Electromagnetic Waves and Polarization Physics 102: Lecture 15 Electromagnetic Waves and Polarization HE2: Monday Mar. 14 Sign up for conflicts before Thursday! Review session Sunday, Mar. 13, 3pm, 141 Loomis Remember Daylight Savings! 1

Today: Electromagnetic Waves Energy Intensity Polarization

Doppler Effect l = c/f A police car emits light of wavelength le Now the car is moving to the left. Observed wavelength lo different! Wavefronts le lo < le lo > le u Moving toward observer: fo = fe(1 + u/c) l = c/f Moving away from observer: fo = fe(1 – u/c) Only relative velocity matters: u = v1 + v2 moving in opposite directions u = v1 – v2 moving in same direction

ACT: Doppler Practice V = 32 m/s V = 50 m/s In the jeep, the frequency of the light from the troopers car will appear: (1) higher (more blue) (2) Lower (more red) What value should you use for u in the equation? (1) 32 (2) 50 (3) 50+32 (4) 50-32 Cars are getting closer together: fo = fe (1 + u/c) Cars are moving in same directions: u = v1 – v2

Preflight 15.1, 15.2 “In order to find the loop that detects the electromagnetic wave, we should find the loop that has the greatest flux through the loop.” x z y E B loop in yz plane loop in xy plane loop in xz plane Note wavelength must be much larger than loop size Radio waves: 3 meters Demo 158 30% 22% 48% 1 2 3 30% 22% 48% Only the loop in the xy plane will have a magnetic flux through it as the wave passes. The flux will oscillate with time and induce an emf. (Faraday’s Law!!!)

Propagation of EM Waves x z y Changing B field creates E field Changing E field creates B field E = c B Note E=cB is only true for EM wave, not in general This is important ! If you decrease E, you also decrease B!

Preflight 15.4 Suppose that the electric field of an electromagnetic wave decreases in magnitude. The magnetic field:       1 increases 2 decreases 3 remains the same 13% 80% 7% E=cB

Energy in E field E Electric Fields A d Recall Capacitor Energy: U = ½ C V2 Energy Density (U/Volume): uE = ½ e0E2 A d

Energy in B field Magnetic Fields Recall Inductor Energy: U = ½ L I2 Energy Density (U/Volume): uB = ½ B2/m0 A

Energy in EM wave Light waves carry energy but how? Electric Fields Recall Capacitor Energy: U = ½ C V2 Energy Density (U/Volume): uE = ½ e0E2 Average Energy Density: uE = ½ (½ e0E02) = ½ e0E2rms Magnetic Fields Recall Inductor Energy: U = ½ L I2 Energy Density (U/Volume): uB = ½ B2/m0 Average Energy Density: uB = ½ (½ B02/m0) = ½ B2rms/m0

Energy Density Example Calculate the average electric and magnetic energy density of sunlight hitting the earth with Erms = 720 N/C Example Again note energy density is same only for EM wave, not in general Use

Energy in EM wave Light waves carry energy but how? Electric Fields Recall Capacitor Energy: U = ½ C V2 Energy Density (U/Volume): uE = ½ e0E2 Average Energy Density: uE = ½ (½ e0E02) = ½ e0E2rms Magnetic Fields Recall Inductor Energy: U = ½ L I2 Energy Density (U/Volume): uB = ½ B2/m0 Average Energy Density: uB = ½ (½ B02/m0) = ½ B2rms/m0 In EM waves, E field energy = B field energy! ( uE = uB ) utot = uE + uB = 2uE = e0E2rms

Intensity (I or S) = Power/Area Energy (U) hitting flat surface in time t = Energy U in red cylinder: U = u x Volume = u (AL) = uAct Power (P): L=ct P = U/t = uAc Intensity (I or S): S = P/A [W/m2] = uc = ce0E2rms A U = Energy u = Energy Density (Energy/Volume) A = Cross section Area of light L = Length of box

Polarization Transverse waves have a polarization (Direction of oscillation of E field for light) Types of Polarization Linear (Direction of E is constant) Circular (Direction of E rotates with time) Unpolarized (Direction of E changes randomly) x z y

Linear Polarizers Linear Polarizers absorb all electric fields perpendicular to their transmission axis (TA) TA TA

Linearly Polarized Light on Linear Polarizer (Law of Malus) TA Etranmitted = Eincident cos(q) Stransmitted = Sincident cos2(q) q q is the angle between the incoming light’s polarization, and the transmission axis Transmission axis Incident E Eabsorbed q ETransmitted = Eincidentcos(q)

Unpolarized Light on Linear Polarizer demo 324 Most light comes from electrons accelerating in random directions and is unpolarized. Averaging over all directions: Stransmitted= ½ Sincident Always true for unpolarized light!

ACT/Preflight 15.6 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 zero      1/2 what it was before      1/4 what it was before      1/3 what it was before      need more information

ACT/Preflight 15.7 Now, horizontally polarized light passes through the same glasses (which are vertically polarized). The intensity of the light when it emerges is zero      1/2 what it was before      1/4 what it was before      1/3 what it was before      need more information

Law of Malus – 2 Polarizers Example S = S0 S1 S2 1) Intensity of unpolarized light incident on linear polarizer is reduced by ½ . S1 = ½ S0 Demo 2) Light transmitted through first polarizer is vertically polarized. Angle between it and second polarizer is q=90º. S2 = S1 cos2(90º) = 0

How do polaroid sunglasses work? incident light unpolarized reflected light partially polarized the sunglasses reduce the glare from reflected light

Law of Malus – 3 Polarizers Example I1= ½ I0 I2= I1cos2(45) 2) Light transmitted through first polarizer is vertically polarized. Angle between it and second polarizer is q=45º. I2 = I1 cos2 (45º) = ½ I0 cos2 (45º) Demo 3) Light transmitted through second polarizer is polarized 45º from vertical. Angle between it and third polarizer is q=45º. I3 = I2 cos2 (45º) = ½ I0 cos4 (45º) = I0/8

ACT: Law of Malus A B S2 S2 E0 E0 S0 S0 S1 S1 90 ° TA S1 S2 S0 60 TA S1 S2 S0 60 ° E0 E0 A B S1= S0cos2(60) S1= S0cos2(60) S2= S1cos2(30) = S0 cos2(60) cos2(30) S2= S1cos2(60) = S0 cos4(60) 1) S2A > S2B 2) S2A = S2B 3) S2A < S2B

See You Monday!