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Electromagnetic Waves and Polarization

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lectures through 14 (resonance) discussions through 7 ... How do polaroid sunglasses work? incident light unpolarized. reflected light partially polarized ... – PowerPoint PPT presentation

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Title: Electromagnetic Waves and Polarization


1
Electromagnetic Wavesand Polarization
Physics 102 Lecture 15
  • HE2 Monday Oct. 29
  • Material covered
  • lectures through 14 (resonance)
  • discussions through 7
  • homework through 7
  • labs through 6
  • Review
  • Sunday October 26, 3-430
  • Will go over Fall 2007 Exam

2
Today Electromagnetic Waves
  • Energy
  • Intensity
  • Polarization
  • But firsta leftover from Monday

3
Doppler Effect
  • Doppler Example Audio
  • Doppler Example Visual
  • fo fe (1 u/c) moving toward each other
  • fo fe (1 - u/c) moving away from each other
  • Notes
  • These are easier than equations for sound!
  • If f increases then ? decreases (and vice versa),
    since speed is always c (c ?f)
  • Finding relative velocity
  • u v1 v2 moving in opposite directions
  • u v1 v2 moving in same direction

demos
45
4
ACT Doppler Practice
Example
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) 5032 (4) 50-32
Cars are getting closer together fo fe (1
u/c)
Cars are moving in same directions u v1 v2
48
5
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
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.
(Faradays Law!!!)
7
6
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!
10
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
19 72 9
EcB
8
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

13
9
Energy Density
  • Calculate the average electric and magnetic
    energy density of sunlight hitting the earth with
    Erms 720 N/C

Example
18
10
Energy Density
  • Calculate the average electric and magnetic
    energy density of sunlight hitting the earth with
    Erms 720 N/C

Example
Use
18
11
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 e0E2 rms

13
12
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

Lct
U Energy u Energy Density (Energy/Volume) A
Cross section Area of light L Length of box
23
23
13
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)

25
14
Linear Polarizers
  • Linear Polarizers absorb all electric fields
    perpendicular to their transmission axis.

Molecular View
30
15
Unpolarized Light on Linear Polarizer
  • Most light comes from electrons accelerating in
    random directions and is unpolarized.
  • Averaging over all directions Stransmitted ½
    Sincident

33
16
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 lights
polarization, and the transmission axis
Eabsorbed
q
ETransmitted
Eincidentcos(q)
36
17
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

37
18
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

38
19
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
2) Light transmitted through first polarizer is
vertically polarized. Angle between it and second
polarizer is q90º. S2 S1 cos2(90º) 0
Cool Link
39
20
How do polaroid sunglasses work?
incident light unpolarized
reflected light partially polarized
the sunglasses reduce the glare from reflected
light
21
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 q45º. 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 q45º. I3 I2 cos2 (45º)
½ I0 cos4 (45º) I0/8
43
22
ACT Law of Malus
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 gt S2B 2) S2A S2B 3) S2A lt S2B
48
23
See You Monday!
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