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.