Phys Nov. 3, 2017 Today s Topics. Continue Chapter 2: Electromagnetic Theory, Photons, and Light Reading for Next Time

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1 Phys 31. No. 3, 17 Today s Topcs Cou Chap : lcomagc Thoy, Phoos, ad Lgh Radg fo Nx Tm 1

2 By Wdsday: Radg hs Wk Fsh Fowls Ch. (.3.11 Polazao Thoy, Jos Macs, Fsl uaos ad Bws s Agl

3 Homwok hs Wk Chap Homwok (du Moday No. 6 #6, 7, 8, 15, 17 3

4 Supplmal: Loz Modl fo Ma How Dos Lgh acs wh Maals? Maxwll s uaos Do Hlp Us Cosd a Loz Modl lcos ( aoms Osclla wh a Rsog Foc d x d ( x κ x γ dx m m d (d hamoc oscllao Whch ca b sold fo x f w guss a hamoc soluo: x( x ω ad l ω κ x m ad γ, w ca s ad sol fo x : x( / m ω ω ( ω / m ω ( ω ( A ala appoach s o ak h Fou asfom of h dff. uao o ca a algbac uao, sol, h asfom back (cool!: ω x(ω+ γωx(ω+ω x(ω m (ω ad sol fo x(ω. Th mog lcos poduc a polazao P ( N ν x( wh N ν s h umb dsy of lcos. So: P ε χ x Whch lads o a dsplacm: D ε + P ε ε (1+ χ (f + boud lcos Th polazao P ε χ dpds o h "spg cosas." Upo subsuo fo x o h dff. uao h soluo s: ω p P x ( ω ω + γω ε wh ω x p N ε m No ha h amplud g y lag f dg fucy s soac wh h "oscllaos" (ω ω. Ths mas ha: ( ( +γω ω p ε ( ω ω + γω ω p ω ω ω pωγ o: ω ω ( ω ω +γ ω ε ε ε (al ad magay pas ad f w oduc complx fac dx: κ whch cas ε ad so a maal wll ha a fucy-dpd. 4

5 Chap : aco of Lgh & Ma Th lcomagc Appoach o Rfaco ad Rflco &M am s mo compl ad uaa ha Sll s laws. Cosd M was a a fac f w mag h fld a fsmal dsac o h sd of h fac h compos ag o h sufac should b ual. Cosd a wa cd o a fac bw wo mda ( ad : o ( k ω Th flcd ad asmd was a smlaly: o ( k ω +ε ad o ( k ω +ε Sc h agal compos mus b ual h coss poduc s ag: û + û û o: û o ( k ω + û o ( k ω +ε û o ( k ω +ε Sc hs codo mus b u of ay m ad a ay po w h og: ( k yb ( k +ε yb ( k +ε yb (a yb Fom h fs wo ms: $ ( k k % & ' ε whch says ha ( k k s paalll o û yb o û ( k k ad k s k s. Thus: (law of flco Bu f k ad k ad û a h sam pla h: $ ( k k % & ' ε ad sc h agal compos a ual: yb k s k s bu mulplyg boh sds by c / ω gs: s s sc /c (Sll's law of faco 5

6 Chap : aco of Lgh & Ma Th Fsl uaos Cosd a pla wa cd o a fac bw wo mda (wha h polazao. W ha s ha h cd, flcd ad asmd was df a pla-of-cdc. Nx cosd wo cass: Cas 1: fld s ppdcula o pla of cdc Sc h cos a ppdcula o h cd pla: + Th agal compo of h B fld mus also b couous: B + B B ad sc B /, B /, B /, ad : 1 ( 1 (usg allows us o oduc Now ms of h dx of faco: ( Solg fo ampluds gs: # & % ( $ ' # + ad % $ f h maal s o magc: # & % ( $ ' + # ad & % ( $ ' & ( ' + + 6

7 7 Chap : aco of Lgh & Ma Th Fsl uaos Cas : fld s paalll o pla of cdc B ad : Wh boh maals a o - magc: ad : Combg ylds : fld mus also b couous : h compo of ad sc h agal fld mus also b couous : h compo of Th agal !!

8 Chap : aco of Lgh & Ma Amplud Coffcs of h Fsl uaos Wh combd wh Sll's Law w ca smplfy fuh: s( s( + + s s( + ad + a( a( + s ad s( + ( Wha dos hs ma (s sc x? Rug h ad B fld o b couous a h fac cosas h ampluds of h facd ad asmd was. Th sul dpds o whh h fld s oscllag ppdcula o paalll o h sufac ad also dpds o h dcs of faco. Fo abaly od was o ca cosd h compos. *No ha wh + 9 h alu of bcoms ad h flcd wa s fully polazd. Ths s h polazao agl p. 8

9 Chap : aco of Lgh & Ma Mag of h Fsl uaos Ampluds of h flcd ad asmd was ca b calculad. Nomal compo of udgos phas shf of p upo flco f < (ga sg dcas phas chag: lk a sadg wa p Bws s Agl > (xampl fo 1.5 < (xampl fo 1.5 9

10 Chap : aco of Lgh & Ma Fsal uaos ad phas shfs Nomal compo of udgos phas shf of p upo flco f < (gh Tagal compo s mo complcad (fgus blow show phas chag wh 1 <. 1

11 11 Chap : aco of Lgh & Ma Fsl uaos ad h Rflcd ad Tasmd sy Dpds o boh h sua of h amplud ad h coss-scoal aa of h bam. Lf fgu shows flco sy fo wo wa oaos. No ha sy gos o 1% a hgh cdc ad o zo fo was ppdcula o h sufac. Rgh fgu shows smla ffc fo al flco. as. compos bu ad ppdcula s ald fo h paalll Ths / ad 1 sc : as ad h asmac (T ad f : W df h flcac (R as T c / T R A A R º º

12 Chap : aco of Lgh & Ma Toal al Rflco ad h asc Wa Fusad oal al flco occus wh wo sufacs of a aspa subsac a bough o coac o dsoy (fusa h oal al flco ha would ohws occu a h fac. Ths occus gadually as h wo mda a bough o coac as phoos ul hough h ba bw h wo mda! Phoos a o pfcly localzd spac (uaum mchacs so hy ca lak hough a gap. O applcao s h cosuco of bamspls. 1

13 Homwok hs Wk Chap Homwok (du Moday No. 6 #6, 7, 8, 15, 17 13

k of the incident wave) will be greater t is too small to satisfy the required kinematics boundary condition, (19)

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