1. 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

2. Today: Electromagnetic Waves
Energy
Intensity
Polarization

3. 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

4. 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) (4) 50-32
Cars are getting closer together: fo = fe (1 + u/c)
Cars are moving in same directions: u = v1 – v2

5. 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%
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!!!)

6. Propagation of EM Wavesx 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!

7. 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

8. 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

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

10. 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

11. 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

12. 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

13. 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

14. 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

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

16. 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)

17. 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!

18. 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

19. 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

20. 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

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

22. 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

23. ACT: Law of Malus A B S2 S2 E0 E0 S0 S0 S1 S190 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

24. See You Monday!