Electromagnetic WavesSlide 2Maxwell’s RainbowSlide 4Slide 5Slide 6A Most Curious WaveSlide 8Slide 9Energy Transport and the Poynting VectorSlide 11Variation of Intensity with DistanceRadiation PressurePolarizationPolarized LightPolarizing SheetIntensity of Transmitted Polarized LightReflection and RefractionSound WavesChromatic DispersionSlide 21RainbowsTotal Internal ReflectionPolarization by ReflectionSlide 251 Chapter 33 Today’s information age is based almost entirely on the physics of electromagnetic waves. The connection between electric and magnetic fields to produce light is one of the greatest achievements produced by physics, and electromagnetic waves are at the core of many fields in science and engineering. In this chapter we introduce fundamental concepts and explore the properties of electromagnetic waves. Electromagnetic Waves33-2When the amplitude of the oscillator in a series RLC circuit is doubled:A.the impedance is doubled.B. the voltage across the capacitor is halvedC. the capacitive reactance is halvedD. the power factor is doubledE. the current amplitude is doubled3Fig. 33-1The wavelength/frequency range in which electromagnetic (EM) waves (light) are visible is only a tiny fraction of the entire electromagnetic spectrumMaxwell’s Rainbow33-Fig. 33-24An LC oscillator causes currents to flow sinusoidally, which in turn produces oscillating electric and magnetic fields, which then propagate through space as EM waves 33-Fig. 33-3Oscillation Frequency:1LCw =Next slideThe Travelling Electromagnetic (EM) Wave, Qualitatively5EM fields at P looking back toward LC oscillator33-Fig. 33-4The Travelling Electromagnetic (EM) Wave, Qualitatively1. Electric and magnetic fields always perpendicular to direction in which wave is travelling transverse wave (Ch. 16)2. always perpendicular to 3. always gives direction of E BE BE B��r rr rr rwave travel4. and vary sinusoidally (in time and space) and are (in step) with each otherE Bin phaser r633-Fig. 33-5Mathematical Description of Travelling EM WavesElectric Field:( )sinmE E kx tw= -Magnetic Field:( )sinmB B kx tw= -Wave Speed:0 01cme=Wavenumber:2kpl=Angular frequency:2pwt=Vacuum Permittivity:0eVacuum Permeability:0mAll EM waves travel a c in vacuumAmplitude Ratio:mmEcB=Magnitude Ratio:( )( )E tcB t=EM Wave Simulation7•Unlike all the waves discussed in Chs. 16 and 17, EM waves require no medium through/along which to travel. EM waves can travel through empty space (vacuum)!•Speed of light is independent of speed of observer! You could be heading toward a light beam at the speed of light, but you would still measure c as the speed of the beam!A Most Curious Wave33-299 792 458 m/sc ==0.9833192622 ft/ns8Changing magnetic fields produce electric fields, Faraday’s law of induction33-Fig. 33-6The Travelling EM Wave, QuantitativelyInduced Electric Field( ) ( )cos and cosm mE BkE kx t B kx tx tw w w� �= - =- -� �BdE d sdtF=-�rrg�( ) E d s E dE Eh h dE= + - =�rrg�( ) ( ) BB h dxF = dB dE dBh dE h dxdt dx dt� = � =-E Bx t� �=-� �( ) ( )cos cosmm mmEkE kx t B kx t cBw w w- =- - � =9Changing electric fields produce magnetic fields, Maxwell’s law of induction33-The Travelling EM Wave, QuantitativelyInduced Magnetic Field0 0EdB d sdtmeF=�rrg�( ) B d s B dB Bh h dB=- + - =�ur rg�( ) ( ) EEd dEE h dx h dxdt dtFF = � =0 0 dBh dB h dxdtme� �� - =� �� �0 0B Ex tme� �- =� �( ) ( )0 0cos cosm mkB kx t E kx tw me w w- - =- -Fig. 33-7( )0 0 0 00 01 1 1mmEc cB k cme w meme= = = � =10Energy Transport and the Poynting Vector33-EM waves carry energy. The rate of energy transport in an EM wave is characterized by the Poynting vector SrPoynting Vector:01S E Bm= �rr rinst instenergy/time powerarea areaS� � � �= =� � � �� � � �The magnitude of S is related to the rate at which energy is transported by a wave across a unit area at any instant (inst). The unit for S is (W/m2)The direction of at any point gives the wave's travel directionand the direction of energy transport at that pointSr11Energy Transport and the Poynting Vector33-Instantaneous energy flow rate:01S EBcm=Note that S is a function of time. The time-averaged value for S, Savg is also called the intensity I of the wave. 0Since 1 and since E B E B EBES EB Bcm^ � � == =r r r ravgavg avgenergy/time powerarea areaI S� � � �= = =� � � �� � � �( )2 2 2avgavg avg0 01 1sinmI S E E kx tc cwm m� � � �= = = -� � � �2mrmsEE =( )22220 0 000 01 1 1 12 2 2 2E BBu E cB B ue e emme� �� �= = = = =� �� �� �� �� �� �201rmsI Ecm=12Variation of Intensity with Distance33-Fig. 33-82powerarea 4SPIrp= =Consider a point source S that is emitting EM waves isotropically (equally in all directions) at a rate PS. Assume energy of waves is conserved as they spread from source.How does the intesnity (power/area) change with distance r?13EM waves have linear momentum as well as energylight can exert pressureRadiation Pressure33-incidentSrpDincidentSrreflectedSrpDTotal absorption:UpcDD =Total reflectionBack along path:2 UpcDD =pFtD=Dpower energy/timearea area IU tA= =D D= (total absorption)2 (total reflection back along path) Radiation PressurerU IA tIAFcIAFcFpAD = D===2 rIpc=rIpc=14The polarization of light is describes how the electric field in the EM wave oscillates.Vertically plane-polarized (or linearly polarized)Polarization33-Fig. 33-1015Unpolarized or randomly polarized light has its instantaneous polarization direction vary randomly with timePolarized Light33-Fig. 33-11One can produce unpolarized light by the addition (superposition) of two perpendicularly polarized waves with randomly varying amplitudes. If the two perpendicularly polarized waves have fixed amplitudes and phases, one can produce different polarizations such as circularly or elliptically polarized light.Polarized Light Simulation16Polarizing Sheet33-Fig. 33-12Only electric field component along polarizing direction of polarizing sheet is passed (transmitted), the perpendicular component is blocked (absorbed)I0I17Intensity of Transmitted Polarized Light33-Fig. 33-13Intensity of transmitted light,unpolarized incident light:012I I=Since only the component of the incident electric field E parallel to the polarizing axis is transmittedtransmittedcosyE E E q= =Intensity of transmitted light,polarized incident
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