33. 전자기파 (Electromagnetic waves)
33-2. Maxwell 의무지개 눈의감도
33-3. 진행하는전자기파 : 정성적 전자기파의발생기구에따른분류 장파, 라디오파 ( 방송파 ) - LC회로 : 고전전자기학이론 가시광, x-선, 감마선 - 원자또는핵 : 양자물리학이론 라디오파의발생과전파 1) LC 발진기 = 교류전류공급원 2) 안테나 ( 전자기파방출원 ) = 진동전기쌍극자
Question: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical 2) Horizontal 3) 45 Degrees + Direction wave travels - Alternating E field moves charges up and down thru antenna!
진행하는전자기파 : 정성적 Antenna
Electromagnetic Waves y z x Transverse: 횡파 (vs. sound waves longitudinal: 종파 ) E perpendicular to B and always in phase E & B increase and decrease at same times Can travel in empty space (sound waves can t!) Speed of light : v = c = 1/ (ε 0 μ 0 ) = 3 x 10 8 m/s (300,000 km/second!) Frequency: f = v/λ = c/λ
Which of the following are transverse waves? sound light radio X-ray microwave water waves The Wave ( 응원파도타기 ) All but sound!
33-3. 진행하는전자기파 : 정성적 안테나가방출하는전자기파의시 공간적변화 1 관측점 P 에서의시간적변화 2 진행방향에따른공간적변화
전자기파속력 전자기장벡터 E r 2π k λ ω 2π f ω = f λ = k c B r r r E B 속력 C E m B = c m 증명해보자
33-3. 진행하는전자기파 : 정량적 E x B t dφb E r r ds = dt E r r ds = ( E + de) h Eh = hde dφ B d db = { B ( hdx) } = ( hdx) dt dt dt de db E B = = dx dt x t Faraday s Law: = { Emsin( kx ωt) } = kemcos( kx ωt) x = { Bmsin( kx ωt) } = ωbmcos( kx ωt) t r E E m c B = r m B = c
Propagation of EM Waves y z x Changing B field creates E field Changing E field creates B field E = c B This is important! If you decrease E, you also decrease B!
전자기파속력 dφe B r r ds = εμ 0 0 dt B r r ds = ( B + db) h + Bh = hdb d E d de εμ Φ 0 0 = εμ 0 0 { E( hdx) } = εμ 0 0 ( hdx) dt dt dt Maxell s Law: B = εμ 0 0 x E t c = m kb cos( kx ωt) = εμωe cos( kx ωt) m 0 0 0 0 0 0 Em 1 1 c B = εμ( ω/ k) = εμc = 1 ε μ 0 0 m
확인문제 1. E+dE E c B+dB E B (1) B 가증가하고있을때, box 양옆에서의전기장의방향과상대적인크기는? (2) 자기장의방향과상대적인크기는?
질문 At t = 0, z = 0, the electric field of an electro-magnetic wave is oriented at an angle θ with respect to the x- axis, as shown. Which arrow indicates the direction of the magnetic field at the same location and instant of time? (a) A (b) B A y B θ ê x This question cannot be answered unless the direction of propagation is specified: If the wave propagates in the +z direction, then B-field is along A If the wave propagates in the z direction, then B-field is along B
33-5. 에너지수송과 Pointing 백터 포인팅벡터 (Poynting vector) r 1 r r S E B μ 0 [unit : W/m 2 ] 전자기파에실려옮겨지는단위시간당, 단위면적당에너지흐름의크기와방향 B r E r r r r S E B 단위면적당일률을나타내는벡터량 크기 : 방향 : 전자기파의진행방향 확인문제 2. 에너지는음의 z 축방향자기장의방향은? B r S r
Intensity (I or S) = Power/Area Energy (U) in box: U = u x Volume = u (AL) Power (P): P = U/t = U (c/l) = u A c Intensity (I or S): S = P/A = uc A L=ct U = Energy u = Energy Density (Energy/Volume) A = Cross section Area of light L = Length of box
전자기파의세기 (intensity) I S avg = 점원으로부터거리에따른전자기파의세기변화 s 2 = ()(4 π ) () = P I r r I r Ps 4π r 2 전자기파에서의전기및자기에너지밀도비교 2 1 2 1 2 1 1 2 B ue = ε0e = ε0( cb) = ε0 B = = u 2 2 2 εμ 2μ 0 0 0 u E = u B 전기장과자기장이가지고있는에너지는항상동일하다. 2 B
33-6. 복사압 (Radiation pressure) 전자기파가물체에조사되었을때, 운동량 (p = U/c) 변화량 Δ p= Q PR ΔU c Δ U = IAΔt Newton 제 2 법칙으로부터 Δp F = Δ t IA F = QPR c P r F = = Q A PR I c Power incident on the Earth's surface due to radiation from the sun is about 1370 W/m 2 Radiation Pressure at Earth's surface is 1370/c = 4.5710-6 N/m 2 or 4.57mPa
보기문제 33-2.
33-7. 편광 (Polarization) 편광방향 : 전기장 (E) 이진동하는방향 편광된전자기파 (Polarized EM wave) 막편광, 비편광된전자기파 (Unolarized EM wave) 전자기파의 E 진동방향이일정할때 ( 혹은, 일정하게변화할때 ) 전자기파의 E 진동방향이시간에따라마구잡이로변할때 y r ) ) E = Ex+ Ey x y x
편광판 (Polarizer) 어느한방향의선편광성분을선택적으로투과시키는판 (sheet) I = E = E cos θ = I cos 2 2 2 2 y 0 0 2 I S cos θ θ = (Malus 법칙 )
선편광판 (Linear Polarizers) Linear Polarizers absorb all electric fields perpendicular to their transmission axis.
Unpolarized Light on Linear Polarizer Most light comes from electrons accelerating in random directions and is unpolarized. Averaging over all directions: S transmitted = ½ S incident Always true for unpolarized light!
Linearly Polarized Light on Linear Polarizer (Law of Malus) E tranmitted = E incident cos(θ) S transmitted = S incident cos 2 (θ) θ TA θ is the angle between the incoming light s polarization, and the transmission axis Incident E E absorbed Transmission axis θ E Transmitted =E incident cos(θ)
Question Unpolarized light (like the light from the sun) passes through a polarizing sunglass (a linear polarizer). The intensity of the light when it emerges is 1. zero 2. ½ what it was before 3. ¼ what it was before 4. ⅓ what it was before 5. need more information Now, horizontally polarized light passes through the same glasses (which are vertically polarized). The intensity of the light when it emerges is 1. zero 2. ½ what it was before 3. ¼ what it was before 4. ⅓ what it was before 5. Need more information
Law of Malus 60 E 0 E 0 60 TA 90 TA TA S 0 S 1 S 2 TA S 0 S 1 S 2 A B S 1 = S 0 cos 2 (60) S 1 = S 0 cos 2 (60) S 2 = S 1 cos 2 (30)= S 0 cos 2 (60) cos 2 (30) S 2 = S 1 cos 2 (60) = S 0 cos 4 (60) 1) S 2A > S 2 B 2) S 2A = S 2 B 3) S 2A < S 2 B
Law of Malus 3 Polarizers E 0 TA 45 E 1 TA unpolarized light 90 TA I = I 0 B 1 I 1 = ½ I 0 I 2 = I 1 cos 2 (45) I 3 2) Light transmitted through first polarizer is vertically polarized. Angle between it and second polarizer is θ=45º. I 2 = I 1 cos 2 (45º) = ½ I 0 cos 2 (45º) 3) Light transmitted through second polarizer is polarized 45º from vertical. Angle between it and third polarizer is θ=45º. I 3 = I 2 cos 2 (45º) = ½ I 0 cos 4 (45º)
33-8. 반사 (reflection), 굴절 (refraction) Light incident on an object Absorption Reflection (bounces) See it Mirrors Refraction (bends) Lenses Often some of each Everything true for wavelengths << object size
33-8. 반사 (reflection), 굴절 (refraction) n 1 n 2 n 2 > n 1 굴절률 (index of refraction) : 반사법칙 : θ = θ ' 1 1 n c 진공중에서의속력 = v 매질내에서의속력 굴절법칙 (Snell 법칙 ) : n sinθ = n sinθ = 일정 1 1 2 2 n 2 < n 1
Apparent Depth Apparent depth: d = d n 2 n 1 n 2 d d n 1 apparent fish actual fish 50
굴절률 (refractive index ) c 진공중에서의속력 n = v 매질내에서의속력 (ε, μ) 매질 : v = 1 με ε κε 0 μ μ 0 n c με = = = v με 0 0 κ θ 2 Wavefronts θ 1 θ 2 Wavefronts θ 1 굴절시전자기파의진동수는변하지않는다 v 1 = fλ 1 v = f 2 v = λ v λ 1 2 1 2 2 λ l 0 nλ = n λ = 일정 λ = 1 1 2 2 λ n
색의분산 (Color dispersion) 빛의파장에따라굴절률이다름 굴절률이다름 빛이퍼짐 분산 파장 λ = 589 nm 에서의굴절률
무지개 (Rainbow) 쌍무지개 In second rainbow pattern is reversed
33-9. 내부전반사 (Total internal reflection) 빛이굴절율이높은매질에서낮은매질로들어갈때 ( n 1 > n 2 ), 그경계면에서빛이모두반사되는현상 프리즘 광섬유 임계각 (critical angle) : θ c n n sinθ = n sin 90 = n θ = sin n > n { } o 1 2 1 c 2 2 c 1 2 n1
Fiber Optics At each contact w/ the glass air interface, if the light hits at greater than the critical angle, it undergoes total internal reflection and stays in the fiber. n outside n cladding n inside Add cladding so outside material doesn t matter! We can be certain that n cladding < n inside
33-10. 반사에의한편광 브루스터법칙 (Brewster s Law) 반사광선과굴절광선이 90 도를이룰때, 편광방향이입사평면에대해나란한빛은전혀반사되지않는현상 ( 따라서이때반사되는빛은편광방향이입사평면에대해수직 ) 브루스터각 (Brewster angle) : θ B o θ1 + θ2 = 90 일때, n sinθ = n 1 1 2 2 tanθ 1 = 2 2 sinθ o ( θ1 ) = n sin 90 = n n n 2 1 cosθ θ B 1 n tan 1 2 n1 θ 1 θ 2
Question: Brewster s Angle When a polarizer is placed between the light source and the surface with transmission axis aligned as shown, the intensity of the reflected light: (1) Increases (2) Unchanged (3) Decreases T.A.
Flat Lens (Window) Incident ray is displaced, but its direction is not changed. θ = θ 3 1 n 1 n 2 n 1 θ 1 If θ 1 is not large, and if t is small, the displacement, d, will be quite small. t θ3 d d n θ n 2 1 = t 1 n2
33. Summary : EM waves B r E r r r E B 속력 C c = E = cb 0 1 ε μ 0 0 r 1 r r S E B μ [unit : W/m 2 ] c 진공중에서의속력 n = v 매질내에서의속력 θ = θ n ' 1 1 sinθ = n sinθ = 일정 1 1 2 2 θ c θ B n { n n } 1 2 = sin 1 > 2 n1 n tan 1 2 n1