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1、Aroughsimulationofrainbow1351956ThomasXia,SchoolofAutomotiveStudies,TongjiUniversity1.AbstractInthisproject,Iwouldliketoexplorehowrainbowscomeintobeingandsimulatearainbowbysoftware.Equipment:Laptop(ASUSA450E47JF-SL),Software(MatlabR2014a、PhotoshopCC2014).2.Analysis&Calculation2.1Afterashowerofraino
2、rnearbyawaterfall,thinfogconsistoftinywaterdropswillbewidespreadintheair.Theparallelsunlightcastonasingledropwillhavetworefractionsandonereflectiononthesurface.Sincewaterhasdifferentindexesofrefractiontolightsofdifferentfrequency,asaresult,thedropbendslightofdifferentcolorsbydifferentangles.2.2Supp
3、osethesunlightishorizontal,relativeindexofreflectionoflightwithfrequencyvisn21.Theradiumofthedropisr.Abeamhasadistancehfromthecenterofthedrop.Angleofincidenceisθi.Angleofrefractionisθr。Theanglethatlightisbentα.RΘr”Θi”hΘiΘrΘr’Θi’αsinθisinθr=n21,θr=θi,=θr,=θi,,,sinθi,,sinθr,,=1n21,θi=arcsinhR,α=2π-2π
4、-θi,-θr,-θi-θr-θr,,-θi,,,α(h)=4∙arcsinhR∙n21-2∙arcsinhRBecauseparallelbeamsofsunlightareevenlydistributedin0≤h≤R,fortwonearpointsonfunctionα(h),independentvariabledifferenceΔhcanrepresentnumberofbeamsshootoutbyanglefromα0to(α0+Δα)：αh0=α0,αh0+∆h=α0+∆α,then，limΔα→0ΔhΔα=dhdα=α-1(α0)canrepresentthedens
5、ityoflightsshootoutbyangleα0.【InMatlab,wecanalsousefunctionα(h)togetmanyrandomdata(αi,hi)first,andthenusefunction“ksdensity”tocalculateα’sdistributiontorepresentlightdensity】 Chapter2.2calculatedthefunctionbetweenlightdensityandangleαbytwoways,wemarkthisfunctionasρ(α).Thefunctionfitseverysingledrop
6、inthefog. Sydydαα2.3Wesimplifythethinwaterfogdescribedin2.1intoaverytallcube,whichisfromobserver’seyesbydistanceS.Andonlydropsonitssurfacecansparkledirectlyintoobserver’seyes.y=S∙tanαdy=S∙sec2α∙tanα∙dαLuminancereceivedbytheobserverLα=C∙ρα∙numberdrop=C∙ρ(α)∙(μ∙dx∙dy)=C'∙ρ(α)∙sec2α∙tanα(C、C’areconst
7、ants,μisdrops’numberdensityonthesurface,dxisunitwidth)Hereweignoretheenergylosswhenlighttravellongdistancethroughtheair.1.Simulationprocess3.1LookupindexofrefractionofdifferentlightsontheInternet.wavelength
