Chapter 8 - 汕头大学医学院

Chapter8WaveOptics(1)(May11,2005)Abriefsummarytothelastlecture1.ThestructureoftheeyeCornea(角膜)　(1.376)Aqueoushumor　(水状液，1.336)Iris(虹膜)CrystallinelensRetinaYellowspotVitreoushumorThecross-sectionofhumaneyeCiliarymuscles(睫状肌)PupilTheeyeisnearlysphericalinshape&1inchindiameter.OpticnerveO2.Visionofthehumaneyevisionofthehumaneye1from0.1~1.5istheviewingangleandinunitofminute.3.Correctiveeyeglassesforvisualdefects(1)Myopia(nearsighted);(2)Hyperopiceye(farsighted);(3)Astigmaticeye(散光眼)4.Opticalinstrumentsusedinmedicine(1)Magnifyingglass(2)Compoundmicroscope(3)Fibrescopef252125ffsMWaveoptics(part1)1.Thecorpuscular(微粒)theoryoflight(Untilthemiddleof17thcentury,Newton(1642-1727)supported).2.Rayopticscanexplainmanyofthepropertiesoflight,butthereexistmanyotherinterestingandbeautifuleffectsthatcannotbeexplainedbythegeometricoptics.Forexample,Experimentsshowthatlightbendsaroundcorners.3.Thewavetheoryoflight(Huygens(1629-95))4.InterferenceeffectsoflightwerefirstobservedbyThomasYongin1800.8.1Interference(干涉)oflight•Interferenceofwavemotion,Whatisthephenomenon?•Twocoherentwavesshouldbesatisfiedwiththethreeconditions:whatarethey?(1)thesamefrequency(2)thesamevibrationaldirection(3)thesameinitialphaseorconstantphasechange.AchartofelectromagneticspectrumVisiblelight(veryapproximately):400~450nmViolet450~500nmBlue500~550nmGreen550~600nmYellow600~650nmOrange650~700nmRed8.1.1Opticallength(opticallength,distance,path)InChapter4,welearnedthatthephasedifferenceoftwowavesareexpressedas21122xxLightisalsoapartofelectromagneticwaves.ThelightinterferencefollowstheruleofwaveinterferenceasyouknowinYong’sdouble-slitexperiment.Itisknownthatlighttravelsatadifferentspeedindifferentmedium.Thespeedoflightinamediumdependsontherefractiveindexofthemedium.Fromthedefinitionoftherefractiveindex,weobtainncvFromthedefinitionofwavelength,whichistheperiodofthewavemultiplyingthespeedofthewave,wehavenncTvT0Where0iswavelengthoflightinfreespace.Sothewavelengthoflightbecomesshorterinmedium.Lightpathlengthisnotthegeometricallengthofthelighttravelanditisdefinedastheproductofrefractiveindexandthegeometricaldistancethelighttravels.Let’shavealookatthelightpathlengthatthesameperiodtwhenittravelsintwodifferentmedium.Wechoosemediumoneisfreespaceandmediumtwowithrefractiveindexn.infreespace:opitacllength=n0S=n0ct=ctInmedium:opticallength=cttncnvtnLnSoitisfoundthatthoughthelightstravelingindifferentmediumhavedifferentgeometricalpath(SandL)atthesameperiod,theyhavethesamelightpathlength.Sowhenwecalculatethephaseinmediumn,wecanusetheformuladirectlynL02Again0iswavelengthoflightinfreespace,Listhegeometricallengthinthemedium.Alsowecanusethesimilarformulatocalculatethephasedifference028.1.2Young’sdouble-slitexperiments20~100cm1~5mSlitsare0.1~0.2mmwide,separationoftwoslits1mm1.Coherentconditionsoflight:(1)Thewavehasfixedwavelength.Theincidentbeamshouldbemonochromatic(单色的).(2)Thesecondarywaveletsthatoriginatefromthetwosmallopeningsareinphaseattheirpointoforiginintheopenings.(3)Theopeningsaresmallincomparisonwiththewavelengthoftheincidentlight.(4)Thedistancebetweenthetwoopeningsisnottoobigcomparedwiththewavelengthoftheincidentlight.2.Yong’sformulasforbrightanddarkfringesIntheabovefigure,S1P=BP,thelightpathdifferenceisS2B=.Therefore,LxdLOPdddtansindPOS0LS1S2Bx•whatistheconstructiveconditionsfortwowaves?•byphasedifference•bypathdifference•whatistheinitialphasechangeindouble-slitinterferenceexperiment?•howabouttotalphasechange?Whatdoesitdependon?Totalphasechangeisthereforecausedbythelightpathchanges.•ConstructiveinterferenceAccordingtotheinterferencetheoryofwavemotion,wheneverthepathdifferenceisanintegermultipleofthewavelength,=m,theconstructiveinterferenceorreinforcementinterferenceshouldoccursaslongaslightiswave.Therefore,mdsinmLxdForbrightfringes:∴dmsin•DestructiveinterferenceOntheotherhand,theoppositephenomenonoccursthatthetwolightwavesarecancelledeachother.Thisconditioniscalleddestructiveinterferenceorcancellationandinthiscase,whatisthelightpathdifferenceshouldbeequalto?陈文灯Ldmxm)(sin21md(m=0,1,2,…))(21mLxd211sinmdSofordarkfringes:Lmdxm21•Thespacingoftwobrightordarkfringes:LdLdmLdmxxxmm)1(1Yong’sexperimentsshowthatalltheaboveformulascandescribethephenomenaobservedinhisexperimentsverywell,sothewavepropertyoflightisproved.•TheanalysisoftheresultsLdxxxmm11.Thespacingbetweentwodarkorbrightfringesisindependentfromm,sotheyareequallyspaced.2.Asissmall,sodcannotbetoobig,otherwise,theycannotbedistinguished.3.Whatwillyougetifyouusethesun(white)lightasalightsource?陈善源Example1:Inaninterferencepatternfromtwoslits,theseventh-orderbrightfringeis32.1mmfromthezeroth-orderbrightfringe.Thedoubleslitis5metersawayfromthescreen,andthetwoslitsare0.691mmapart.Calculatethewavelengthofthelight.Solution:thedataweknowarex7=3.21×10-2m,d=6.91×10-4m,m=7,L=5m,Sowehave:nmmLdxLdmxmm634571091.61021.342Lightinterferencegivesusanimportantmethodformeasuringthewavelengthoflight.8.1.3Lloyd’smirrorLl