Title: Electromagnetic Waves and Polarization
1Electromagnetic 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
2Today Electromagnetic Waves
- Energy
- Intensity
- Polarization
- But firsta leftover from Monday
3Doppler 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
4ACT 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
5Preflight 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
6Propagation 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
7Preflight 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
8Energy 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
9Energy Density
- Calculate the average electric and magnetic
energy density of sunlight hitting the earth with
Erms 720 N/C
Example
18
10Energy Density
- Calculate the average electric and magnetic
energy density of sunlight hitting the earth with
Erms 720 N/C
Example
Use
18
11Energy 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
12Intensity (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
13Polarization
- 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
14Linear Polarizers
- Linear Polarizers absorb all electric fields
perpendicular to their transmission axis.
Molecular View
30
15Unpolarized Light on Linear Polarizer
- Most light comes from electrons accelerating in
random directions and is unpolarized. - Averaging over all directions Stransmitted ½
Sincident
33
16Linearly 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
17ACT/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
18ACT/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
19Law 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
20How do polaroid sunglasses work?
incident light unpolarized
reflected light partially polarized
the sunglasses reduce the glare from reflected
light
21Law 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
22ACT 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
23See You Monday!