IPhOexperimental competition.docx

IPhOexperimental competition.docx

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IPhOexperimentalcompetition

ExperimentalCompetition

Saturday,June30th,2001

Pleasereadthisfirst:

1.Thetimeavailableis5hoursfortheexperimentalcompetition.

2.Useonlythepenprovided.

3.Useonlythefrontsideofthepaper.

4.Begineachpartoftheproblemonaseparatesheet.

5.Foreachquestion,inadditiontotheblanksheetswhereyoumaywrite,thereisananswerformwhereyoumustsummarizetheresultsyouhaveobtained.Numericalresultsshouldbewrittenwithasmanydigitsasareappropriatetothegivendata.

6.Writeontheblanksheetsofpapertheresultsofallyourmeasurementsandwhateverelseyouconsiderisrequiredforthesolutionofthequestion.Pleaseuseaslittletextaspossible;expressyourselfprimarilyinequations,numbers,figuresandplots.

7.FillintheboxesatthetopofeachsheetofpaperusedbywritingyourCountrynoandCountrycode,yourstudentnumber（StudentNo.）,thenumberofthequestion（QuestionNo.）,theprogressivenumberofeachsheet（PageNo.）andthetotalnumberofblanksheetsusedforeachquestion（TotalNo.ofpages）.Writethequestionnumberandthesectionlabelofthepartyouareansweringatthebeginningofeachsheetofwritingpaper.Ifyouusesomeblanksheetsofpaperfornotesthatyoudonotwishtobemarked,putalargeXacrosstheentiresheetanddonotincludeitinyournumbering.

8.Attheendoftheexam,arrangeallsheetsinthefollowingorder;

∙answerform

∙usedsheetsinorder

∙thesheetsyoudonotwishtobemarked

∙unusedsheetsandtheprintedquestion

Placethepapersinsidetheenvelopeandleaveeverythingonyourdesk.Youarenotallowedtotakeanysheetsofpaperandanymaterialusedintheexperimentoutoftheroom.

ROTATINGLIQUID

Thisexperimentconsistsofthreebasicparts:

1.investigationoftheprofileoftherotatingliquid’ssurfaceandthedeterminationoftheaccelerationduetogravity,

2.investigationoftherotatingliquidasanopticalsystem,

3.determinationoftherefractiveindexoftheliquid.

Whenacylindricalcontainerfilledwithaliquidrotatesabouttheverticalaxispassingthroughitscenterwithauniformangularvelocity,theliquid’ssurfacebecomesparabolic（seeFigure1）.Atequilibrium,thetangenttothesurfaceatthepointP（x,y）makesananglewiththehorizontalsuchthat

（1）

whereRistheradiusofthecontainerandgistheaccelerationduetogravity.

Itcanfurtherbeshownthatfor

atx=x0=

y（x0）=h0

（2）

thatis;theheightoftherotatingliquidisthesameasifitwerenotrotating.

Theprofileoftherotatingliquid’ssurfaceisaparaboladefinedbytheequation

（3）

wherethevertexisatV（0,y0）andthefocusisatF（0,y0+C）.Whenopticalraysparalleltotheaxisofsymmetry（opticalaxis）reflectattheparabolicsurface,theyallfocusatthepointF（seeFig.1）.

Apparatus

∙Acylindricalrigidplasticcupcontainingliquidglycerin.Millimetricscalesareattachedtothebottomandthesidewallofthiscup.

∙Aturntabledrivenbyasmalldcelectricmotorpoweredbyavariablevoltagesupply,whichcontrolstheangularvelocity.

∙Atransparenthorizontalscreenonwhichyoucanputtransparentorsemi-transparentmillimetricscales.Thelocationofthescreencanbeadjustedalongtheverticalandhorizontaldirections.

∙Alaserpointermountedonastand.Thepositionofthepointercanbeadjusted.Theheadofthepointercanbechanged.

∙Additionalheadforthelaserpointer.

∙Aruler.

∙Ahighlighterpen.

∙Astopwatch.Pushtheleftbuttontoreset,themiddlebuttontoselectthemode,andtherightbuttontostartandstopthetiming.

∙Transmissiongratingswith500or1000lines/mm.

∙Bubblelevel.

∙Glasses.

IMPORTANTNOTES

∙DONOTLOOKDIRECTLYINTOTHELASERBEAM.BEAWARETHATLASERLIGHTCANALSOBEDANGEROUSWHENREFLECTEDOFFAMIRROR-LIKESURFACE.FORYOUROWNSAFETYUSETHEGIVENGLASSES.

∙Throughoutthewholeexperimentcarefullyhandlethecupcontainingglycerin.

∙Theturntablehasalreadybeenpreviouslyadjustedtobehorizontal.Usebubblelevelonlyforhorizontalalignmentofthescreen.

∙Throughouttheentireexperimentyouwillobserveseveralspotsonthescreenproducedbythereflectedand/orrefractedbeamsatthevariousinterfacesbetweentheair,theliquid,thescreen,andthecup.Besuretomakeyourmeasurementsonthecorrectbeam.

∙Inrotatingtheliquidchangethespeedofrotationgraduallyandwaitforlongenoughtimesfortheliquidtocomeintoequilibriumbeforemakinganymeasurements.

EXPERIMENT

PART1:

determinationofgUsingaRotatingLıquıd[7.5pts]

∙DeriveEquation1.

∙Measuretheheighth0oftheliquidinthecontainerandtheinnerdiameter2Rofthecontainer.

∙Insertthescreenbetweenthelightsourceandthecontainer.MeasurethedistanceHbetweenthescreenandtheturntable（seeFigure2）.

∙Alignthelaserpointersuchthatthebeampointsverticallydownwardandhitsthesurfaceoftheliquidatadistancex0=

fromthecenterofthecontainer.

∙Rotatetheturntableslowly.Besurethatthecenteroftherotatingliquidisnottouchingthebottomofthecontainer.

∙Itisknownthatatx0=

theheightoftheliquidremainsthesameastheoriginalheighth0,regardlessoftheangularspeed.Usingthisfactandmeasurementsoftheangleofthesurfaceatx0forvariousvaluesof,performanexperimenttodeterminethegravitationalaccelerationg.

∙Preparetablesofmeasuredandcalculatedquantitiesforeach.

∙Producethenecessarygraphtocalculateg.

∙Calculatethevalueofgandtheexperimentalerrorinit

∙Copythevalues2R,x0,h0,Handtheexperimentalvalueofganditserrorontotheanswerform.

PART2:

OpticalSystem

Inthispartoftheexperimenttherotatingliquidwillbetreatedasanimageformingopticalsystem.Sincethecurvatureofthesurfacevarieswiththeangularspeedofrotation,thefocaldistanceofthisopticalsystemdependson.

2a）Investigationofthefocaldistance[5.5pts]

∙Alignthelaserpointersuchthatthelaserbeamisdirectedverticallydownwardatthecenterofthecontainer.MarkthepointPwherethebeamstrikesthescreen.Thusthelinejoiningthispointtothecenterofthecupistheopticalaxisofthissystem（seeFigure2）.

∙Sincethesurfaceoftheliquidbehaveslikeaparabolicmirror,anyincidentbeamparalleltotheopticalaxiswillpassthroughthefocalpointFontheopticalaxisafterreflection.

∙Adjustthespeedofrotationtolocatethefocalpointonthescreen.MeasuretheangularspeedofrotationandthedistanceHbetweenthescreenandtheturntable.

∙RepeattheabovestepsfordifferentHvalues.

∙Copythemeasuredvaluesof2Randh0andthevalueofateachHontotheanswerform.

∙Withthehelpofanappropriategraphofyourdata,findtherelationshipbetweenthefocallengthandtheangularspeed.Copyyourresultontotheanswerform.

2b）Analysisofthe“image”（whatyouseeonthescreen）[3.5pts]

Inthispartoftheexperimentthepropertiesofthe“image”producedbythisopticalsystemwillbeanalyzed.Todoso,followthestepsgivenbelow.

∙Removetheheadofthelaserpointerbyturningitcounterclockwise.

∙Mountthenewhead（providedinanenvelope）byturningitclockwise.Nowyourlaserproducesawelldefinedshaperatherthananarrowbeam.

∙Adjustthepositionofthelaserpointersothatthebeamstrikesataboutthecenterofthecupalmostnormally.

∙Putasemitransparentsheetofpaperonthehorizontalscreen,whichisplacedclosetothecup,suchthatthelaserbeamdoesnotpassthroughthepaper,butthereflectedbeamdoes.

∙Observethesizeandtheorientationofthe“image”producedbythesourcebeamandthebeamreflectedfromtheliquidwhenitisnotrotating.

∙Starttheliquidrotating,andincreasethespeedofrotationgraduallyuptothemaximumattainablespeedwhilewatchingthescreen.Asincreasesyoumightobservedifferentfrequencyrangesoverwhichthepropertiesofthe“image”aredrasticallydifferent.Todescribetheseobservationscompletethetableontheanswerformbyaddingarowtothistableforeachsuchfrequencyrangeandfillitinbyusingtheappropriatenotationsexplainedonthatpage.

PART3:

RefractiveIndex[3.5pts]

Inthispartoftheexperimenttherefractiveindexofthegivenliquidwillbedeterminedusingagrating.Whenmonochromaticlightofwavelengthisincidentnormallyonadiffractiongrating,themaximaofthediffractionpatternareobservedatanglesmgivenbytheequation

（4）

where,mistheorderofdiffractionanddisthedistancebetweentherulingsofthegrating.Inthispartoftheexperimentadiffractiongratingwillbeusedtodeterminethewavelengthofthelaserlightandtherefractiveindexoftheliquid（seeFigure3）.

∙Usethegratingtodeterminethewavelengthofthelaserpointer.Copyyourresultontotheanswerform.

∙Immersethegratingperpendicularlyintotheliquidatthecenterofthecup.

∙Alignthelaserbeamsuchthatitenterstheliquidfromthesidewallofthecupandstrikesthegratingnormally.

∙Observethediffractionpatternproducedonthemillimetricscaleattachedtothecupontheoppositeside.Makeanynecessarydistancemeasurements.

∙Calculatetherefractiveindexnoftheliquidbyusingyourmeasurements.（Ignoretheeffectoftheplasticcuponthepathofthelight.）

∙Copytheresultofyourexperimentontotheanswerform.

P（x,y）

Figure1.DefinitionsofthebankangleatpointP（x,y）,thevertexVandthefocusFforthep