Class 33: OutlineLast time: Microwaves (mw)We Use InterferenceThis is also how we know that light is a wave phenomenaInterference: The difference between waves and bulletsInterference: The difference between waves and bulletsInterferenceDemonstration:Microwave InterferenceInterference – Phase ShiftMicrowave InterferenceInterference – Phase ShiftPRS Question:InterferenceExtra Path LengthExtra Path LengthThin Film Interference - IridescenceThin Film Interference - IridescenceThin Film: Extra PathPhase Shift = Extra Path?Two TransmittersMicrowave InterferenceTwo In-Phase Sources: GeometryInterference for Two Sources in PhaseIn-Class: Lecture DemoHow we measure 1/10,000 of a cmThe Light Equivalent:Two SlitsYoung’s Double-Slit ExperimentPRS QuestionDouble Slit Path DifferenceLecture Demonstration:Double SlitDiffractionDiffractionSingle-Slit DiffractionIntensity DistributionPutting it TogetherPRS Question:Two Slits with WidthTwo Slits With Finite Width aTwo Slits With Finite width aLecture Demonstration:Double Slits with WidthBabinet’s PrincipleExperiment 13: To Do1P33-Class 33: OutlineHour 1:InterferenceHour 2:Experiment 13: Interference2P33-Last time: Microwaves (mw)9210 15mw mwcfHz cmfλ=× = =This time: Visible (red) light:14 54.610 6.5410red redcfHz cmfλ−=× == ×How in the world do we measure 1/10,000 of a cm?3P33-We Use InterferenceThis is also how we know that light is a wave phenomena4P33-Interference: The difference between waves and bullets Interference: If light is a wave we see spreading and addition and subtractionNo Interference:if light were madeup of bullets5P33-Interference: The difference between waves and bullets http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/08-waves2d/08-waves320.html6P33-InterferenceInterference: Combination of two or more waves to form composite wave – use superposition principle.Waves can add constructively or destructivelyConditions for interference:1. Coherence: the sources must maintain a constant phase with respect to each other2. Monochromaticity: the sources consist of waves of a single wavelength7P33-Demonstration:Microwave Interference8P33-Interference – Phase ShiftConsider two traveling waves, moving through space: Look here as function of time Look here as function of timeConstructive InterferenceDestructive Interference9P33-Microwave Interference10P33-Interference – Phase ShiftWhat can introduce a phase shift?1. From different, out of phase sources2. Sources in phase, but travel different distances1. Thin films2. Microwave Demonstration3. Double-slit or Diffraction grating11P33-PRS Question:Interference12P33-Extra Path LengthIn Phase Here L∆Constructive InterferenceLmλ∆=⇓Still in Phase Here(m=0, ±1, ±2…)13P33-Extra Path LengthIn Phase Here L∆()12Destructive InterferenceLmλ∆= +⇓Not in Phase Here(m=0, ±1, ±2…)14P33-Thin Film Interference -Iridescence Image courtesy of John M. Sullivan, University of Illinois and Technical University of Berlin.15P33-Thin Film Interference -Iridescence •Bubbles•Butterfly Wings•Oil on Puddles16P33-Thin Film: Extra PathdExtra path length ~ 2d()122Constructive2 Destructivedmdmλλ=⇒=+ ⇒Oil on concrete, non-reflective coating on glass, etc.17P33-Phase Shift = Extra Path?What is exact relationship between ∆L & φ?()sin( ) sin( )2sin( ) sin( )kx L kx kLkx L kxπϕλ+∆ = + ∆=+∆≡+2Lφλπ∆=12mm⎧=⎨+⎩constructivedestructive18P33-Two Transmitters19P33-Microwave Interference20P33-Two In-Phase Sources: Geometry():sinLddδθ=Assuming Extra path length LdλAssume tan sinyL Lθθ=≈()()()12sin Constructivesin Destructivedmdmδθλδθ λ== ⇒==+ ⇒21P33-Interference for Two Sources in Phasemδλ=(1) Constructive:sinconstructiveymdd Lδλθ== =0,1...constructiveLymmdλ==(2) Destructive:(1/2)mδλ=+10,1,...2destructiv eLymmdλ⎛⎞=+ =⎜⎟⎝⎠22P33-In-Class: Lecture Demo10,1,...2destructiveLymmdλ⎛⎞=+ =⎜⎟⎝⎠2destructiveLydλ=For m = 0 (the first minimum):Just Found:From our lecture demo, we measure:L ~ 1.16 m; d ~ 0.24 m; ydestructive~ ? mEstimate the wavelength & frequency of our microwaves23P33-How we measure 1/10,000 of a cmQuestion: How do you measure the wavelength of light?Answer: Do the same experiment we just did (with light)2destructiveLydλ=First λ is smaller by 10,000 times.But d can be smaller (0.1 mm instead of 0.24 m)So y will only be 10 times smaller – still measurable24P33-The Light Equivalent:Two Slits25P33-Young’s Double-Slit ExperimentBright Fringes: Constructive interferenceDark Fringes: Destructive interference26P33-PRS QuestionDouble Slit Path Difference27P33-Lecture Demonstration:Double Slit28P33-Diffraction29P33-Diffraction Diffraction: The bending of waves as they pass by certain obstaclesNo DiffractionDiffractionSpreading after passing though slitsNo spreading after passing though slits30P33-Single-Slit Diffraction“Derivation” (Motivation) by Division:Divide slit into two portions:13 24sin2arr rrδθ=−=−=Destructive interference:()12sin2amδθλ==+sin 1, 2,...ammθλ==± ±Don’t get confused – this is DESTRUCTIVE!31P33-Intensity Distributionsin 1, 2,...ammθλ==±±Destructive Interference:32P33-Putting it Together33P33-PRS Question:Two Slits with Width34P33-Two Slits With Finite Width aWith more than one slit having finite width a, we must consider1. Diffraction due to the individual slit2. Interference of waves from different slits35P33-Two Slits With Finite width aZero Order MaximumFirst Order Maximumsindθλ=sinaθλ=First Diff. Minimum36P33-Lecture Demonstration:Double Slits with Width37P33-Babinet’s PrincipleCase I: Put in a slit, get diffractionCase II: Fill up slit, get nothingCase III: Remove slit, get diffractionBy superposition, the E field with the slit and the E field with just the filling must be exact opposites in order to cancel:EE=−filling slitII=filling slitSo the intensities are identical:38P33-Experiment 13: To DoDownload Excel File!1. Single Slit – 4 different slits. Use known width a and zeroes ydestructiveto Estimate wavelength of red light2. Human Hair (Babinet says just single slit). Use λred(from 1) and zeroes ydestructiveto Estimate thickness of hair3. Double Slit – 4 different slits. Use known spacing d and zeroes to Estimate wavelength of red light4. CD Track Spacing (Diffraction Grating) Estimate track
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