b g b g b g Chapter 2 Wave Motion 2.1 One Dimensional Waves A wave : A self-sustaining disturbance of the medium Hecht;8/30/2010; 2-1

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1 Chape Wave Moon Hech;8/30/010; -1.1 One Dmensonal Waves A wave : A self-susanng dsubance of he medum Waves n a spng A longudnal wave A ansvese wave : Medum dsplacemen // Decon of he wave : Medum dsplacemen Decon of he wave The dsubance advances, bu no he medum (Ths s why waves can popagae a gea speeds) b g A wave s gven by a funcon of poson and me: ψ=f x, The shape of he dsubance a a cean me The pofle of he wave ψ x, 0 = f x, 0 f x : Takng a phoogaph a = 0 b g b g b g A wave on a sng

2 Hech;8/30/010; - Popagaon of a pulse Movng efeence fame A new coodnae sysem, S, movng wh he wave ψ= fbx g : Indep. of me. The pofle s measued along x' In hs case x' = x v ψ x, = f x v : 1-D wavefuncon b g b g A a lae me + Δ f x v + Δ f x v change poson x x + vδ b g b g : Same pofle A wave n -x decon ψ= fbx + vg F + F x v v I HG K J b + Ohe expessons F x/ v g The Dffeenal Wave q. Sa wh ψ=f x v ψ x b g and x' = x v f x' f = = x' x x', ψ x = f x' Smlaly ψ f x' = = v f, x' x' ψ = v f x

3 Combnng he eqs. ψ 1 ψ = : 1-D dffeenal wave eq. x v Is soluon ψ= C f x v + C g x + v b g b g 1 Thee ae wo knds of 1-D wave(+ and waves) 1-D dffeenal wave eq. should be of second-ode. Hech;8/30/010; -3. Hamonc waves A wave wh sne o cosne pofle ψ ( x,0) = Acoskx = f ( x) k : popagaon numbe A : amplude A avelng wave by eplacng x by ( x v) ψ ( x, ) = Acos [ kx ( v) ] = f( x v) : Peodc n boh space and me The spaal peod : Wavelengh, λ [m] ψbx ± λ, g = ψbx, g cos[ k( x v)] cos k ( x ± λ) v cos[ k( x v) ± λk] [ ] poson change by ±λ phase, ϕ = π k = π / λ The elaon beween ϕ and x ψ = A cosϕ ϕ = π 0 π π π π π 3 π π π ψ = Acos x λ x λ λ λ 3λ 5λ 3π 7π x = 0 λ The empoal peod : Fequency, ν = 1/ τ [Hez] ψbx, ± τg = ψbx, g cos[ k( x v)] cos k [ x v( ± τ )] cos k {( x v ) vτ } me change by ±τ, = π /k τ = λ/v The empoal fequency : ν = 1/ τ Theefoe v =νλ Angula fequency : ω = πν

4 .3 Phase and Phase Velocy A hamonc wave ψ ( x, ) = Acos( kx ω+ ε) nal phase ϕ, phase The physcal meanng of ε Inal conbuon a he geneao Hech;8/30/010; -4 = ( ) ψ( x, ) = Acos ( kx ω+ π/) ψ( x, ) Acos kx ω π/ The ae of change of he phase wh me. Angula fequency ϕ = ω x Velocy of consan phase kx ω + ε = C kδx ωδ = 0 The ae of change of he phase wh dsance Popagaon numbe ϕ = k x x ω =± =± v : Phase velocy k ϕ.4 The Supeposon Pncple Two waves ψ1 and ψ boh sasfy he dffeenal wave eq. ψ1 1 ψ1 ψ 1 ψ =, = x v x v Add wo eqs. 1 ( ψ1 + ψ ) = ( ψ1 + ψ) x v ψ + ψ s also a soluon of he dff. wave eq. ( ) 1 Two waves can add algebacally n he ovelap egon. Ousde he ovelap egon, each popagaes unaffeced. Supeposon of wo waves, Fg..14 Waves, whch ae ou-of-phase, dmnsh each ohe Inefeence

5 .5 The Complex Repesenaon The complex numbe ~z = x + y : = 1 eal, magnay pas Hech;8/30/010; -5 In pola coods. x = cos θ, y = sn θ z~ = cos θ+ sn θ e θ ule fomula e θ = cos θ+ sn θ : magnude, modulus, absolue value θ : phase angle b g b g θ The complex conjugae : ~* * z = x + y = x y = e A hamonc wave s usually epesened by he eal pa of z ~ ψ ω ε x Ae kx b, g b g = ReL + N Acosbkx ω ε M O QP + g The wave funcon, n geneal ω ε ψ x Ae kx, = + b g b g.7 Plane Waves The suface of a consan phase fom a plane. The phase plane s pependcula o he popagaon decon. A plane wave ψ Ae k bg = A consan phase eques k = a consan Assume a = k o consan veco ( o ) k = 0 foms a plane ha s pependcula o k

kx x ky y kz z ω b g d + + ψ xyz,,, = Ae x y z : k = k + k + k The phase velocy (Velocy of he wavefon) ψ + Δk, + Δ ψ, e e j b g k ( + Δ k ) ω( + Δ ) e k ω k Δ = ±ωδ d d ω =± =±v

6 The peodc naue of a plane wave ψ + λk = ψ k : un veco of k ( ) ( ) ( ) Ae k k +λ, Ae k Hech;8/30/010; -6 k = π λ k : Popagaon veco Sufaces jonng pons of equal phase wavefons [Fg.0] A plane wave wh me dependence ω Ae k, = ψ( ) The plane wave n Caesan cood. kx x ky y kz z ω b g d + + ψ xyz,,, = Ae x y z : k = k + k + k The phase velocy (Velocy of he wavefon) ψ + Δk, + Δ ψ, e e j b g k ( + Δ k ) ω( + Δ ) e k ω k Δ = ±ωδ d d ω =± =±v k Two plane waves wh he same wavelengh k1 = k = π/ λ k k z Wave 1 : Ae 1 ω 1 Ae 1 ω = 1, k k y z Wave : Ae ω bsn θ + cos θ g ω = Ae In geneal b g b g α β γ ω ψ xyz Ae k x + y +,,, = z whee k = k = kx + ky + kz α +β + γ = 1 : Decon cosnes Cosne of he angle subended by k and x (1)

7 .8 The Thee-Dmensonal Dffeenal Wave quaon Fom (1) ψ = α k ψ, x ψ ψ ψ + + = k ψ x y z ψ = β k ψ, y ψ z Hech;8/30/010; -7 = γ k ψ Smlaly ψ = ω ψ Combne he wo eqs. 1 ψ ψ = v whee = + + x y z : Thee dmensonal dffeenal wave eq. : Laplacan opeao One of he soluon s a plane wave k x x ky y kz z ω k αx βy γz v b g d + + b + + g ψ xyz,,, = Ae = Ae Noe ha he followng s also a soluon ψ x, y, z, C f k v C g k = + + v b g 1 e j e j.9 Sphecal Waves A sphecal wave s sphecally symmecal, ndependen of θ ψ ( ) = ψ (, θ, φ) = ψ ( ), The dffeenal wave eq. n hs case 1 bψg = bψg v The soluon b g b g ψ, = f v ψ, The hamonc sphecal wave ψ A e kb vg b, g = The wavefon s obaned fom k = consan Concenc sphees b g b g = 1 f v and φ

Hech;8/30/010; -8 The sphecal wave deceases n

10 Cylndcal Waves The cylndcal symmey eques bg b g

8 Hech;8/30/010; -8 The sphecal wave deceases n amplude as popagaes. A pa of a sphecal wave esembles a pa of a plane wave a fa dsance.10 Cylndcal Waves The cylndcal symmey eques bg b g bg ψ = ψ, θ, z = ψ The dffeenal wave eq. F I HG K J = 1 ψ 1 ψ v The soluon s gven by Bessel funcons. As A ψ, b g b g ek v

elecomagnec waves Quanum lecodynamcs : negy ansfe by massless pacles(phoons)

feld lecc cuens, me vayng elecc felds Magnec feld The foce on a chage q F =

Faaday s Inducon Law A me-vayng magnec flux hough a loop Induced lecomove

B ds C zz A d db z dl = B ds ds C dzz A zz : Faaday s law A d Hech;8/30/010;

9 Chape 3. lecomagnec Theoy, Phoons, and Lgh Classcal lecodynamcs : negy ansfe by elecomagnec waves Quanum lecodynamcs : negy ansfe by massless pacles(phoons) 3.1 Basc Laws of lecomagnec Theoy lecc chages, me vayng magnec felds lecc feld lecc cuens, me vayng elecc felds Magnec feld The foce on a chage q F = q + qv B : Loenz foce A. Faaday s Inducon Law A me-vayng magnec flux hough a loop Induced lecomove Foce(emf) o volage d emf = Φ B d z dl. B ds C zz A d db z dl = B ds ds C dzz A zz : Faaday s law A d Hech;8/30/010; -9 (Wong decon of dl n he book) B. Gauss s Law-lecc lecc flux : Φ = DdS= D ds A A The oal elecc flux fom a closed suface = The oal enclosed chage D ds = ρdv A, V whee D = ε, ε = εε o, elecc pemvy Pemvy of fee space Relave pemvy, Delecc consan

10 A pon chage a he ogn D s consan ove a sphee, Φ = q q Coulomb s law, = πε 4 o Φ = 4π. D Hech;8/30/010; -10 C. Gauss s Law-Magnec No solaed magnec chage B ds = A zz 0 D. Ampee s Law A cuen peneang a closed loop nduces magnec feld aound he loop Usng cuen densy JA [ / m ] H dl = J ds : Ampee s law C A whee B = μh wh μ = μ μ o, pemeably Pemeably of fee space Relave pemeably A capaco (1) Cuen hough he suface A 1 0 Magnec feld along cuve C 0 Cuen hough he suface A = 0 Magnec feld along cuve C=0 (???) () Magnec feld aound he we 0. B 0 beween he plaes even f hee s no cuen. (They ae ndsngushable)

11 Hech;8/30/010; -11 Beween he capaco plaes Q = ε = ε A A J D, Dsplacemen cuen densy Dffeenae boh sdes The genealzed Ampee s law D H dl = J + ds C : Maxwell A. Maxwell s quaons In fee space : ε = ε, μ = μ, ρ = = 0 o o J B B dl = ds C = A D D H dl = ds C H = A B ds = 0 B = 0 A D ds = 0 D = 0 A Dffeenal fom (1) () (3) (4) 3. lecomagnec Waves Thee basc popees (1) Pependculay of he felds A me-vayng D geneaes H ha s pependcula o D [Fg. 3.1] B B [Fg. 3.5] Tansvese naue of and H () Inedependence of and H Tme vayng and B egeneae each ohe endlessly (3) Symmey of he equaons The popagaon decon wll be symmecal o boh and H

12 Dffeenal wave equaon Fom (1) = B e j e j Hech;8/30/010; -1 Usng () = εμ e j =0 o o = ε μ o o In Caesan cood. by sepaaon of vaables x x x x ε μ x + + = o o, : y z Wave equaon known long befoe Maxwell εμ wh v = 1/ o o Maxwell calculaed v = = 3 10 m / s : ε oμ 1 7 o π 10 Maxwell concluded ha lgh s an elecomagnec wave. Fzeau's measuemen, c=315,300 Km / s Tansvese Waves A plane wave popagang along x-axs xyz b,,, g xyz b,,, g = = 0 y z = x, ( x, ) x + ( x, ) y + ( x, ) z ( ) Fom dvegence eq. (4) = 0 x y z x x = 0 = ( xy, ) + ( xz, ) Assume = y y x, Fom (1) y x y z x y z 0 0 Only y y b g z B = + + = 0 y z x = 0, x = cons (no a avelng wave) = 0, = 0 x y z : Tansvese wave and B exs : Tansvese wave z z y x B y B x y = z Bz (5) x = 0, = 0, o mach z

13 Hech;8/30/010; -13 A plane hamonc wave x, = cos kx ω + ε y ( ) [ ] o The B- feld fom (5) y 1 Bz = d o cos [ kx ω +ε] x c y = cbz : and B ae n phase B // Beam popagaon decon 3.3 negy and Momenum A. The Poynng Veco The elecomagnec wave anspos enegy and momenum The enegy densy of an elecc feld : u ε = 1 o = 1 μ The enegy densy of a magnec feld : ub B o Fom he elaon = cb : u = u The oal enegy densy of an elecomagnec wave u = u + u B B

Hech;8/30/010; -14 The powe densy of an elecomagnec wave [W/m ] (enegy pe un me pe un aea) S = H : Poynng veco W / m A hamonc plane wave = o cosek ωj, B = B cos k ω o e j e j e j S = c ε B cos k ω

14 Hech;8/30/010; -14 The powe densy of an elecomagnec wave [W/m ] (enegy pe un me pe un aea) S = H : Poynng veco W / m A hamonc plane wave = o cosek ωj, B = B cos k ω o e j e j e j S = c ε B cos k ω (1) o o o Tme aveage of Hamonc Funcons 1 T + / () () cos ( ) [ 1 snc( T)cos( ) ] f T T f d T/ 1 1 ω = + ν ω () T T >> 1/ ν B. The Iadance The me aveage of powe densy Fom (1) and () 1 1 I S = c ε B c ε T o o o o o s moe effcen on a chage han B The Invese Squae Law A pon souce a he cene A sphecal wave Fom he enegy consevaon 4π I = 4π I, 1 bg bg 1 bg bg 1 o 1 = o = cons. lecc feld ~ 1/, Iadance ~ 1/ : Invese squae law s called opcal feld

- The wavefon a a lae me s he envelope of hese waveles. Huygens-Fesnel Pncple The wavefon a a lae me s he supeposon of he seconday waveles. Rays A ay s a lne dawn n he decon of lgh popagaon.

15 Hech;8/30/010; -15 Chape 4. The Popees of Lgh 4.1 Inoducon Scaeng Tansmsson, eflecon, and efacon (mcoscopc) (macoscopc) 4. Raylegh Scaeng 4.3 Reflecon Huygens s Pncple - vey pon on a pmay wavefon behaves as a pon souce of sphecal seconday wavele. - The seconday waveles popagae wh he same speed and fequency wh he pmay wave. - The wavefon a a lae me s he envelope of hese waveles. Huygens-Fesnel Pncple The wavefon a a lae me s he supeposon of he seconday waveles. Rays A ay s a lne dawn n he decon of lgh popagaon. In mos cases, ay s sagh and pependcula o he wavefon A plane wave s epesened by a sngle ay. Law of eflecon (Pa II) : The ncden and efleced ays all le n he plane of ncdence The plane made by he ncden ay and he suface nomal A. The Law of Reflecon A plane wave no a fla medum ( λ>> aomc spacng) Sphecal waveles fom he aoms Consucve nefeence only n one decon λ<<aomc spacng Seveal eflecon (X-ay scaeng).

Devaon of he law Hech;8/30/010; -16 A =0, he wavefon s AB A = 1, he wavefon s CD Noe v 1 = BD = AD sn

4 Refacon The ncden ays ae ben a an neface Refacon A.

n sn θ sn θ = v v = c n, v sn θ c = n = n sn θ : Law of efacon, Snell s law A weak elecc feld A lnea

16 Devaon of he law Hech;8/30/010; -16 A =0, he wavefon s AB A = 1, he wavefon s CD Noe v 1 = BD = AD sn θ, v1 = AC = AD sn θ sn θ sn θ = v v Snce v θ = v = θ : Law of eflecon (Pa I) 4.4 Refacon The ncden ays ae ben a an neface Refacon A. The Law of Refacon A =0 he wavefon s AB A =Δ he wavefon s D vδ = BD = ADsn θ v Δ = A = AD sn θ Snce v n sn θ sn θ = v v = c n, v sn θ c = n = n sn θ : Law of efacon, Snell s law A weak elecc feld A lnea esponse of he aom A smple hamonc vbaon of he aom The fequences of he ncden, efleced and efaced waves ae equal. The ncden, efleced, and efaced ays all le n he plane of ncdence.

4.5 Fema s Pncple Heo poposed he pncple of shoes pah θ = θ S, P and B ae n he

he pah ha akes he leas me Fema s pncple on efacon The me fom S o P SO OP h + x

Lengh The ans me fom S o P : In an nhomogeneous medum OPL = P S ( ) n s ds m s

wh he smalles opcal pah lengh Moden Fema s Pncple The opcal pah lengh of he

x df dx = 0 Rays slghly devae fom he saonay pah The same OPL Consucve nefeence

17 4.5 Fema s Pncple Heo poposed he pncple of shoes pah θ = θ S, P and B ae n he plane of ncdence Hech;8/30/010; -17 Fema poposed he pncple of leas me Lgh akes he pah ha akes he leas me Fema s pncple on efacon The me fom S o P SO OP h + x b + ( a x) = + + v v v v sn θ sn θ = v v : Snell s law d / dx = 0 Opcal Pah Lengh The ans me fom S o P : In an nhomogeneous medum OPL = P S ( ) n s ds m s 1 = v c m = 1 = 1 ns Opcal pah lengh (OPL) Rewe Fema s Pncple Lgh aveses he pah wh he smalles opcal pah lengh Moden Fema s Pncple The opcal pah lengh of he acual lgh pah s saonay wh espec o vaaons of he pah f ( x ) s saonay wh espec o x df dx = 0 Rays slghly devae fom he saonay pah The same OPL Consucve nefeence Fema s pncple s ndependen of ay decon Pncple of evesbly No allowed n he pncple of leas me

18 4.6 The lecomagnec Appoach Hech;8/30/010; -18 A. Waves a an Ineface An ncden plane wave = o cos ( k ω) The efleced and ansmed waves = o cos ( k ω + ε ) = o cos ( k ω + ε) ε, ε, ε ae phase consans The bounday condons: + = ( ) ( ) ( ) angenal angenal angenal u n u u n n Ths elaon should be sasfed egadless of and ω = ω = ω k = k + ε = k + ε (1) Fom he fs wo of (1) ( k k ) = ε : s on he neface plane ( k k) ( o) = 0 : o s a pon on he neface plane ( k k )// u : u n s he suface nomal n k θ k, k and u n fom a plane (Plane of ncdence) k sn θ = k sn θ θ = θ k = k k θ Fom he fs and las of (1) ( k k) = ε ( k k) ( o) = 0 ( k k) The neface plane k, k and u n fom he plane of ncdence k sn θ = k sn θ n sn θ = n sn θ k k θ θ k = nω / c

19 B. The Fesnel qs. Case 1. The plane of ncdence The elaon among, H, and k H // k ˆ k // H ( ) ˆ, ( ) Hech;8/30/010; -19 A he neface o + o = o (1) H + H = H ( o ) ( o ) ( o ) angenal angenal angenal H cos θ x H cos θ x H cos θ x o o o Snce H = / μ v 1 ( 1 ) cos cos μv θ = μv θ o o o () Fom (1) and () wh μ = μ = μ = μo, v = c / n o n cos θ n cos θ = : Amplude eflecon coeff. o n cos θ + n cos θ o n cosθ = o n cos θ + n cos θ : Amplude ansmsson coeff. The physcal meanng of π phase shf on he efleced wave when n > n

= v, μ = μ = μ = μo, v = c / n o n cos θ n cos θ = // : Amplude eflecon coeff. o n cos θ + n cos θ // (3) (4) o n cosθ = n cos θ + n cos θ o // // : Amplude ansmsson coeff.

20 Hech;8/30/010; -0 Case // The plane of ncdence angenal should be connuous acoss he neface + = ( o ) ( o ) ( o ) angenal angenal angenal cos θ x, cos θ x, cos θ x, : s such ha B pons ouwad o o H angenal should be connuous acoss he neface H + H = H ( o ) ( o ) ( o ) angenal angenal angenal 1 o μ v z 1 o μ v z 1 o μ v z o Fom (3) and (4) wh θ = θ, v = v, μ = μ = μ = μo, v = c / n o n cos θ n cos θ = // : Amplude eflecon coeff. o n cos θ + n cos θ // (3) (4) o n cosθ = n cos θ + n cos θ o // // : Amplude ansmsson coeff. Applyng Snell s law assumng θ 0, Fesnel qs. become sn = sn n sn θ = n sn θ ( θ θ) ( θ + θ ) snθ cosθ = sn // an = an ( θ θ) ( θ +θ) // ( θ + θ ) sn ( θ +θ) cos ( θ θ) = snθ cosθ

21 C. Inepeaon of he Fesnel qs. Amplude Coeffcens A nomal ncdence, θ = 0 n n = n, n + n = n + n n n // = n, // n + n = n + n ( ) 1 + = fo all θ // + // = 1 only fo θ = 0 Hech;8/30/010; -1 The exenal eflecon ( n > n ) Fo θ > 0 n > n θ > θ < 0 always. // cosses zeo fom + o - a ( ) 90 o θ + θ =. θ p, polazaon angle,,, vs. θ (xenal eflecon, n > n, n = 15. ) // // A poo suface wll be molke a glancng ncdence [page 116] ven x-ay eflecs a glancng ncdence x-ay elescope The nenal eflecon ( n > n ) θ > θ > 0 always I becomes 1 a he ccal angle θ c : (n sn θ = n sn θ n sn θ = n ) c // cosses zeo fom - o + a ( θ + θ ) = 90 o ( θ p and θ p ae complemens of each ohe) θ p, polazaon angle

beween and Fo n < n, > 0 always n he egon 0 <

always Reflecance and Tansmance The powe pe

phaso fom : ( ) The adan flux densy ( W / m )

22 Hech;8/30/010; - n > n, n = 15. Phase Shfs Fo n > n, < 0 always π ou of phase beween and Fo n < n, > 0 always n he egon 0 < θ < θ In phase beween and Noe ha, // > 0 always Reflecance and Tansmance The powe pe un aea : S = b e, poynng veco 1 * S = H In phaso fom : ( ) The adan flux densy ( W / m ) : Iadance 1 c I = S = εoε o : Aveage enegy pe un me pe un aea n c

Hech;8/30/010; -3 The coss seconal aea of he ncden beam = A cos θ efleced beam = A cos θ ansmed beam = A cos

cos θ n cos θ T = Incden powe IA cos θ o n cos θ n cos θ The addonal faco comes fom (1) dffeen ndces of

negy consevaon IAcos θ = IAcos θ + IAcos θ o o o n cos θ = n cos θ + n cos θ o o cos θ o o cos θ o n 1 = + n

7 Toal Inenal eflecon Assume n > n The Snell s law n sn θ = sn θ : θ < θ n A he ccal angle θ = θc, θ becomes

23 Hech;8/30/010; -3 The coss seconal aea of he ncden beam = A cos θ efleced beam = A cos θ ansmed beam = A cos θ The eflecance I A I R Refleced powe cos θ o Incden powe IAcos θ I The ansmance Tansmed powe IA cos θ o n cos θ n cos θ T = Incden powe IA cos θ o n cos θ n cos θ The addonal faco comes fom (1) dffeen ndces of efacon () dffeen coss-seconal aeas of he ncden and efaced beams. negy consevaon IAcos θ = IAcos θ + IAcos θ o o o n cos θ = n cos θ + n cos θ o o cos θ o o cos θ o n 1 = + n = R =T 4.7 Toal Inenal eflecon Assume n > n The Snell s law n sn θ = sn θ : θ < θ n A he ccal angle θ = θc, θ becomes 90 o n sn θ c = n Fo θ > θc All he ncomng enegy s efleced back no he ncden medum Toal Inenal Reflecon Inenal eflecon and TIR: Tanson fom (a) o (e) whou dsconnuy. (Reflecon nceases whle ansmsson deceases) TIR n psms: The ccal angle a a-glass neface : 4 o

24 A. The vanescen Wave Hech;8/30/010; -4 Usng Snell s law we ewe Fesnel q. as // n cos θ n cos θ = n cos θ + n cos θ n cos θ n cos θ = n cos θ + n cos θ, // ( n n ) / sn θ cosθ ( n n ) become complex when θ > θ * = // // = R = 1 * / sn θ + cosθ ( n n ) ( n n ) / sn θ / cosθ ( n n ) ( n n ) / sn θ + / cosθ c The ansmed wave: k = k x + k y whee x y k k k n x = sn θ n sn θ k o = e ( ω ) n y = cos θ ± 1 sn θ n k k k Snell s law n ± k θ sn 1 n =β θ > θ c z y 0 x k k cos θ θ θ θ k k sn θ k The ansmed wave: = e o n k snθx βy ω n, vanescen wave I advances n x-decon bu exponenal decay along y-axs Consan phase (yz-plane) Consan amplude (xz-plane), Inhomogeneous wave The ne enegy flow acoss he neface = 0 Fusaed Toal Inenal Reflecon (FTIR) Dense medum Rae medum Dense medum (negy ansfe) TIR vanescen wave [Fg. 4.55] FTIR [Fg. 4.56] Beamsple usng FTIR 4.9 The Ineacon of Lgh and Mae Reflecon of all vsble fequency Whe colo 70%~80% eflecon Shny gay of meal Thomas Young : Colos can be geneaed by mxng hee beams of lgh well sepaaed n fequency Thee pmay colos combne o poduce whe lgh No unque se

The common pmay colos : R, G, B Hech;8/30/010; -5 Two complemenay colos combne o poduce whe colo M + G = W, C + R = W, Y + B = W A sauaed colo conans no whe lgh and heefoe s deep and nense.

25 The common pmay colos : R, G, B Hech;8/30/010; -5 Two complemenay colos combne o poduce whe colo M + G = W, C + R = W, Y + B = W A sauaed colo conans no whe lgh and heefoe s deep and nense. An example of an unsauaed colo M + Y = R + B + R + G = W + R : Pnk ( ) ( ) The chaacesc colos of mos subsances come fom selecve absopon xample: (1) Yellow saned glass Whe lgh Resonance n blue Yellow s seen a he oppose sde Red + Geen Song absopon n blue

26 Hech;8/30/010; -6 () H O has esonance n IR and ed No ed a ~30m undewae (3) Blue nk looks blue n ehe eflecon o ansmsson Ded blue nk on a glass slde I looks ed. Vey song absopon of ed. Song absobe s a song efleco due o lage n I. Resonance of maeals Mos aoms and molecules. Resonances n UV and IR Pgmen molecules. Resonances n VIS Oganc dye molecules have Resonance n VIS moble elecons (p elecons) Some aoms have ncomplee Low-enegy excaon shells (Gold.) Subacve coloaon Blue lgh Yellow fle Black a he ohe sde I emoves blue

Lecture 5. Plane Wave Reflection and Transmission

Lecture 5. Plane Wave Reflection and Transmission Lecue 5 Plane Wave Reflecon and Tansmsson Incden wave: 1z E ( z) xˆ E (0) e 1 H ( z) yˆ E (0) e 1 Nomal Incdence (Revew) z 1 (,, ) E H S y (,, ) 1 1 1 Refleced wave: 1z E ( z) xˆ E E (0) e S H 1 1z H (