UNIVERSITY PHYSICS II CHAPTER 24 Physical optics s24.1 Light waves and the coherent condition of waves 1. Light waves Light wave is a small part of the whole electromagnetic wave spectrum. Wavelength(m) 700mm650600550500450400mm
1 1. Light waves §24.1 Light waves and the coherent condition of waves Light wave is a small part of the whole electromagnetic wave spectrum
824.1 Light waves and the coherent condition of waves 2. The interference phenomena of waves 824.1 Light waves and the coherent condition of waves 3. Coherence and the conditions of coherence OA superposition of waves may give rise to variations in the resulting amplitude of the total wave disturbance, known as interference @the conditions of coherence >The same physical type of waves, and same direction of the oscillation The same frequency; )A phase difference that is independent of time The phase difference is the difference between the individual phases of the two waves
2 §24.1 Light waves and the coherent condition of waves 2. The interference phenomena of waves 3. Coherence and the conditions of coherence 1A superposition of waves may give rise to variations in the resulting amplitude of the total wave disturbance, known as interference. 2the conditions of coherence ¾The same physical type of waves, and same direction of the oscillation; ¾ The same frequency; ¾A phase difference that is independent of time. The phase difference is the difference between the individual phases of the two waves. §24.1 Light waves and the coherent condition of waves
8 24.1 Light waves and the coherent condition of waves 4. The phase difference Simple harmonic oscillation x(t=Acos(at+o) Time( A---the amplitude 2兀 a---the angular frequency a 小- the initial phase at+o---phase 824.1 Light waves and the coherent condition of waves Sinusoidal(harmonic) waves Y(x, t)=Acos(lr-@t+o) △x Wave at t=△t Wave at t=0 k 2r ---angular wave number
3 4. The phase difference Simple harmonic oscillation x(t) = Acos(ωt +φ ) A---the amplitude ω---the angular frequency φ---the initial phase ω t + φ ---phase T π ω 2 = §24.1 Light waves and the coherent condition of waves Sinusoidal(harmonic) waves Ψ (x,t) = Acos(kx −ωt +φ ) λ 2π k = ---angular wave number §24.1 Light waves and the coherent condition of waves
8 24.1 Light waves and the coherent condition of waves If two waves Y(r, t)=Acos(kr-@t+Ou) ￥2(x,D)=Acos(kx-ort+中2) The phase difference of the two waves 6=(k n2)-(kx-or+)=中2- If two waves Y(x, t)=Acos(hx, -at+o) Y2(x, t)=Acos(Kx-at+ The phase difference of the two waves 2丌 ath at+o)-(l-at+o) )==44x 824.1 Light waves and the coherent condition of waves 5. The f principle of superpose ition and interference of waves If the amplitudes are not too large, the total wave disturbance at any point x and time t is the sum of the individual wave disturbance (x,D)=1(x,D)+￥2(x,D)+3(x,D)+ Case 1 Y(x, t)=A, cos( lx -@t +u) p2(x, t) t+p2) y(x,D)=y1(x,t)+y2(x,) A, cos(kr-at+o1)+A, cos(kx-at +o2)
4 ( , ) cos( ) ( , ) cos( ) 2 2 1 1 Ψ ω φ Ψ ω φ = − + = − + x t A kx t x t A kx t If two waves The phase difference of the two waves 2 1 2 1 δ = (kx −ωt +φ ) − (kx −ωt +φ ) = φ −φ ( , ) cos( ) ( , ) cos( ) 2 2 1 1 Ψ ω φ Ψ ω φ = − + = − + x t A kx t x t A kx t If two waves The phase difference of the two waves kx t kx t ∆x λ π δ ω φ ω φ 2 ( ) ( ) path = 2 − + − 1 − + = §24.1 Light waves and the coherent condition of waves 5. The principle of superposition and interference of waves If the amplitudes are not too large, the total wave disturbance at any point x and time t is the sum of the individual wave disturbance. Ψ (x,t) =Ψ1 (x,t) +Ψ2 (x,t) +Ψ3 (x,t) +L cos( ) cos( ) ( , ) ( , ) ( , ) 1 1 1 2 1 2 = −ω +φ + −ω +φ = + A kx t A kx t Ψ x t Ψ x t Ψ x t ( , ) cos( ) 1 = 1 − ω + φ 1 Ψ x t A kx t ( , ) cos( ) 2 = 1 − ω + φ 2 Ψ x t A kx t ¾Case 1 §24.1 Light waves and the coherent condition of waves
8 24.1 Light waves and the coherent condition of waves Y(x, t =2A, cos kx-o+中)+(kx-ot+中 (hr-at+ou-ckr-at+e) cos 2 2A, coS( )cos(hr-at n+中2 2 2 Y(x, t)=2A, cos( n2- )cos(kx-at+ +吗2 2 4p=2n丌,A=2A1(n=0,2,…) constructive 4小p=(2n+1)z,A=0(n=0,1,2,…) destructive 824.1 Light waves and the coherent condition of waves YI(x, t) 平(x0)xn) Y(r t y(r,) 2(x,n) △φ=0 △p=丌 p=2x/3 Hxt)
5 ) 2 )cos( 2 2 cos( ] 2 ( ) ( ) cos[ ] 2 ( ) ( ) ( , ) 2 cos[ 2 1 1 2 1 1 2 1 2 1 φ φ ω φ φ ω φ ω φ ω φ ω φ + − + − = − + − − + ⋅ − + + − + = A kx t kx t kx t kx t kx t Ψ x t A ) 2 ) cos( 2 ( , ) 2 cos( 2 1 1 2 1 φ φ ω φ φ + − + − Ψ x t = A kx t (2 1) , 0 ( 0,1,2, ) 2 , 2 ( 0,1,2, ) 1 L L = + = = = = = n A n n A A n ∆φ π ∆φ π constructive destructive §24.1 Light waves and the coherent condition of waves ∆φ = 0 ∆φ = π ∆φ = 2π 3 ( , ) and ( , ) 2 1 Ψ x t Ψ x t ( , ) 1 Ψ x t ( , ) 2 Ψ x t ( , ) 1 Ψ x t ( , ) 2 Ψ x t Ψ(x,t) Ψ(x,t) Ψ(x,t) Ψ Ψ Ψ Ψ Ψ Ψ §24.1 Light waves and the coherent condition of waves