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RainbowScienceTargetGrades:MiddleandHighSchoolTimeRequired:120minutesBackgroundInformationforTeachersandStudentsRainbowsarefascinatingphenomenathatoccurduetotheinteractionofsunlightandwaterdropletssuspendedintheair.Whilestudentsaregenerallysomewhatfamiliarwiththeseparationofwhitelightintoitscomponentcolorsbyprisms,theyarelessfamiliarwiththegeometryinvolvedinrefractionandreflectionoflightasitimpingesontheboundarybetweentwomedia(inthiscase,airandwater).Thislessonplanisaninvestigationintothegeometryrequirementsthatenableustoseerainbows.LessonObjectiveStudentswillinvestigatethegeometryofrainbowproductionbyperforminglaboratoryinvestigationsusingsimpleequipment.Theywillbenefitmostfromtheseexperimentsiftheyfirstunderstandvocabularytermssuchasrefract,reflect,normal,andmedium.Priorknowledgethatlighttravelsinastraightlineinagivenmediumishelpful,althoughtheywillobservethisusingthelasers.Studentsshouldbeabletomeasureanglesusingaprotractor,andshouldunderstandthebasicgeometryofacircle,includingtermssuchascenter,radiusanddiameter.Theactivitiesinthislessonplanwillillustratetostudentsthatscientistsinvestigatenaturalphenomenabyusingappropriatemodels.Studentsshouldbepromptedtothinkaboutwaysthemodelsusedinthislessonserveasgoodrepresentationsforrainbowproduction,andwhatthelimitationsofthemodelsmightbe.MathematicalunderstandingoftheLawofReflectionorSnell’sLawofRefractionisnotrequired,althoughhighschoolstudentswhohavebeenintroducedtoSnell’sLawcanperformcalculationstodeterminerefractiveindicesofglass,acrylic,andwater,basedonthedatacollected.Highschoolteacherscanconsideraddingacalculationcomponenttothelesson.TheactivitiesdescribedbelowintheInstructionalProcesssectionaredesignedtohelpstudentsdiscoverforthemselveshowtheprimaryrainbowisproduced.Anextensionintotheproductionofthesecondaryrainbow,thedarkspacebetweenrainbows,andthedarkandlightinterferencebandssometimesseenaccompanyingrainbows,willalsobepresentedduringtheScienceSaturdayssession.Advancedstudentsinhighschoolphysicswilllikelybeabletounderstandandsubsequentlyexplaintheextensionactivities.Studentsinmoreelementarycoursesshouldbeabletoexplaintheproductionoftheprimaryrainbow,andwillprobablybefascinatedbytheextensionevenifitisbeyondtheircurrentabilitytoexplain.
InstructionalProcessActivity1:DeterminationofCriticalAngleMaterialsneeded:
• Lowpowerredorgreenlasers(5mWorless)
• Protractorimagesprintedonplainpaper
• Semicircularprisms(glassand/oracrylic)Studentsinsmallgroupsaregivenprotractorsprintedonwhitepaper,uponwhichtheysketchanormal(perpendicular)totheflatsideoftheprotractor.Theythenplaceasemicircularprismofatransparentmaterialontheprotractorasshownbelow.
Thestudentsthenshinealaserthroughthematerialsuchthatthebeamisdirectedalongaradius.Forsmalleranglesq,theywillseebothrefractionandreflectionofthelaser,asshownbelow.
Thestudentsmovethelaser,maintainingthebeamalongaradius.Theywillfindthatforlargevaluesofq, 100%ofthelightwillbereflectedoffoftheflatsurfaceofthesemicircle,andthe refractedbeamcompletelydisappears.Thesmallestangleqatwhichtotalreflectionoccursis calledthecriticalangleofincidence.
Thecriticalanglefoundbyeachstudentteamisrecordedelectronicallybytypingtheresults intoaGoogledocumentthatisdisplayedintheauditoriumforalltosee.Studentsrepeatthe experimentfortwodifferenttransparentmaterials,glassandacrylic,tofindthecriticalangle foreachmaterial.
Activity2:DeterminationoftheRainbowAngleMaterialsneeded:
• Lowpowerredorgreenlasers(5mWorless)• Protractors• Graphpaper• Cylindricalbottles• Rulers
Cylindricalbottlesarefilledwithwater.Adropofwholemilkisaddedtoeachbottletocreatea suspensioncapableofscatteringlaserlight.Studentteamsplacethebottlesongraphpaper, tracetheoutlineofthebottomofthebottle,andmarkthepositionofthecenterofthebottomofthebottle.
Studentsthenshinelaserlightintothebottlesuchthatthelaserbeamenteringthebottleis paralleltothegridlinesofthegraphpaper.Theymarkthepathofthebeamenteringand exitingthebottle.Anexampleofthelightpathofinterestappearsbelow,withrepresentativestudentmarkings.Studentsmaynoticeotherlightpathsduetoreflectionandrefraction,butsincethesedonotcontributetothecreationoftheprimaryrainbow,theywillnotbemarked.
Studentsthenanalyzetheirdatabyremovingthebottle,drawinglinesthroughthepointstheypreviouslymarked,andmeasuringtheangleqbetweentheirenteringandexitingbeam.Theyalsomeasuretheshortestdistancedbetweentheenteringbeamandthecenterofthecirclebymeasuredalongagridline.Anexampleappearsbelow:
Studentswillrepeatthemeasurementofθ forarangeofvaluesd.TheywillagainentertheirresultsintoGoogledocs,andcompiledresultswillbedisplayedintheauditorium.Activity3:ColorSeparationinRainbows
• Materialsneeded:• LCDprojector(oralternatively,abrightwhiteincandescentlight)
• Cylindricalbottlesfilledwithwater
• Screenmadeofcardboardorfoamboard(approximately2feettalland3feetwide)intowhichaverticalslit(approximately3inchestalland1/8inchwide)hasbeencut
• Somewaytoholdthescreenverticallysuchthattheprojectorbeamshinesthroughtheslitinthecardboard.
Theprojectorissetuptoprojectaplainwhitelightbeam.OnewaytodothisistoconnecttheprojectortoacomputerdisplayingawhitePowerPointslide.Ifanincandescentlightsourceisused,itmustbequitebright.
Toruntheexperiment,theroomisdarkened.Thecardboardorfoamboardisplacedinfrontoftheprojectorbeamsothatthelightshinesthroughtheslit.Thewaterbottleisplacedinfrontoftheslitsotheresultingnarrow,verticalbeamofwhitelightshinesthroughthebottle.Thegeneralarrangementofequipmentisshownbelow:
Studentsadjustthepositionofthecardboardandbottleuntiltheyseearainbowprojectedonthecardboardontheoppositesidefromtheprojector.Studentsareaskedtoobservethespectralorderingofthecolors,aswellasthecharacteristiccurvedshapeoftherainbow.Assessment/Follow-upTheresultsoftheexperimentsperformedbythestudentswillbetalliedandpresented.Forthepurposeofformativeassessment,studentscanthenbeaskedtodiscusstheproductionoftheprimaryrainbow,usingevidencefromtheirinvestigations.Belowaresomesamplequestionsandstudentresponses.Notethattheresponsesgivenbydifferentgroupsofstudentsmightpromptdifferentlinesofquestioningandsubsequentdiscussion.
• Whatroledoesrefractionplayinrainbowproduction?o Lightmustentertheraindrop,andexititagain.Thisisrefraction.
o Differentcolorsoflightarerefractedthroughslightlydifferentangles.Thisseparatesthecolors.Thewaterdropletsinarainbowactastinyprisms.
• Whichofthesedidyoudemonstrateduringyourexperimentswiththelaser?o Becausewehadjustonecolorlaser,wedidnotdemonstratetheseparationofcolors.o Wediddemonstratewiththelasersthatlightbendswhenitrefracts.
• Inwhichoftheexperimentsdidyoucreateanactualrainbow,andwhatwasdifferentaboutthis
experimenttoenablethistohappen?o Intheexperimentwiththeprojector,wecreatedarainbow.
o Youmusthavewhitelighttocreatearainbow,andthatistheonlyactivitywherewhitelightwasused.
• Couldyouuselaserstoinvestigateseparationofcolorsbyrefraction?Ifso,how?o Yes,butyouwouldneedtorunthesameexperimentwithdifferentcolorlasers,andcomparethe
resultstoseeifthecolorsbendthroughdifferentangles.• Whyisthesunalwaysbehindyouandamistyraininfrontofyouwhenyouseearainbowinthesky?
o Thesun’sraysrefractintowaterdroplets,reflectoffthebacksurfaceofthedrops,andrefractbackintotheairtowardyou.Youseethesunlightwhenitentersyoureyes.
• Whatevidenceistherethatreflectioninvolved?o Ifthelightiscomingfrombehindyou,andyouseeitanyway,youmusthavereflectiongoingon.
Thelightreturnsbacktoyou.• Whatroledoescriticalanglehaveintheproductionofarainbow?
o Ifyouthinkverycarefullyyouwillseethattherayoflightthatjusttouchestheouteredgeofthedropwillbereflectedatthecriticalangleinsidethedrop.
• Whatarethelimitationsofthemodelyouusedinlab,andhowmightitaffecttheresultsyouobtained?o Raindropsarealotsmallerthanwhatweused,butthiswouldnotaffectangle.
o Waterdropletsarespheres,notcylinders.Thismeansthemodelisaccurateinoneplane,butnotothers.
o Waterisinabottle,andthereisacontainerinvolved.Maybethisaffectstheangles.
KeyVocabulary
• Electromagneticradiation:Electromagneticradiationisthenameweapplytoatypeofwavethatcantravelacrossspacewithoutrequiringamediumthroughwhichtotravel.Theword“electromagnetic”referstotheinteractionbetweenelectricandmagneticfieldsthatcreatesthistypeofradiation.Whileelectromagneticradiationdoesnotrequireamediumtotravelfromonepointinspacetoanother,itiscapableoftravelingthroughsomephysicalmedia,althoughthistypicallyaffectsitsspeed.
• Light:Visiblelightisaformofelectromagneticradiation.Unlikeotherformsofelectromagneticradiation,humanscanseelight.
• Normal:Anormalisalinethatisperpendiculartoasurfaceatthepointwhereitmeetsthesurface.Thereisonlyonenormaltoasurfaceatanygivenpoint.Evenacurvedsurfacehasanormalateachpointonthesurface.Forexample,eachradiusordiameteryoucandrawforacircleisnormaltothecirclewhereitmeetsthecircle.
• Reflection:Reflectionisthebouncingoflightoffofasurfacebackintothemediumfromwhichitcame.
• Refraction:Refractionismovementoflightfromonemediumintoanother.Generally,whenlightstrikesasurfacethatistransparentortranslucent,someofthelightwillberefractedandsomewillbereflected.
• Refractiveindex:Whenlightrefracts,itmaychangespeed.Thischangeinspeedoccursattheboundarybetweenthetwomedia.Therefractiveindexisaratioofthespeedoflightinavacuumtothespeedoflightinanothermedium.Hencen=c/v,wherenistherefractiveindexofthematerial,cisthespeedoflightinavacuum,andvisthespeedoflightinthematerial.Thehighertherefractiveindex,theslowerlightwillmoveinthematerial.
• BendingRelativetoaNormal:Typically,iflightdoesnotenteramediumalonganormaltoasurface,thelightwillbendasitrefracts.Ifitslowsdownwhenitentersthemedium,itwillbendtowardthenormalattheboundary.Ifitspeedsupwhenitentersamedium,itwillbendawayfromthenormal.
• AngleofIncidence:Whenlightstrikesaboundarybetweentwomedia,theangleofincidenceistheanglebetweentherayoflightintheoriginalmediumandanormaltotheboundarysurface.
• AngleofReflection:Whenlightstrikesaboundarybetweentwomediaandreflectsbackintotheoriginalmedium,theangleofreflectionistheanglebetweenthereflectedrayoflightandanormaltotheboundarysurface.
• LawofReflection:TheLawofReflectionstatesthattheangleofreflectionisalwaysequaltotheangleofincidence.
• AngleofRefraction:Whenlightstrikesaboundarybetweentwomediaandrefractsintothesecondmedium,theangleofrefractionistheanglebetweentherefractedrayoflightandanormaltotheboundarysurface.Theangleofrefractiondependsupontherefractiveindicesofthetwomediaandtheangleofincidence.
• Snell’sLaw:Snell’sLawmathematicallydescribestherelationshipbetweenanglesofincidenceandrefractionandtherefractiveindicesofthemedia.Inequationform,Snell’sLawiswrittenasn1sin(q1)=n2sin(q2),wherenxistherefractiveindexofmediumx,andqistheanglebetweenthelightrayandthenormalinthatmedium.
• CriticalAngle:Whenlightstrikesaboundarybetweentwomediaandwouldspeedupinsecondmedium,itmayhavetobendsofarawayfromthenormalinthesecondmediumthatitcannotrefractatall.Inthiscircumstance,theallofthelightwillreflectbackintotheoriginalmedium.Thesmallestangleatwhichthisoccursiscalledthecriticalangle.
SafetyandCleanupRequiredBecauselasersareusedinActivity1and2ofthislesson,caremustbetakentoinsuresafety.Studentsmustbeadequatelysupervised,andshouldnotbeallowedtohandlethelaserswithoutdirectadultengagement.Lasersafetyrules(notwavingthelaseraround,notshiningitintoeyes)shouldbeexplicitlyaddressedbeforetheexperimentsareperformed.Aftertheinvestigationsarecomplete,studentsshouldreturnallmaterials.AlignmentwithTNScienceandMathStandardsElementarySchoolAsearlyasfourthgrade,studentsconsiderlighttravelingthroughmaterials(GLE0407.10.2,SPI0407.10.2,andcheckforunderstanding0407.10.2)
MiddleSchoolStudentsshouldbeabletoapplypriorknowledgeaboutreflectionandrefractionastheyperforminquiry-basedlaboratoryinvestigations.Theemphasisisexperimentation,observation,anddatarecording.Studentsarebecomingfamiliarwithmakingclaimsfromevidence.(GLE0607.Inq.2,0607.Inq.3,0607.Inq.5,SPI0607.Inq.4,andcheckforunderstanding0607.Inq.3)
HighSchoolHighschoolphysicscoursesaddressopticsphenomena.Somesamplehighschoolstandardsaddressedbythisinvestigationinclude:Physics:CLE3231.4.3Exploretheopticsoflenses.CLE3231.4.4Analyzetheopticsofmirrors.SPI.3231.4.3SolveproblemsrelatedtoSnell’sLaw.SPI.3231.4.6Usinglightraydiagrams,identifythepathoflightusingaconvexlens,aconcavelens,aplanemirror,aconcavemirrorandaconvexmirror.PhysicalWorldConcepts:CLE3237.3.8Exploretheopticalprinciplesofmirrorsandlenses.CFU3237.3.12Investigatereflection,refraction,diffraction,andinterferenceoflightwaves.