Chapter 4. The Properties of Light 4.1 Introduction Scattering Transmission, reflection, and refraction

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Chape 4. The Popees of Lgh 4.1 Ioduco Scaeg Tasmsso, efleco, ad efaco (mcoscopc) (macoscopc) Hech by YHLEE;100510; 4-1 4. Raylegh Scaeg Scaeg of sulgh Sulgh he a Goud-sae vbao of Re-emsso of lgh.

1 Chape 4. The Popees of Lgh 4.1 Ioduco Scaeg Tasmsso, efleco, ad efaco (mcoscopc) (macoscopc) Hech by YHLEE;100510; Raylegh Scaeg Scaeg of sulgh Sulgh he a Goud-sae vbao of Re-emsso of lgh. oge, oxyge, ec. Hghe feq. of lgh Lage amplude of goud-sae vbao. Soge scaeg. The esy of he scaeed lgh ~ ν 4 Blue scaes moe sogly ha ed (Blue sky) Raylegh scaeg : Scaeg fom pacles < λ /15 A. Scaeg ad Iefeece Rae medum (sepaao λ). Opcal pah dffeece o P >> λ. Ieses ae added a P The dese medum (sepaao λ). Elecc felds ae added a P. Less laeal scaeg due o efeece.

Hech by Fowad Popagao The same opcal pah legh o P Cosucve efeece

Sumed o zeo Moe dese, ufom ad odeed medum Moe complee laeal desucve

2 Hech by Fowad Popagao The same opcal pah legh o P Cosucve efeece fowa deco. B. The Tasmsso of Lgh Though Dese Meda Lle scaegs he laeal o he backwad decos A fxed phase dffeece amog waveles he laeal deco. Sumed o zeo Moe dese, ufom ad odeed medum Moe complee laeal desucve efeece Fowad popagao whou dmsh Example Glass, plasc : amophous solds Quaz, mca : cysals Laeal scaeg Smalle laeal scaeg YHLEE;100510; 4-

Hech by YHLEE;100510; 4-3 C. Tasmsso ad he Idex of Refaco A pmay wave a delecc. Goud-sae vbaos of aoms Sphecal waveles Iefeece of waveles o fom secoday wave.

3 Hech by YHLEE;100510; 4-3 C. Tasmsso ad he Idex of Refaco A pmay wave a delecc. Goud-sae vbaos of aoms Sphecal waveles Iefeece of waveles o fom secoday wave. The pmay + The secoday wave The asmed wave Same speed of c The phase velocy =c, <c, >c. Refacve dex chage. Pmay wave Eleco oscllao Secoday wave 0 ~ π phase shf 90 o phase lag, aual esul Loez model (3.5) Fo ω Fo ω Fo ω << ω o : The secoday lags he pmay by 90 o ω o, a esoace : 180 o ou of phase. Reduced efaced wave (absopo) >> ω o : 70 o phase lag Dashed : educed dampg Accumulaed phase lag o lead Speed chage of he wave.

Hech by YHLEE;100510; 4-4 4.3 Refleco A beam of lgh a dese medum Scaeg mosly he fowad deco A beam of lgh acoss a eface Some backwad scaeg.

of glass hckess Huyges s Pcple Evey po o a pmay wavefo behaves as a po souce of sphecal secoday wavele. The secoday waveles popagae wh he same speed ad fequecy wh he pmay wave.

4 Hech by YHLEE;100510; Refleco A beam of lgh a dese medum Scaeg mosly he fowad deco A beam of lgh acoss a eface Some backwad scaeg. Refleco The chage of ove a dsace > λ Lle efleco The chage of ove a dsace < λ /4 Abup eface Ieal ad Exeal Refleco Upaed aomc oscllaos Refleco Idep. of glass hckess Huyges s Pcple Evey po o a pmay wavefo behaves as a po souce of sphecal secoday wavele. The secoday waveles popagae wh he same speed ad fequecy wh he pmay wave. The wave a a lae me s he supeposo of hese waveles. Beam I : Exeal efleco ( < ) Beam II : Ieal efleco ( > ), 180 o phase shf Rays A ay s a le daw he deco of lgh popagao. I mos cases, ay s sagh ad pepedcula o he wavefo A plae wave s epeseed by a sgle ay. A. The Law of Refleco A plae wave o a fla medum ( λ >> aomc spacg) Sphecal waveles fom he aoms. Cosucve efeece oly oe deco.

Hech by YHLEE;100510; 4-5 Devao of he law

CD Noe v 1 = BD = AD s θ, v1 = AC = AD s

=Δ he wavefo s ED vδ = BD = ADs θ vδ = AE

= = s θ : Law of efaco, Sell s law A weak

5 Hech by YHLEE;100510; 4-5 Devao of he law A =0, he wavefo s AB A = 1, he wavefo s CD Noe v 1 = BD = AD s θ, v1 = AC = AD s θ s θ s θ = v v Sce v = v θ = θ : Law of efleco (Pa I) 4.4 Refaco The cde ays ae be a a eface Refaco A. The Law of Refaco A =0 he wavefo s AB A =Δ he wavefo s ED vδ = BD = ADs θ vδ = AE = AD s θ s θ s θ = v v Sce v = c, v s θ c = = s θ : Law of efaco, Sell s law A weak elecc feld A lea espose of he aom A smple hamoc vbao of he aom The fequeces of he cde, efleced ad efaced waves ae equal. 4.5 Fema s Pcple Heo poposed he pcple of shoes pah θ = θ S, P ad B ae he plae of cdece Fema poposed he pcple of leas me Lgh akes he pah ha akes he leas me

Hech by YHLEE;100510; 4-6 Refleco by Fema s pcple The me fom S o P

/ dx = 0 Opcal Pah Legh The as me fom S o P m m s 1 = s v c = 1 = 1

Fema s Pcple The opcal pah legh of he acual lgh pah s saoay wh

Rays slghly devae fom he saoay pah The same OPL Cosucve efeece

6 Hech by YHLEE;100510; 4-6 Refleco by Fema s pcple The me fom S o P θ s θ v v ( ) SO OP h + x b + a x = + + v v v v s = : Sell s law d / dx = 0 Opcal Pah Legh The as me fom S o P m m s 1 = s v c = 1 = 1 I a homogeeous medum P OPL = ( s) ds S Opcal pah legh (OPL) Mode Fema s Pcple The opcal pah legh of he acual lgh pah s saoay wh espec o vaaos of he pah df dx = 0 No allowed he pcple of leas me Rays slghly devae fom he saoay pah The same OPL Cosucve efeece Saoay pahs a ellpsodal mo Fema ad Mages [Fg ] Bedg of ays due o Fema s pcple

7 4.6 The Elecomagec Appoach A. Waves a a Ieface A cde plae wave E = Eo cos ( k ω) The efleced ad asmed waves E = Eo cos ( k ω + ε ) E = Eo cos ( k ω + ε) ε, ε, ε ae cosa phases Hech by YHLEE;100510; 4-7 The bouday codos E + E = E ( ) ( ) ( ) ageal ageal ageal u E u E u E Ths elao should be sasfed egadless of ad ω = ω = ω k = k + ε = k + ε (1) Fom he fs wo of (1) ( k k ) = ε : s o he eface plae ( k k) ( o) = 0 : o s a po o he eface plae ( k k )// u : u s he suface omal k, k ad u fom a plae (Plae of cdece) k s θ = k s θ θ = θ k = k Fom he fs ad las of (1) ( k k) = ε ( k k) ( o) = 0 ( k k) The eface plae k, k ad u fom he plae of cdece k s θ = k s θ s θ = s θ k k k k θ θ θ θ k = ω / c

) ( o ) ageal ageal ageal H cos θ x H cos θ x H cos θ x o o o Sce H = E / μ v 1 1 ( ) cos μv E μv E cos o o o () Fom (1) ad

8 Hech by YHLEE;100510; 4-8 B. The Fesel Eqs. Case 1. E The plae of cdece The elao amog E, H, ad k E H // k ˆ k E // H ( ) ˆ, ( ) A he eface Eo + Eo = Eo (1) H + H = H ( o ) ( o ) ( o ) ageal ageal ageal H cos θ x H cos θ x H cos θ x o o o Sce H = E / μ v 1 1 ( ) cos μv E μv E cos o o o () Fom (1) ad () wh μ = μ = μ = μo, v = c / Amplude efleco coeffce Eo cos θ cos θ = Eo cos θ + cos θ Amplude asmsso coeffce Eo cosθ = Eo cos θ + cos θ The physcal meag of π phase shf he efleced wave whe >.

9 Hech by YHLEE;100510; 4-9 Case. E // The plae of cdece E ageal should be couous acoss he eface E + E = E ( o ) ( o ) ( o ) ageal ageal ageal E cos θ x, E cos θ x, E cos θ x, : E s such ha B pos ouwad o o H ageal should be couous acoss he eface H + H = H ( o ) ( o ) ( o ) ageal ageal ageal 1 o μ v E z 1 o μ v E z 1 o μ v E z o (3) (4) Fom (3) ad (4) wh θ = θ, v = v, μ = μ = μ = μ, v = c / o Amplude efleco coeffce Eo cos θ cos θ = E cos θ + cos θ o // Amplude asmsso coeffce Eo cosθ = E cos θ + cos θ o // // // ] Applyg Sell s law assumg θ 0, Fesel Eqs. become s = s s θ = s θ ( θ θ) ( θ + θ ) sθ cosθ = s // a = a ( θ θ) ( θ +θ) // ( θ + θ ) s ( θ +θ) cos ( θ θ) = sθ cosθ

10 Hech by YHLEE;100510; 4-10 C. Iepeao of he Fesel Eqs. Amplude Coeffces A omal cdece, θ = 0 = = + The exeal efleco ( >, θ > θ ) < 0. = whe ( ) 90 o // 0 θ + θ = : Bewse agle, Polazao agle of θ = θ p. The eal efleco ( >, θ > θ ) = 1 whe θ 90 o = : Ccal agle of θ =θ c = whe ( ) 90 o // 0 θ + θ = : Bewse agle of θ =θ p'. ( 90 o p p s θ = >, = 15. >, = 15. Soge efleco a glacg agle Reflecace ad Tasmace The powe pe u aea : S = b e, poyg veco 1 * S = E H I phaso fom : ( ) The esy ( W / m ) : Iadace 1 c I = S = εoε Eo : Aveage eegy pe u me pe u aea

Hech by YHLEE;100510; 4-11 The coss secoal aea of he cde beam = A cos θ efleced beam = A cos θ asmed beam = A cos θ The eflecace I A I R Refleced powe cos θ Eo Icde powe IAcos θ I E The

11 Hech by YHLEE;100510; 4-11 The coss secoal aea of he cde beam = A cos θ efleced beam = A cos θ asmed beam = A cos θ The eflecace I A I R Refleced powe cos θ Eo Icde powe IAcos θ I E The asmace Tasmed powe IA cos θ Eo cos θ cos θ T = Icde powe IA cos θ Eo cos θ cos θ Eegy cosevao IAcos θ = IAcos θ + IAcos θ o cos θ = o cos θ + o cos θ Eo cos θ Eo = + Eo cos θ Eo E E E 1 R T o

4.7 Toal Ieal efleco The Sell s law fo > s θ =

ccal agle, θ = 90 o s θ c = Fo θ > θ c All he

Ieal Refleco Ieal efleco ad TIR: Taso fom (a)

(Refleco ceases whle asmsso deceases) TIR psms

12 4.7 Toal Ieal efleco The Sell s law fo > s θ = s θ : θ < θ Hech by YHLEE;100510; 4-1 A he ccal agle, θ = 90 o s θ c = Fo θ > θ c All he comg eegy s efleced back o he cde medum Toal Ieal Refleco Ieal efleco ad TIR: Taso fom (a) o (e) whou dscouy. (Refleco ceases whle asmsso deceases) TIR psms The ccal agle a a-glass eface : 4 o TIR ems of scaeg A suface wave whe θ o = 90

13 Hech by YHLEE;100510; 4-13

14 Hech by YHLEE;100510; 4-14 A. The Evaesce Wave Usg Sell s law we ewe Fesel Eq. as //, // cos θ cos θ = cos θ + cos θ cos θ cos θ = cos θ + cos θ become complex whe θ > θ * = // // = R = 1 * ( ) ( ) / s θ cosθ / s θ + cosθ ( ) ( ) ( ) ( ) / s θ / cosθ / s θ + / cosθ c The asmed wave: E k o = E e ( ω ) k k x k y whee = x + y k k k x = s θ s θ ky = k cos θ ± k 1 s θ ± k s θ 1 = β Sell s law θ > θ k sθx βy ω The asmed wave : E = Eoe, Evaesce wave I advaces x-deco bu expoeal decay alog y-axs Cosa phase (yz-plae) Cosa amplude (xz-plae), Ihomogeeous wave No e eegy flow acoss he eface. Fusaed Toal Ieal Refleco (FTIR) Dese medum Rae medum Dese medum (Eegy asfe) TIR Evaesce wave c [Fg. 4.55] FTIR [Fg. 4.56] Beamsple usg FTIR Low-dex space cools he asmace

15 Hech by YHLEE;100510; Opcal Popees of Meals Fee elecos meals J =σ E Coducvy Uboud Cue desy A pefec coduco : σ= Elecos follow he elecc feld exacly (No esog foce, o aual feq., o absopo, oly eemsso) I eal meals : σ Collso of elecos wh lace o mpefecos Eegy loss by hea Waves a meal The Maxwell s eqs. meals B E =, = E + H ε σ E με μσ E E E E E + + = + ( ω μoεo ωμoσ) E σ ω μoε o + E x y z ωεo The plae wave soluo ω ω y I k ω c c E = Eoe Eoe k =ω μ ε yˆ Dampg = ( + ) + Ry ω o o c The adace I ( y) = I ( 0) e αy ω, α = I c = π f μσ : aeuao coeffce Fo y = 1 1 he adace dops by a faco of e α : sk deph, δ c R I Example Sk deph of Coppe Fo UV ( λo 100m ) δ=06. m λ 10,000m δ=6m Fo IR ( ) o Lle peeao Hgh efleco of lgh Meals eflec almos all he cde lgh (85%~95%) egadless of waveleghs Cololess (Slvey gay)

The Dspeso Equao Vbao of a boud eleco due o he elecc feld q/ m x( ) = E( ) : q > 0, x measues fom - o + ω ω γω o No esog foce meals : ω o = 0 x ( ) s always 180 o ou of phase wh E( ) The eadaed wave

16 The Dspeso Equao Vbao of a boud eleco due o he elecc feld q/ m x( ) = E( ) : q > 0, x measues fom - o + ω ω γω o No esog foce meals : ω o = 0 x ( ) s always 180 o ou of phase wh E( ) The eadaed wave cacels he comg wave The Dspeso Relao Neglec boud chages ad eglec γ assumg hgh fequecy Fo ω fo ω Nq ωp ω 1 = 1 ε mω ω ( ) o : ω p = plasma fequecy < ωp, becomes complex. Expoeal decay of he wave Hech by YHLEE;100510; 4-16 > ωp, becomes eal. Small absopo. The coduco becomes aspae Ioosphee : Dsbuo of fee elecos < 1 ad eal fo ω ω > p Refleco fom a meal A omal cdece o a meal ( R 1) ( ) * c 1 c 1 + I 1 1 c + c + R I R = : c = R + I If I = 0 Delecc maeal If I > 0 R becomes lage If I >> c puely magay, R=1 R Reflecace fom a absobg medum I ad R deped o ω [p130] Vso of space su Th gold coag 70% efleco (Reduco of IR asmsso sll asmg VIS)

4.9 The Ieaco of Lgh ad Mae Refleco of all vsble fequecy Whe colo 70%~80% efleco Shy gay of meal Hech by YHLEE;100510; 4-17 Thomas Youg : Colos ca be geeaed by mxg hee beams of lgh well sepaaed

17 4.9 The Ieaco of Lgh ad Mae Refleco of all vsble fequecy Whe colo 70%~80% efleco Shy gay of meal Hech by YHLEE;100510; 4-17 Thomas Youg : Colos ca be geeaed by mxg hee beams of lgh well sepaaed fequecy Thee pmay colos combe o poduce whe lgh : No uque se The commo pmay colos : R, G, B Two complemeay colos combe o poduce whe colo M + G = W, C + R = W, Y + B = W A sauaed colo coas o whe lgh (deep ad ese) A example of a usauaed colo M + Y = R + B + R + G = W + R : Pk ( ) ( ) The chaacesc colo comes fom selecve absopo Example: (1) Yellow saed glass Whe lgh Resoace blue Yellow s see a he oppose sde Red + Gee Sog absopo blue () H O has esoace IR ad ed No ed a ~30m udewae (3) Blue k looks blue ehe efleco o asmsso Ded blue k o a glass slde looks ed. Vey sog absopo of ed. Sog absobe s a sog efleco due o lage I. Resoace of maeals Mos aoms ad molecules Resoaces UV ad IR Pgme molecules. Resoaces VIS Ogac dye molecules Resoace VIS Subacve coloao Blue lgh Yellow fle Black a he ohe sde I emoves blue

18 Hech by YHLEE;100510; 4-18

Fresnel Equations cont.

Fresnel Equations cont. Lecure 12 Chaper 4 Fresel quaos co. Toal eral refleco ad evaesce waves Opcal properes of meals Laer: Famlar aspecs of he eraco of lgh ad maer Fresel quaos r 2 Usg Sell s law, we ca re-wre: r s s r a a