W14D2:
EM Waves, Dipole Radiation,
Polarization and Interference
Today’s Reading Course Notes: Sections 13.8, 13.10,
14.1-14.3
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Announcements
No Math Review Week 15 Tuesday
PS 11 is only for practice. It will not be graded.
Final Exam Review
Friday May 16 from 12 noon-2 pm in 26-152
Friday May 16 from 2 pm-4 pm in 26-152
Final Exam May 19 from 9 am -12 noon Second floor Johnson
Athletic Center
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Outline
Generating Plane EM Waves
Generating Electric Dipole EM Waves
Microwaves
Polarization
Interference
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Generating Plane EM
Waves
First, how do you generate waves on a
string and where does the energy carried
away by the wave come from?
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Demonstration:
Vibrating Rubber Tube
(hand driven)
You Do Work Pulling the String Down
Against Tension (Restoring Force)
The Work You Do Appears in the
Energy Radiated Away By Wave
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=C 35&show=0
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Generating Plane EM
Waves
You can generate EM waves in an
analogous way (to the string) by shaking
the field lines(strings) attached to charges.
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Shaking a Sheet of Charge
Students: go to this
applet, observe for a bit,
then UNCHECK
“Motion On” box and
generate some EM
waves by left clicking on
silver ball and moving
mouse
http://peter-edx.99k.org/PlaneWave.html
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How to Think About Radiation E-Field
E-Field lines like strings tied to plane of
charge
This is the
static field
This is the
radiation field
Simple geometry:
E1
v
= tan θ =
E0
c
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Concept Q.: Generating Plane Waves
When you are pulling the charged plane down, the
radiation electric field right at the position of the plane of
charge is
1.
2.
3.
4.
up
down
zero
cannot tell, depends on past history
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Generating Electric Dipole
EM Waves
In the real world there are no infinite
planes of charge.
The radiation pattern from shaking just one
charge is as follows:
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Generating Electric Dipole
Radiation Applet
http://web.mit.edu/viz/EM/simulations/radiationcharge.jnlp
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Concept Q.: Generating Plane Waves
The point charge below got a kick a little before the
moment shown. The direction of the kick was:
1.
2.
3.
Up or down
Left or right
Cannot tell, depends on past history
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State of Polarization:
Describes how the direction of the electric field
in an EM wave changes at a point in space.
1.  Linear polarization
2.  Circular polarization
3.  Elliptical polarization
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Lecture Demonstration:
Polarization of Microwaves K3
Some materials can absorb waves with
the electric field aligned in a particular
direction (for example, sunglasses)
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=K 3&show=0
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Lecture Demonstration:
Polarization of Radio Waves
Dipole Antenna K4
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=K 4&show=0
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Spark Gap Generator:
An LC Oscillator
This is what Hertz did in 1886
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Spark Gap Antenna
http://web.mit.edu/viz/EM/movies/light/hiResAntenna.avi
http://youtu.be/SV4kTSbFWRc
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Our spark gap antenna
2)  Oscillation after
breakdown! (LC)
1) Charging time scale (RC)
3) Repeat
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Spark Gap Antenna
Accelerated charges are the source of EM waves.
Most common example: Electric Dipole Radiation.
λ
4
λ
4
t=0
t = T/4
t = T/2
t=T
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Experiment 5
Spark Gap Generator:
Find the Angular Distribution
of Radiation, and its
Polarization
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Interference
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Interference: The difference
between waves and particles
No Interference:
if light were made
up of particles
Interference: If light is
a wave we see spreading
and addition and subtraction
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Interference
Interference: Combination of two or more waves to form
composite wave – use superposition principle.
Waves can add constructively or destructively
Conditions for interference:
1.  Coherence: the sources must maintain a constant
phase with respect to each other
2.  Monochromaticity: the sources consist of waves of a
single wavelength
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Interference – Phase Shift
Consider two traveling waves, moving through space:
In phase:
Look here as function of time
Constructive
Interference
Phase shift:
Look here as function of time
Destructive
Interference
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Interference – Phase Shift
What can introduce a phase shift?
1.  From different, out of phase sources
2.  Sources in phase, but travel different distances because
they come from different locations
constructive
destructive
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Extra Path Length
ΔL = mλ , m = 0, ± 1, ± 2,⋅ ⋅ ⋅
⇓
Constructive Interference
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Extra Path Length
ΔL = (m + 1 / 2)λ , m = 0, ± 1, ± 2,⋅ ⋅ ⋅
⇓
Destructive Interference
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Phase Shift = Extra Path?
What is exact relationship between extra path length
and phase shift?
sin(k(x + ΔL)) = sin(kx + kΔL)
2π
= sin(kx +
ΔL) ≡ sin(kx + φ )
λ
⎧
ΔL φ ⎪ m constructive
=
=⎨
λ
2π ⎪ m + 12 destructive
⎩
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Demonstration:
Microwave Interference
Two Transmitters
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=P 4&show=0
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Microwave Interference
http://youtu.be/-O8V2QHkaLI
http://web.mit.edu/viz/EM/movies/light/distant.avi
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Microwave Interference
http://youtu.be/SkEdqP86hmU
http://web.mit.edu/viz/EM/movies/light/close.avi
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Concept Question
Two Slits with Width
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Concept Question: Double Slit
Coherent monochromatic
plane waves impinge on two
apertures separated by a
distance d. An approximate
formula for the path length
difference between the two
rays shown is
1.  d sin θ
2.  L sin θ
3.  d cos θ
4.  L cos θ
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Concept Q. Answer: Double Slit
Answer: 1. Extra path length = d sin θ
The difference between
the two paths can be
seen to have this value
by geometrical
construction (using the
triangle shown in yellow).
Two In-Phase Sources: Geometry
Assuming L >> d :
Extra path length
δ = d sin(θ )
δ
φ ⎧⎪ m constructive
=
=⎨
λ 2π ⎪ m + 12 destructive
⎩
δ = d sin θ = mλ
⇒ Constructive
δ = d sin θ = (m + 12 )λ ⇒ Destructive
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Interference for Two Sources in
Phase
Assume L >> d >> λ
y = L tan θ ≈ Lsin θ
⇒ δ = d sin θ = d( y / L)
Constructive:
δ = mλ
yconst = mλ L / d; m = 0, ± 1, ⋅ ⋅ ⋅
Destructive:
δ = (m + 1/ 2)λ
ydest = (m + 1 / 2)λ L / d; m = 0, ± 1, ⋅ ⋅ ⋅
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Group Problem: Lecture Demo
!
When L = 1.16 m and d
= 0.24 m, suppose the
distance to the first
minimum is measured
to be 7.25 cm. What is
the wavelength and
frequency of the
microwaves?
The distance to the interference minima are given by
ydest = (m + 1 / 2)λ L / d; m = 0, ± 1, ⋅ ⋅ ⋅
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Appendix
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The Light Equivalent:
Two Slits
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Measure 1/10,000 of a Cm
Question: How do you measure the
wavelength of light?
Answer: Do the same experiment we
did above with microwaves, but now
with light!
First ydest = λ L / 2d
Light wavelength is smaller by 10,000 times compared to
microwave
But d can be smaller (0.1 mm instead of 0.24 m)
So y will only be 10 times smaller – still measurable
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Young’s Double-Slit Experiment
Bright Fringes: Constructive interference
Dark Fringes: Destructive interference
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Concept Q.: Two Slit Interference
A
B
In the two 2-slit interference patterns above, is the frequency
of the wave on the left (A) is larger or smaller than the
frequency of the wave on the right (B)? The slit spacing d is
the same in both cases.
1.
2.
3.
Frequency in A is larger than in frequency B
Frequency in A is smaller than infrequency B
Frequency in A is equal to frequency in B
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