1、Lecture 15 Interference Chp.35Opening Demo Topics Interference is due to the wave nature of light Huygens principle,Coherence Change in wavelength and phase change in a medium Interference from thin films Examples Youngs Interference Experiment and demo Intensity in double slit experiment Warm-up pr
2、oblemDemosHuygens Principle,Wavefronts and CoherenceMaci nt osh PI CTi mage f or mati s not suppor t edkMacintosh PICTimage formatis not supportedExamples of coherence are:Laser light Small spot on tungsten filament WavefrontMost light is incoherent:Two separate light bulbs Two headlight beams on a
3、car Sun is basically incoherent Interference is the combination of two or more waves to form a composite wave,based on the principle of superpositionIn order to form an interference pattern,the incident light must satisfy two conditions:(i)The light sources must be coherent.This means that the plane
4、 waves from the sources must maintain a constant phase relation.For example,if two waves are completely out of phase with =,this phase difference must not change with time.(ii)The light must be monochromatic.This means that the light consists of just one wavelength =2/k.Light emitted from an incande
5、scent lightbulb is incoherent because the light consists of waves of different wavelengths and they do not maintain a constant phase relationship.Thus,no interference pattern is observed.Once light is in phase there are three ways to get light out of phase1.Rays go through different material with di
6、fferent index of refraction2.Reflection from a medium with greater index of refraction3.The selected rays travel different distances.Now lets look at examples In Phase Out of Phase by 180 degrees or p radians or l/2In betweenConcept of path length difference,phase and index of refractionPath length
7、difference=Phase difference=c=f lVacuumVacuumvn=f ln=f l/n n=c/vRays are in phase if where m=1,2,3.Rays are out of phase if where m=1,2,31 l is the same as 2p radian(rad),l/2 is the same as p rad,etc.Macintosh PICTimage formatis not supportedMaci nt osh PI CTi mage f or mati s not suppor t edM acint
8、osh P IC Tim age form atis not supportedMa c i n t o s h P I C Ti ma g e f o r ma ti s n o t s u p p o r t e dMaci nt osh PI CTi mage f or mati s not suppor t edWave reflects 180 degrees out of phase when n1 n2M a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dn2n1airwaterEair 1.0air 1.
9、00soap 1.30Leye21Reflection180 deg phase changeThin film Interference Phenomenon:ReflectionMacintosh PICTimage formatis not supportedMaci nt osh PI CTi mage f or mati s not suppor t edMacintosh PICTimage formatis not supportedMaci nt osh PI CTi mage f or mati s not suppor t edM a c in to s h P IC Ti
10、m a g e fo r m a tis n o t s u p p o r te dMacintosh PICTimage formatis not supportedConstructive InterferenceNow consider the path length differencesMacintosh PICTimage formatis not supportedFirst consider phase change upon reflectionShow wave demosoap 1.30Thin film Interference PhenomenonTransmiss
11、ionair 1.0air 1.00LeyeTransmission21Maci ntosh PI CTi mage formati s not supportedm=1,2,3,4.Constructive interferenceNo phase changes upon reflectionn=1.3039.A disabled tanker leaks kerosene(n=1.20)into the Persian Gulf,creating a large slick on top of the water(n=1.30).(a)If you are looking straigh
12、t down from an airplane while the Sun is overhead at a region of the slick where its thickness is L=460 nm,for which wavelength(s)of visible light is the reflection brightest because of constructive interference?Path difference between ray 1and ray 2=2L.Phase changes cancel outFor constructive inter
13、ference path differencemust =integral number of wavelengthsair 1.0Water 1.30Kerosene 1.20L21180 deg phase changeMaci ntosh PI CTi mage formati s not supportedWe note that only the 552 nm wavelength falls within the visible light range.Macintosh PICTimage formatis not supported(b)If you are scuba div
14、ing directly under this same region of the slick,for which wavelength(s)of visible light is the transmitted intensity strongest?(Hint:use figure(a)with appropriate indices of refraction.)Scuba diverFor transmission,ray 2 undergoes 180 deg phase shift upon reflection at theKerosene-water interface.Th
15、erefore,for constructive interference 2L=integral number of wavelengths in n2 plus half a wavelength.air 1.0Water 1.30Kerosene 1.20L21Maci nt osh PI CTi mage f or mati s not suppor t edMa c i nt os h PI CTi ma ge f or ma ti s not s uppor t e d We note that only the 441.6 nm wavelength(blue)is in the
16、 visible range,Ma c i n t o s h P I CTi ma g e f o r ma ti s n o t s u p p o r t e dMacintosh PICTimage formatis not supportedMacintosh PICTimage formatis not supportedMacintosh PICTimage formatis not supportedVisible spectrum is 430 nm-690 nmThe wave from S1 travels a distance x and the wave from S
17、2 travels a distance M a c in t o s h P IC Tim a g e f o r m a tis n o t s u p p o r t e d 27.S1 and S2 in Fig.36-29 are point sources of electromagnetic waves of wavelength 1.00 m.They are in phase and separated by d=4.00 m,and they emit at the same power.(a)If a detector is moved to the right alon
18、g the x-axis from source S1,at what distances from S1 are the first three interference maxima detected?xdetectorM a c in t o s h P IC Tim a g e f o r m a tis n o t s u p p o r t e dThe path difference is Maci nt osh PI CTi mage f ormati s not support edM a c i n t o s h P I C Ti m a g e f o r m a ti
19、 s n o t s u p p o r t e dxMacintosh PICTimage formatis not supportedThe solution for x of this equation isFor constructive interference we haveSolve for xMaci ntosh PI CTi mage formati s not supportedMacintosh PICTimage formatis not supportedMacintosh PICTimage formatis not supportedMacintosh PICTi
20、mage formatis not supportedM a c i n t o s h P I C Ti m a g e f o r m a ti s n o t s u p p o r t e dMacintosh PICTimage formatis not supportedm=3What about m=4?This corresponds to x=0.Path difference=4 meters.M a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dm=2Maci ntosh PI CTi mage f
21、ormati s not supportedm=1Maci nt osh PI CTi mage f ormati s not support edAlthough the amplitudes are the same at the sources,the waves travel different distances to get to the points of minimum intensity and each amplitude decreases in inverse proportion to the square of the distance traveled.The i
22、ntensity is not zero at the minima positions.Macintosh PICTimage formatis not supportedm=3m=2m=1Ma c i nt o s h PI CTi ma ge f or ma ti s not s upp or t e dWhere do the minima occur?Ma c i n t o s h P I C Ti ma g e f o r ma ti s n o t s u p p o r t e dMacintosh PICTimage formatis not supportedm=0 x=
23、15.75 mm=1 x=4.55 mm=2 x=1.95 mm=3 x=0.55 mm=0m=1Demo with speakers using sound wavesSet oscillator frequency to 1372 Hz,Then wavelength of sound is 343/1372=0.25 mSet speakers apart by 1m.Then maxima occur atM a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dMacintosh PICTimage formatis not supportedMacintosh PICTimage formatis not supported
