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W14D1:EM Waves, Dipole Radiation,Polarization and Interference

Today’s Reading Course Notes: Sections 13.8, 13.10, 14.1-14.3

AnnouncementsMath Review Week 14 Tuesday 9-11 pm in 26-152

PS 10 due Week 14 Tuesday at 9 pm in boxes outside 32-082 or 26-152

Next Reading Assignment W14D2 Course Notes: Sections 14.4-14.9

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Outline

Generating Plane EM Waves

Generating Electric Dipole EM Waves

Microwaves

Polarization

Interference

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HistoryMaxwell’s Equations: 1865

Predicted that light was an electromagnetic wave, but no way to prove this experimentally. No general acceptance of his theory

Hertz: 1888

Figured out how to generate electromagnetic waves exactly the way we do it in class today. All of a sudden, Maxwell was golden

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HistoryHertz: 1888

“There will never be any practical use for my discovery. It is a laboratory curiosity”

Marconi: 1894

Practical “wireless telegraphy”, commercial success

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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 theEnergy 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

http://peter-edx.99k.org/PlaneWave.html

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

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How to Think About Radiation E-Field

E-Field lines like strings tied to plane of charge

This is the radiation field

This is the static field

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Simple geometry:

tanE v

E c

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Concept Q.: Generating Plane WavesWhen you are pulling the charged plane down, the radiation electric field right at the position of the plane of charge is

1. up2. down3. zero4. cannot tell, depends on past history

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Concept Q. Ans: 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. Up

The radiation electric field right at the sheet resists you pulling the charged sheet down, just like tension in a string.

The work you do overcoming that resistance is the source of the energy radiated away by the wave.

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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 WavesThe point charge below got a kick a little before the moment shown. The direction of the kick was:

1. Up or down2. Left or right3. Cannot tell, depends on past history

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Concept Q. Ans: Generating Plane WavesThe point charge below got a kick a little before the moment shown. The direction of the kick was:

2. Left or right

When you move the charge left or right, it does not put a kink in the horizontal field lines, and that is what we observe above.

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State of Polarization:

1. Linear polarization

2. Circular polarization

3. Elliptical polarization

Describes how the direction of the electric field

in an EM wave changes at a point in space.

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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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Our spark gap antenna

1) Charging time scale (RC)

2) Oscillation after

breakdown! (LC)

3) Repeat

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Spark Gap Antenna

Accelerated charges are the source of EM waves. Most common example: Electric Dipole Radiation.

t = 0 t = T/4 t = T/2 t = T

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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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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 madeup of particles

Interference: If light is a wave we see spreading and addition and subtraction

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InterferenceInterference: 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

Look here as function of time

Consider two traveling waves, moving through space:

Look here as function of time

Constructive Interference

Destructive Interference

In phase:

Phase shift:

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Interference – Phase ShiftWhat 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

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Extra Path Length

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Phase Shift = Extra Path?

What is exact relationship between extra path length

and phase shift?

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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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Two In-Phase Sources: Geometry

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Interference for Two Sources in Phase

Constructive:

Destructive:

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Concept QuestionTwo 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

Concept Q. Answer: Double Slit

The difference between the two paths can be seen to have this value by geometrical construction (using the triangle shown in yellow).

Answer: 1. Extra path length = d sin θ

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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

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The Light Equivalent:Two Slits

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Lecture Demonstration:Double Slit

http://tsgphysics.mit.edu/front/?page=demo.php&letnum=P 10&show=0

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Measure 1/10,000 of a Cm

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 then the above experiment – still measurable

Question: How do you measure the wavelength of light?

Answer: Do the same experiment we did above with microwaves, but now with light!

/ 2desty L dFirst at 1st minimum

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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

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.

A B

1. Frequency in A is larger than in frequency B2. Frequency in A is smaller than infrequency B3. Frequency in A is equal to frequency in B

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Con. Q. Answer: Two Slit Interference

Two ways to see this: First: By eye, ; ;

Second:

so the smaller in B means smaller wavelength and thus higher frequency.

Answer: 2. Frequency in A is smaller than in B

A B