Physics'2020'' Lab'13' Wave'Interference'

Transcription

1 Find this and other activities on the PhET site at Physics2020 Lab13 WaveInterference Name Section Tues Wed Thu 8am 10am 12pm 2pm 4pm Introduction Considerthefourpicturesshownbelow,showingpureyellowlightsshiningtowardascreen.Inpictures 3and4below,thereisasolidwallbetweenthelightandscreen,withoneortwoslitscutintoletthe lightthrough.comparethefourscenarios. Whatdoyouthinkmightbehappeningtothelighttocreatethesedifferentpatterns?Discusswith yourgroupandwriteyourideasinthespacebelow.

2 Part1:WaveInterferenceSimulation A. OpenthePhETsimulation WaveInterference. Explorethesimulationtogetafeelforthecontrols. Trytorecreatethepicturesshownonpage1withthesimulation.Describewhatyouhadtodo withthesimulationtoreproducethepictures. Comparewhatyoulearnedfromthesimulationtoyourideasfrompage1.Whichideaswould youkeep?whatideaswouldyouchange?(didyounoticethethirdbrightspotrightbehindthe wallincase4?) Whathappenstothepatternonthescreenwhenthelightsarebroughtclosertoeachother? Whathappenstothepatternonthescreenwhenthelightsarefartherapart? Whathappenstothepatternwhentheslitsarebroughtcloserandfartherapart?

3 B. InterferencefromTwoSlits Thepicturesbelowshowtwowaysofrepresentinglightwavesfromtwoslits.Ontherightpicture, threepointsaremarked1,2,and3. Estimatethebrightnessofthelightyouwouldseeonascreenplacedatpoints1,2,and3. Describehowyoumightuseapictureliketheoneonthelefttosupportyourpredictionand explainwhatishappeningatpoints1,2,and3ontheright.weareinterestedinyourideas. Writedownalltheideasyoucanthinkof.Youcanusethesimulationtohelpyou.

4 PART2:DoubleSlitInterference A. Inthepicturesonthelastpage,therayswereemittedin alldirectionsfromtheslits.butnow,let sconcentrateon theraysthatareemittedinadirectionθtowardadistant screen (θ is measured from the normal to the barrier). Oneoftheserayshasafurtherdistancetotraveltoreach thescreen;thispathdifferenceisequaltod?sin(θ). Predict the brightness on the distant screen if the path difference is exactly one wavelength λ (or any integer numberofwavelengths)?explainyourreasoning. Predictthebrightnessifthepathdifferenceisλ/2,3λ/2,or5λ/2,etc.? Foreachequationbelow,identifywhichonewouldtellyoutheangles(θ)atwhichyouwouldsee brightspotsandwhichonewilltellyoutheangles(θ)fordarkspots. BrightorDark? m=0,±1,±2, d sin θ = mλ d sin θ = ( m + 1 )λ 2 Whatideasfrompart1Bwouldyoukeepandwhichwouldyourevise? Howdotheequationsabovesupportyourpredictionsof brightnessandthepatternshownontheright?

5 Smallanglesimplification: Ifθissmall(<<1radian),then sin( θ ) θ (inradians)andbrightspotsoccuronthescreenat m λ λ θ = ;darkspotswouldoccurat θ = ( m + 1 ).Asshownbelow,theangleθ(measured d 2 d fromthecenterofthescreen)isrelatedtothedistancexmeasuredonthescreenby tan(θ ) = x/l,wherelisthedistancefromthescreentothesourceoflight(theaperture). laser aperture tanθ = x/ L θ screen x L Iftheangleθissmall(lessthanafewdegrees),thensin(θ) tan(θ) θ(inradians)isan excellentapproximation.thus,thelocationsoftheinterferencebrightspotsaregivenby x λ θ = = m. L d Whathappenstotheinterferencepatternifdisincreased?Explainyourreasoning. Whathappenstotheinterferencepatternifdisdecreased?Explainyourreasoning. Areyouranswerstoaboveconsistentwithyouranswerstopart1A(page2)?

6 Part3:DiffractionPatternfromDoubleSlits The light source in this part of the experiment is a He\Ne laser which produces a monochromatic beam with a wavelength of λ = nm. The power output of our lasers is small,butstillenoughtodamageyourretinaifyoulookdirectlyintothebeam. Theplateyouhavecontainsseveralsingle,double,andmultipleslits.(Seefiguretotheright.) Thenumbersarethosegivenbythemanufacturerandarenotalwaysaccurate. Placetheplateinitsholderandmountiton theopticalbenchafewcentimetersinfront ofthelaser.placeapieceofwhitepaperin theclipboardandplaceitatthefarendof thebench. Spendafewminutesexploring.Whatdo younotice?isitwhatyouexpect? N = number of lines (top), D = width in mm (middle), d= spacing in mm(bottom) JustforthedoubleJslitsintheplate,listallthethingsthataffectthepatternonthescreen.

7 PART4:TestingPlateSpecifications Inthispartwewilltestthemanufacturer sspecificationsforthedouble\slitsintheplate. MeasurethedistanceLfromtheslittothescreenandrecordithere: Howfarapartwouldyouexpectthepeaksintheintensitytobeforaslit\spacingof0.35mmand wavelengthof632.8nm?givetheanswerbothinangle(radians)andinmm, using your screen distancel. Observetheinterferencepatternonyourpaperscreenforthedouble\slitlabeledwithaseparationof 0.35 mm (the one in the middle of the right\most column on the plate). With a pencil, mark the positionsofasmanyofthedarkspotsthatyoucanseeandmeasurethespacingxbetweenadjacent darkspotsonthescreen. Whatishappeningtothelighttomakethedarkspotsappearonthescreen? What measurements do you need to make to allow you to compute the actual slit separation? Recordthosemeasurementshere. Computed,theactualslitseparation.Howcloseisittothemanufacturer snumber?(e.g.within 10%?within1%?) Computed,theactualslitseparation,fortwooftheotherdouble\slitsintheplate(pickanytwo). Howclosearetheytothemanufacturer snumbers? Basedonyourmeasurements,wouldyoubuyanymoreplatesfromthismanufacturer?Whyorwhy not? IntheWaveInterferencePhETsimulation,wouldyousaythattheflashlightisdrawntoscale?Ifit wasdrawntoscale,howbigwouldtheflashlightbe?

8 PART5:ResolvingPoweroftheHumanEye(iftimeallows) Let smeasuretheresolvingpowerofyoureyestoseehow close your vision is to perfect, that is, let s examine diffraction\limited performance. Diffraction effects limit the resolution of any optical instrument to an angle λ θ,whereλisthewavelengthofthelightused,and D D is the diameter of the light\gathering optical element (e.g.thepupilofyoureye).thislimitistheangularsizeof the smallest thing you can see. Any details that are smaller than this will blur together, even if you have excellent( perfect )vision. 1. MeasurethediameterDofthepupilofyoureye(innormalroom\light).Withoneeyeopen,look closelyattheimageofyourpupilinamirrorandmeasureyourpupilsdiameterwithaclearplastic rulerplacedonthemirrororoveryoureye. Recordyourpupildiameterhere: 2. To measure the angular resolution of your eye, your partner will first stand on a zero position markonthefloor.beginbystandingsofarthatthechartcannotpossiblyberesolved (Beyonda certaindistance,thehumaneyecannotresolvethebarsduetodiffractioneffects,andthearrays appearasunresolvedgrayblotchesratherthanstripes.youshouldnotknowwhichorientationis used) 3. ComeupwithasimpleprocedurewithyourpartnerstodeterminethemaximumdistanceLaway fromthepaperatwhichyoucanconsistentlydistinguishbetweenhorizontalorverticalbars. DescribeyourprocedureandresultsforL(foreachlabpartner)below. 4. Ifthecenter\to\centerseparationofthelinesiscalled"x",theangleθyoucanresolveisθ=x/L. Measurex,andthencalculateandrecordθinradiansandindegreeshere: Comparethisanglewiththetheoreticaldiffraction\limitedresolutionofθ=λ/D.Useλ=550nm (middleofthevisiblespectrum). Howcloseareyourvisionandyourpartners visionto perfect?

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