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TRANSCRIPT
Physics 102: Lecture 15, Slide 1
Electromagnetic Wavesand Polarization
Physics 102: Lecture 15
Physics 102: Lecture 15, Slide 2
Today: Electromagnetic Waves
• Energy
• Intensity
• Polarization
Physics 102: Lecture 15, Slide 3
xz
y
E
B
loop in xy plane
loop in xz plane
loop in yz
plane
1 2 3
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.”
Physics 102: Lecture 15, Slide 4
Physics 102: Lecture 15, Slide 5
Propagation of EM Waves
• Changing B field creates E field
• Changing E field creates B field
E = c B
xz
y
If you decrease E, you also decrease B!
This is important !
Physics 102: Lecture 15, Slide 6
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
Physics 102: Lecture 15, Slide 7
Energy in EM waveLight waves carry energy but how?
Electric Fields • Recall Capacitor Energy:
U = ½ C V2
• Energy Density (U/Volume): uE = ½ 0E2
• Average Energy Density: uE = ½ (½ 0E0
2)
= ½ 0E2rms
Magnetic Fields
• Recall Inductor Energy:
U = ½ L I2
• Energy Density (U/Volume):
uB = ½ B2/0
• Average Energy Density:
uB = ½ (½ B02/0)
= ½ B2rms/0
Physics 102: Lecture 15, Slide 8
Physics 102: Lecture 15, Slide 9
Energy Density
Calculate the average electric and magnetic energy density of
sunlight hitting the earth with Erms = 720 N/C
Physics 102: Lecture 15, Slide 10
Energy Density
Calculate the average electric and magnetic energy density of
sunlight hitting the earth with Erms = 720 N/C
202
1rmsE Eu
2212
2
1 C N8.85 10 720
2 Nm C
0
2
21
rms
B
Bu 2
0
2
21
cErms
00
1
cUse
ErmsB uEu 202
1 36106.42
mJ
uuuu EBEtotal
63
J2.3 10
m
Physics 102: Lecture 15, Slide 11
Energy in EM waveLight waves carry energy but how?
Electric Fields • Recall Capacitor Energy:
U = ½ C V2
• Energy Density (U/Volume): uE = ½ 0E2
• Average Energy Density: uE = ½ (½ 0E0
2)
= ½ 0E2rms
Magnetic Fields
• Recall Inductor Energy:
U = ½ L I2
• Energy Density (U/Volume):
uB = ½ B2/0
• Average Energy Density:
uB = ½ (½ B02/0)
= ½ B2rms/0
In EM waves, E field energy = B field energy! ( uE = uB )
utot = uE + uB = 2uE = 0E2 rms
Physics 102: Lecture 15, Slide 12
Physics 102: Lecture 15, Slide 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):A
L=ctP = U/t
= uAc
• Intensity (I or S): S = P/A [W/m2]
= uc = c0E2rms
23
U = Energy u = Energy Density (Energy/Volume)A = Cross section Area of lightL = Length of box
Physics 102: Lecture 15, Slide 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)
xz
y
Physics 102: Lecture 15, Slide 15
Linear Polarizers• Linear Polarizers absorb all electric fields
perpendicular to their transmission axis.
Physics 102: Lecture 15, Slide 16
Physics 102: Lecture 15, Slide 17
Unpolarized Light on Linear Polarizer
• Most light comes from electrons accelerating in random directions and is unpolarized.
• Averaging over all directions: Stransmitted= ½ Sincident
Always true for unpolarized light!
Physics 102: Lecture 15, Slide 18
Linearly Polarized Light on Linear Polarizer (Law of Malus)
Etranmitted = Eincident cos()
Stransmitted = Sincident cos2()
TA
is the angle between the incoming light’s polarization, and the transmission axis
Transmission axisIncident E
ETransmitted
Eabsorbed
=Eincidentcos()
Physics 102: Lecture 15, Slide 19
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
1. zero 2. 1/2 what it was before 3. 1/4 what it was before 4. 1/3 what it was before 5. need more information
Physics 102: Lecture 15, Slide 20
Physics 102: Lecture 15, Slide 21
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
Physics 102: Lecture 15, Slide 22
Law of Malus – 2 Polarizers
Cool Link
unpolarized light
E1
I = I0
TATA
TA
E0
I3
B1
unpolarized light
E1
I = I0
TATA
TA
E0
I3
B1
1) Intensity of unpolarized light incident on linear polarizer is reduced by ½ . S1 = ½ S0
S = S0
S1
S2
2) Light transmitted through first polarizer is vertically polarized. Angle between it and second polarizer is =90º. S2 = S1 cos2(90º) = 0
Physics 102: Lecture 15, Slide 23
How do polaroid sunglasses work?
incident light unpolarized
reflected light partially polarized
the sunglasses reduce the glare from reflected light
Physics 102: Lecture 15, Slide 24
Physics 102: Lecture 15, Slide 25
unpolarized light
E1
I = I0
TATA
TA
E0
I3
B1
unpolarized light
E1
I = I0
TATA
TA
E0
I3
B1
Law of Malus – 3 Polarizers
2) Light transmitted through first polarizer is vertically polarized. Angle between it and second polarizer is =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 =45º. I3 = I2 cos2 (45º)
I2= I1cos2(45)
= ½ I0 cos4 (45º) = I0/8
I1= ½ I0
Physics 102: Lecture 15, Slide 26
TA
TA
S1
S2
S0
TATA
S1
S2
S0
ACT: Law of Malus
A B
1) S2A > S2
B 2) S2A = S2
B
3) S2A < S2
B
S1= S0cos2(60)
S2= S1cos2(30)= S0 cos2(60) cos2(30)
S1= S0cos2(60)
S2= S1cos2(60)= S0
cos4(60)
Cool Link
E0E0
Physics 102: Lecture 15, Slide 27