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Understanding Electromagnetic Waves: Energy, Intensity, Polarization

Explore electromagnetic waves, energy properties, intensity calculations, and polarization effects in physics. Learn about E and B fields, wave propagation, energy density, and polarization types. Delve into the concepts of linear, circular, and unpolarized light waves, including how polarizers affect light transmission. Practice using the Law of Malus to understand light polarization through various angles. Enhance your knowledge of EM waves by calculating energy densities and intensities.

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Understanding Electromagnetic Waves: Energy, Intensity, Polarization

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  1. Physics 102: Lecture 15 Electromagnetic Wavesand Polarization

  2. Today: Electromagnetic Waves • Energy • Intensity • Polarization

  3. E B loop in xy plane loop in yz plane loop in xz plane y x z Preflight 15.1, 15.2 “In order to find the loop that dectects the electromagnetic wave, we should find the loop that has the greatest flux through the loop.” 1 2 3

  4. y x z This is important ! Propagation of EM Waves • Changing B field creates E field • Changing E field creates B field E = c B If you decrease E, you also decrease B!

  5. 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 E=cB

  6. Energy in EM wave 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 Light waves carry energy but how?

  7. Energy Density Calculate the average electric and magnetic energy density of sunlight hitting the earth with Erms = 720 N/C Example

  8. Energy Density Calculate the average electric and magnetic energy density of sunlight hitting the earth with Erms = 720 N/C Example Use

  9. Energy in EM wave 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 Light waves carry energy but how? In EM waves, E field energy = B field energy! ( uE = uB ) utot = uE + uB = 2uE = e0E2rms

  10. 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): A • P = U/t • = uAc • Intensity (I or S): • S = P/A [W/m2] • = uc = ce0E2rms L=ct U = Energy u = Energy Density (Energy/Volume) A = Cross section Area of light L = Length of box 23

  11. y x z 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)

  12. Linear Polarizers • Linear Polarizers absorb all electric fields perpendicular to their transmission axis.

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

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

  15. 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

  16. 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

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

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

  19. Example Law of Malus – 3 Polarizers 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) 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

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

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