Reflection & Transmission Of EM Waves

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Reflection & Transmission of EM WavesReading – Shen and Kong – Ch. 4Outline Everyday Reflection Reflection & Transmission (Normal Incidence) Reflected & Transmitted Power Optical Materials, Perfect Conductors, Metals1

TRUE or FALSE1. Destructive interference occurs when two waves areoffset by a phase of ½πm, or half a wavelength.2. The intensity of a plane wave oscillates in time. Thismeans it is always constructively and destructivelyinterfering with itself.3. In a double-slitexperiment, asyou decrease thespace betweenthe slits, theinterferencepeaks ectionBarrier withdouble cedetectorscreen2

Waves in Materialsk (n jκ )Index of refractionAbsorption coefficient2κω 4πκ α cλ3ωc

Incident and Transmitted Waves Esame amplitudes HNormal Incidenceincident wavetransmitted wavereflected waveMedium 1Medium 2Incident WaveTransmitted Wave4

EM Wave ReflectionMetal ReflectionDielectric ReflectionImage in the Public DomainThin Film InterferenceMetal Reflection Kyle Hounsell. All rights reserved. This contentis excluded from our Creative Commons license.For more information, seeImage by Ali Smiles photos/77682540@N00/2789338547/ on flickrCell Phone ReflectionAM Radio Reflection5

Incident and Transmitted WavesEincident wave HNormal Incidencetransmitted wavereflected waveMedium 1 Medium 2Incident WaveKnownTransmitted WaveDefine reflectioncoefficient asReflected WaveDefine transmissioncoefficient as6

Key Takeaways Define the reflection coefficient as Define the transmission coefficient as27

E-Field Boundary ConditionsEA area A EB δ n̂ρssurfaceNormalEA Cn̂δEB is discontinuous at a surface charge.surfaceTangentialLKnown8is continuous at a surface.

H-Field Boundary Conditionsμo HA areaAδμo HB HA HB n̂surfaceNormalC Kδis continuous at a surface.n̂Tangentialis discontinuous ata surface current.L9

Incident EM Waves at Boundaries E HMedium 1Incident Waveincident waveMedium 2Known i x̂E i e jk1 zEo11 i jk1 z Hi ẑ Ei yˆ Eo eη1η110Normal Incidence

Reflected EM Waves at Boundaries E HNormal Incidencereflected waveMedium 1Reflected WaveMedium 2UnknownDEFINE REFLECTIONCOEFFICIENT AS r x̂E r e jk1 zEor1E r ( z) r yˆ o e jk1 zˆ EHη1η111

Transmitted EM Waves at Boundaries E HNormal Incidencetransmitted waveMedium 1Transmitted WaveMedium 2UnknownDEFINE TRANSMISSIONCOEFFICIENT AS r x̂E t e jk2 zEot1E t ẑ E t yˆ o e jk2 zHη2η212

Reflection & Transmission of EM Waves at Boundaries 2 E tE 1 E i E rEMedium 11 1 H i H rHMediumMedium22 2 H rH13

Reflection of EM Waves at Boundaries 1(z 0) E 2(z 0)E 1(z 0) H 2(z 0)H η 14μ

Reflectivity & Transmissivity of Waves Define the reflection coefficient as Define the transmission coefficient asWhat are the ranges for r and t? Is energy conserved?15

Reflection & Transmission of EM Waves at Boundaries E Hincident waveNormal Incidencetransmitted waveMedium 1Medium 2Additional Java simulation athttp://phet.colorado.edu/new/simulations/16

Reflectivity & Transmissivity of EM Waves Note that The definitions of the reflection and transmission coefficientsdo generalize to the case of lossy media. For loss-less media, r and t are real: For lossy media, r and t are complex: Incident Energy Reflected Energy Transmitted EnergyR r 2 fraction of incident power that is reflectedT 1 – R fraction of incident power that is transmitted17

Reflectivity of DielectricsConsider nearly-lossless optical materials. For typical dielectrics,μ1 μ2 μ0.r μ2μ1 ε2ε1μ2μ1 ε2ε1Result ε1 ε 2n1 n2 n1 n2ε1 ε 2μ1 μ2μ1 μ2Image by Will Montague 10/ on flickr18

Reflection of EM Waves at BoundariesREMEMBER:In terms ofthe index ofrefraction,assumingμ1 μ2 μ0In terms of thecharacteristicimpedancesAnimations Dr. Dan Russell, Kettering University. All rights reserved. Thiscontent is excluded from our Creative Commons license. For more information,see http://ocw.mit.edu/fairuse.What is different in the two reflected waves ?Which side is air and which side is glass ?19

Why does metal reflect light? Kyle Hounsell. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/fairuse.20

Microscopic Lorentz Oscillator Model21

T-A-R-TTAR70T60Reflection %50403020TART100T-A-R-T - the material has four distinct regions of optical properties:Transmissive,ω ω0 - γ/2,Absorptive,ω0 - γ/2 ω ω0 γ/2Reflective,ω0 γ/2 ω ωpTransmissive,ω ωp22

Reflection of aNormally IncidentEM Wave from aPerfect Conductor i x̂Eo e jkzE i ŷ Eo e jkzHηoreflected waveIncident waveStanding wave patternof the E-fieldkz 2πkz πStanding wave patternof the H-fieldkz 3π/2 kz π/223

Microscopic Lorentz Oscillator Model for FREE ELECTRONS IN METALS0.50.40.3γ/2Drude Model for metals r i60.2ωp-5ωn, κ r , i0.1-10κ5 rR432Tnn1-20-25ωp-3024ω

Reflectivity of Silverγ/21006κR43280TnReflection(%)n, κ5n1ωp6040TR20ωωp25ω

Ice is more reflective than water10% reflectedby ocean water70-80% of sunlightreflected by snow2620% reflectedby vegetationand dark soil

Thin Film iroilwaterImage by Yoko Nekonomania 7/ on flickr27

MIT OpenCourseWarehttp://ocw.mit.edu6.007 Electromagnetic Energy: From Motors to LasersSpring 2011For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

Reflection & Transmission of EM Waves Outline Reading – Shen and Kong – Ch. 4 Everyday Reflection Reflection & Transmission (Normal Incidence) Reflected & Transmitted Power Optical Materials, Perfect Conductors, Metals TRUE or FALSE . 1. Destructive interference occurs when two waves are

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