在距圆柱形容器中心轴 R/2 处旋转液体的高度仍为h 0,不随旋转液体的转动角速度改变而改变.调节激光笔使让 激光束竖直入射到旋转液体液面的不动点B处.设入射光线为A B ,经抛物液面反射的光线为B C ,其中A和C分别为入射光线和反射光线与水平半透明屏幕的交点，经过抛物面折射后的光线为B D. 9为入射光线A B的入射角，B为折射光线B D

6、的 折射角.设液体折射率为n ,根据折射定律有：n =si n9 1sin 9 2图2旋转液体中的光路下面来计算9 和 9 2设B点在圆柱形容器底面的投影点为F.设经过圆柱形容器底面反射镜反射的光线为D E,E为反射光线D E和透明圆柱形容器侧壁交点,E在圆柱 形容器底面的投影为G点.由图2有：12/ A B C =12arctan A C A B,(3 9 2二(E1FB D = 9 -arctanFD.（4另有几何关系 B D F sED G,则有FD GD =B FEG.（5又因GD =FG -FD ,将GD和（5式代入（4式有:0 2= BdrctanFGEG +B F（6设透明屏幕上

7、部到圆柱形容器底面的距离为H ,EG =h 1,A C =d.已知 B F =h 0,A B =H -h 0,FG =R -R2将上述A B ,A C ,FG,EG和B F的结果代入（3式和（6式得:1=12arctan dH -h 0,(70 2= BdrctanR -R2h 1+h 0.(8调节转速使点E恰好打在抛物液面与容器壁的交线上，则E点距圆柱形容器底面的距离h 1满足抛物线方程 (1式,则有h 1= 3 2R 22g +h 0L 2R 24g = 3 2R24g +h 0.(9又由3 =2n T ,为液体旋转周期，将3 =2nT和(9 式代入 (8 式有2=0-a1rctan1-1

8、2R 2h 0+ n 2R 2g T2.（10实验中只要测出R ,h 0,d ,H和T ,代入（7和（10式算得9 1和 9 2再根据式（2即可 求得液体折射率 n.3 实验内容利用气泡水平仪和平台下的 3个可调螺丝 ,调节平台水平用游标卡尺（精度为0.02mm测量出圆柱形容器的直径2R.利用 自准法调节激光笔使其发出的激光竖直照射于液面,然后保持激光笔的竖直状态 ,将竖直光线平移到距圆柱容器底面中心R/2处.用直尺测量液体静止时液面到容器底部的距离 h 0及透明屏幕到容器底面的距 离H.打开电机并调节电机转速 ,使经圆柱形容器底面平面镜反射的光线刚好打在抛 物液面与圆柱容器侧壁的交线上 .待

9、稳定后记下 XY 21 旋转液体物性仪计时器显示 的容器旋转10周所用时间10T 用直尺测量激光束入射光线和经抛物液面反射的光线与透明屏幕的交点之间的距离 d.改变透明屏幕到圆柱形容器底面的距离 H 及液面高度 h 0,重复上述过程 ,记录试验数据 .4 实验结果待测液体为甘油 ,实验测量的数据如表 1 所34第 7期高 严,等:利用旋转液体特性测量液体折射率示.表 1 中 R=5.564cm.表 1 实验测量数据5 结束语本文对旋转液体实验装置的圆柱形容器稍作改进,根据旋转液体的几何特性和折射定律 ,提出一种测量液体折射率的新方法.新方法原理简单 ,仪器改进非常容易 ,只需在原有实验装置中添

10、加平面反射镜即可.用这种新方法测液体折射率是对旋转液体特性研究实验实验内容的一个很好的扩充 .参考文献 :1 包奕靓黄吉,陆申龙新型旋转液体实验J.大学物理 ,2003,22(2:2730.2 袁野,晏湖根,陆申龙,等.旋转液体实验装置的设计J.物理实验,2004,24(2:4346.3 贾起民，郑永令.力学（上册M.上海:复旦大学出版社 ,1989.116117.R efractive index of liquids determined by rotating liquid methodGAO Yan1,FAN Kai1,WAN G Ai2jun2,TAN G J un2jie2(1.D

11、epartment of Resource and Information,China University of Petroleum2Beijing,Beijing102249,China;2.Department of Mathematics and Physics,China University of Petroleum2Beijing,Beijing102249,ChinaAbstract:The XY12type rotating liquid apparat us is modified by adding circular plane mirror un2 der t he c

12、ylindrical glass bottom.The refractive index of liquids can be measured using t he geometric characteristic of rotating liquid and t he Fresnell reflective law.K ey w ords:rotating liquid;rotating parabolic;ref ractive index责任编辑 :郭 伟利用透鏡組及相關成像設備，求出已知濃度鹽水的折射率，進 而求出凸透鏡的曲率半徑。並討論鹽水的折射率與濃度大小的關係 為何？原理1. 將

13、一物體置於凸透鏡焦點上，經平面鏡反射，再經此凸透鏡 聚光成像後，在原焦點上得到大小不變的倒立影像。用此成 像原理，將可經由實驗求出任何凸透鏡組的焦距。光線成像RiR22.由造鏡者公式f ( n-1)11可以得到以液體為材料的平凹透鏡焦距f液滿足(1)( n 液-1)- 可以得到配合組合透鏡焦距公式F丄nw 1 Fw f 凸厂丄丄Fxf凸其中，nw :水的折射率 nx :待求鹽水的折射率Fw :的透鏡及水組合透鏡'勺焦距 Fx:的透鏡及未知液體組合透鏡 '勺焦距 f凸：凸透鏡的焦距Fx及f凸，代入式，得鹽水的折射率nx，(2)式的推導見附錄。 經由實驗可測得Fw、再將nx代入(1

14、)式，得凸透鏡的曲率半徑。 探實驗步驟：1製作箭頭光柵後，架設實驗裝置，如下頁裝置圖:2. 移動光柵位置，找到與箭頭光柵同大小但倒立之清晰像，此光柵與透鏡的距離即為透鏡之焦距f凸。3. 在水平放置的平面鏡上滴上幾滴水，再將雙面對稱的薄凸透 鏡置於水滴上，兩鏡之間不能有任何氣泡，水填滿兩鏡間的 空隙。則此系統可視為雙凸透鏡（以玻璃為折射材料）及平凹 透鏡（以水為折射材料）的薄透鏡組。4. 移動光柵位置找出 Fw （凸透鏡及水之組合透鏡的焦距）。5. 將水改成5%鹽水，找出Fs （凸透鏡及5%鹽水之組合透鏡 的焦距）。6. 改變鹽水的濃度為10%、15%重複步驟5,找出Fi。、F15。 探結果：測

15、量出f凸、Fw、F5、F10、F15平均值見附表（一）（五），將其值 代入（2）式計算鹽水的折射率，並由（1）式計算出凸透鏡的曲率半徑 R 列於下表。水5%鹽水10%鹽水15 %鹽水平均值標準差折射率1.33001.34271.34751.3644計算的R（cm）35.300035.298135.306035.303135.30180.0030此實驗求出凸透鏡之曲率半徑 R，都非常接近，標準差亦非常小, 可見相當精確。從上表亦可得到，鹽水的濃度愈大折射率也愈大。附錄1利用£(n液-1)1及1 1f液RFf凸1 “111(nw1)()f水RF wf凸1111(眼1)()f鹽水RFxf凸

16、(2)式的推導如下:丄2得兩式可得表(一)凸透鏡的焦距f凸第一次第二次第三次第四次第五次平均值焦距(cm)33.633.333.233.333.433.36表(二)加水透鏡組的焦距第一次第二次第三次第四次第五次平均值焦距(cm)48.848.748.848.748.548.7表(三)加5 %鹽水透鏡組的焦距第一次第二次第三次第四次第五次平均值焦距(cm)49.549.249.349.249.549.34表(四)加10%鹽水透鏡組的焦距第一次第二次第三次第四次第五次第六次第七次平均值焦距(cm)49.749.550.249.749.750.049.949.67表(五 )加15%鹽水透鏡組的焦距第

17、一次第二次第三次第四次第五次第六次平均值1焦距(cm)51.051.050.850.950.850.850.88利用星载 SAR 差分干涉测量改进变形含水层系统的绘图、监测和分析美国 研究委员会地面沉降座谈会（NRC; 1991 ）就3种信息需求达成了共 识：“第一，有关地面沉降大小和分布的基本的地球科学数据和信息要得到认 可并用来评价未来的问题。这些数据不仅能够帮助研究局部地区的沉降问 题，也能识别 范围内的问题。第二，针对地面沉降开展沉降治理和工程方 法的研究为了有效阻止或控制破坏第三，尽管美国现行的地面沉降减轻 方法有很多种，但是对这些方法的成本效益进行研究将有助于决策者做出更好 的选择

18、。”有各种基于地面和卫星的方法可用来测量含水层系统的压缩和地面沉降（表 1）。 SAR 干涉测量理论上适合测量与含水层系统压缩相关的地面变形的 空间范围和大小。 InSAR 可以提供一个区域内覆盖整个含水层系统的数百万个 数据点，与使用大量人力而只能获得有限个点测量数据的水准测量，和GPS测量相比，通常而言，花费要更低一些。通过识别研究区内某一变形的特定区 域， SAR 干涉测量也可以用于定点测量并同时监测局部和区域尺度上的地面沉 降（如钻孔伸长计、GPS监测网络、水准路线；Bawden等，2003）。SAR干 涉测量的这些优势，尤其是InSAR，能够满足NRC提出的每一种信息需求。 SAR干

19、涉测量的另一个重要优势就是 SAR历史数据的存档文件越来越多。在很 多地区，从上世纪 90年代初开始，就已经有了大量的数据集，因而这一时期的 地面形变历史测量数据即可应用。此外，为满足新需求可以定制新数据。详细 的过程和费用要依赖于使用的传感器Space-based Tect onic Modeli ng in Subducti onAreas Usi ng PSI nSARR. M. W. Muss onBritish Geological SurveyM. HaynesNPA GroupA. FerrettiTeleRilevame nto EuropaINTRODUCTIONWhile

20、the applicati on of In SAR (INterferometric Syn thetic ApertureRadar) tech niq ues to seismology has bee n well known since themid-1990s (Massonnet et al. ,1993 ; Massonnet et al. , 1996 ), PSInSAR is gen erally un familiar to the Earth scie nee com mun ity.The PS sta ndsfor "perma nent scatter

21、er", and it is the use ofthese (al ong with thevolume of sce nes employed) that dist in guishesthe method from morefamiliar In SAR tech niq ues. A perma nent scattereris any persiste ntlysuch as build ing roofs, boulders. The use of thesemeasureme nts of groundreflective pre-existing ground fea

22、ture, metallic structures, and eve n large features offers the possibility ofand over periods of time, in terferometry. Furthermore, of displaceme nts over the full (started in 1991) for anydisplaceme nts to a degree of accuracy, previously un obta in able from conven ti onal it is possible to con s

23、truct histories temporal exte nt of the SAR data archivetherefore represe ntsextremely dense twelve years.part of the globe with data coverage. PSIn SAR the equivale nt of a n ewly discovered, superaccurate, GPS network that has been in existence for the lastThe high resolution of PSInSAR data, coup

24、led with its being particularly suited to urba ni zed areas (nu merous build in gs,thereforemany PS poin ts), makes it an excelle nt tool for study ingthings suchas urban subsidence ( Ferretti et al., 2000; Mizuno and Kuzuoka, 2003 Dehls and Nordgule n, 2004). It also has applicati ons in seismology

25、:as a substitute for GPS data where these do not exist, and asanenhan ceme nt where they do .In this paper we report on a pilotprojectin Japa n, the prin cipal aim of which was to calibrateand test thePSI nSAR measureme nts in an area where ground truth is very well established from GPS and leveli n

26、g data. This workresults from aEuropea n Space Age ncy (ESA) "Earth Observati onMarket Developme nt"project en titled "Developi ng markets forEO-derived land motio nmeasureme nt products", i nvolving NPA (lead), the British Geological Survey (UK), Imperial College (UK), TeleRilev

27、ame nto Europa (Italy), Image One (Japa n), the Geographic Survey In stitute (Japa n), Oyo Corporatio n (J apan),Fugro (Netherla nds), and SARCOM (the ESA datadistribut ing en tity).TECHNICAL BASIS OF PSI nSARConven ti onal satellite radar in terferometry invo Ives the phase comparis on of syn theti

28、c aperture radar (SAR) images gatheredatdifferent times (Massonnet et al. ,1993 ; Massonnet et al. ,1994 ;Zebker et al. , 1994 ; Gens and van Genderen, 1996 ; Massonnet and Feigl, 1998). This technique has the potential to detect millimeter-level target displaceme nts along the lin e-of-sight (LOS)

29、directio n. Theaimof the in terferometric tech niq ues is to highlight possiblerangevariati ons of the target by means of a simple phase differe nee betwee n two images gathered at differe nt times. If the local reflectivity remains unchanged in time, its phase contribution disappears in the differe

30、 ntiatio n and possible range variatio nscanthen be detected.Si nee the wavele ngth of the illu min at ing radiati on is usuallya fewcen timeters (satellite SAR operates in the microwave doma in),eve n amillimetric range variatio n tran slates to a phase cha ngethat can bedetected. Due to low sig na

31、l-to-no ise ratio valuestypically prese ntin SAR phase values (n ever greater tha n 12dB), however, themon itori ng of subside nee rates of more tha n6-7 cm/year is notfeasible.Apart from cycle ambiguity problems, other limitati ons are duetotemporal and geometrical decorrelati on and to atmospheric

32、artifacts.Temporal decorrelatio n makes in terferometric measureme ntsso con sta nt be ane.g. , seismicun achievable where the electromag netic profiles an d/or the positi onsisi.e.of the scatterers change with time within the resolution cell, that the reflectivity phase contribution cannot be assum

33、ed with time. The use of short revisiting times proves to unsuitable solution, since very slow terrain motion ( creep) cannot be detected.Reflectivity variations as a function of the incidence angle ( geometrical decorrelatio n) further limit the nu mber of image pairs suitable for in terferometric

34、applicati ons, uni ess the cha ngeconfined to a pointwise character of the target (e.g. , a cornerreflector). In areas affected by either kind of decorrelati on, gen erati on of the in terferogram no Ion ger compe nsates the reflectivity phase con tributi on, and possible phase variati ons due to ta

35、rget motion cannot be highlighted.Fin ally, atmospheric heteroge neity creates an atmospheric phase scree n superimposed on each SAR image that can seriously compromise accurate deformati on mon itori ng. In deed, eve n con sideri ng areas slightly affected by decorrelati on, it may prove extremely

36、difficult to discrimi nate the sig nal of in terest from the atmosphericsig nature,at least using in dividual in terferograms.The PSInSAR method, developed by TeleRilevame nto Europa of the Politecnico di Mila no in Italy, provides a way to overcome these limitati ons. Although temporal decorrelatio

37、 n and atmospheric disturba nces still stro ngly affect in terferogram quality, reliable deformati on measureme nts can be obta ined in a multi-image framework on a small subset of image pixels corresp onding to stable areas.These poin ts, the perma nent scatterers (PS), can be used asa"n atura

38、l GPS n etwork" to mon itor terrain moti on, by an alyz ingthephase history of each one.every in time.in time and depe nding on the water pump ing, fault buildi ngs, etc.). removed by such as those gatheri ng data sinceAtmospheric artifacts show a stro ng spatial correlati on within single SAR

39、acquisition (Hanssen, 1998 ) but are uncorrelatedimages, and improve the that are not greatly are selected.Conv ersely, target moti on is usually stro ngly correlated can exhibit differe nt degrees of spatial correlatio n phe nomenon at hand ( e.g. , subside nee due to displaceme nts, localized slid

40、 ing areas, collaps ing Atmospheric effects can therefore be estimated and combi ning data from Ion g-time series of SAR images, available in the ESA ERS archive, which has bee n late 1991. To exploit all the available accuracy of the estimatio n, only scatterers affected by temporal and geometrical

41、 decorrelati onPossible stable and point targets, known as perma nent scatterers(PS),are detected on the grounds of the stability of theiramplitudereturns ( Ferretti et al. , 2001 ): i.e. , how constant their brightness or in te nsity remai ns from one SAR image tothe n ext. This allowspixel-by-pixe

42、l select ion with no spatialaverag ing. Due to the highspatial correlati on of the atmosphericcon tributi on, proper sampli ngof the atmospheric comp onents can be achieved with a sparse grid of measureme nts, provided that the PS den sity is high eno ugh (greater than 4-5 PS/km2; Ferretti et al. ,

43、2000, 2001). A sufficient number ofimages is needed (usually more than 30) to identify PS and separate the differe nt phase con tributi ons.areEve n though precise satellite positi on and velocity state vectorsimpact on atmospheric atmospheric corresp ond to cha nge the low wave- the sparse PS grid.

44、available for ERS satellites, orbit ambiguities and their the in terferograms cannot be n eglected. The estimated phase screen is actually the sum of two contributions: effects and frin ges due to orbital errors. The latter low-order phase polyno mials, however, and do not nu mber character of the s

45、ig nal to be estimated onAt the PS point, submeter accuracy elevati on and millimetricterrainmoti on detect ion (due to the high phase cohere nee ofthese scatterers)can be achieved once atmospheric con tributi onsare estimated andremoved. Relative target LOS velocity canbe estimated withun precede n

46、ted accuracy, sometimes eve n better tha n 0.1 mm/year, due to the long time spa n of the data used.The higher the accuracy ofthe measureme nts, the more reliable the differe ntiati ons betwee n models of the deformatio n processun der study.PILOT PROJECTThe area selected for the pilot project was t

47、he Tokai area inJapa n,in itially around Hamamatsu and the n exte nded to coverthe rest of thewest side of Suruga Bay and the n orther n partof the Izu Penin sula(Figure 1 ). This area was attractive forthe project for severalreas on s. It is one of the most inten sivelystudied areas in Japa n,becau

48、se it was ide ntified as the likely locati onof the next majorearthquake as long ago as the 1970s. It isan area of activetectonics in a complex structural setti ng.The prin cipal comp onent of the tecto nic structure in the Tokaidistrict is the collisio n of the n orthward-movi ng Philippi neSeaPlat

49、e (PSP) with Japa n ( Figure 1 ). This collisi onal processstartedabout 6-7 million years ago ( Niitsuma, 1982 ) and has been responsibleas the PSP subductsHon shu the situatio n subduct ion model. district is very muchThe subducti on tren ch, which,for most of the seismicity of souther n Japa n und

50、er the overlying Eurasian Plate. In southern is relatively simple and follows the conventional The plate boun dary geometry around the Tokai more complex, however ( Takahashi, 1994 ).as the Nan kai Trough, is orie nted n ortheast-southwestto the south ofHon shu, bends to an almost n orthsouth orie n

51、tatio nas the SurugaTrough in Suruga Bay. The most n ortherly pointof the PSP is occupiedby the Izu Penin sula, which is collidi ngwith Hon shu rather tha nbeing subducted ben eath it. The reas onfor this is believed to be therelative light ness of the volca nicrocks of the Izu Penin sula, thebuoya

52、ncy of which preve nts subduct ion (Takahashi, 1994 ). Theno rthward moveme nt of the PSP in the Izu area is thereforea processof collisi on tect onics akin to continen tal collisi onrather tha nnormal subduction ( Niitsuma and Matsuda, 1985; Koyama, 1991). Priorto the collisio n of the Izu Penin su

53、la, the Tan awa Blockcollided withthe Hon shu mainland duri ng the Mioce ne, and the process by which the Tan awa Block accreted to the mai nland is now being repeated with the Izu Penin sula ( Ama no, 1991). The process is described in detail by Takahashi ( 1994).The possibility, or eve n the proba

54、bility, of a large and disastrous earthquake in the Tokai district has been of concern since the area was ide ntified as a dan ger area and seismic gap by Mogi (1970) andIshibashi (1976). The subduct ion front from Shikoku to Hamamatsu hasbee n ide ntified as being partiti oned into several prin cip

55、al fault pla nes that appear to rupture in characteristic earthquakes. These segme nts were labeled A to D (from west to east) by Ando (1975), andthis system was expa nded by Sugiyama (1994) to in clude segme ntZ(Bungo Chann el) in the west and segme nt E (Suruga Bay) in theeast(Figure 1 ). Any larg

56、e earthquake may rupture one of thesesegme ntsen tirely, or in the worst case all six at on ce, asappare ntlyoccurred in the 1707 Hoei earthquake ( Sugiyama, 1994 ). For historical eve nts, the exte nt of the rupture can be deducedfrom in formatio n oninten sity distributi on, tsun ami distributi on,and ground deformati on(Utsu, 1974 ; An do, 1975)