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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. Math 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

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w14d1 em waves dipole radiation polarization and interference

W14D1:EM Waves, Dipole Radiation,Polarization and Interference

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

announcements

Math 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

Announcements

outline
Outline

Generating Plane EM Waves

Generating Electric Dipole EM Waves

Microwaves

Polarization

Interference

history
History

Maxwell’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

history1
History

Hertz: 1888

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

Marconi: 1894

Practical “wireless telegraphy”, commercial success

generating plane em waves

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?

slide7

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

generating plane em waves1

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.

shaking a sheet of charge
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

how to think about radiation e field
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

concept q generating plane waves
Concept Q.: Generating Plane Waves

up

down

zero

cannot tell, depends on past history

When you are pulling the charged plane down, the radiation electric field right at the position of the plane of charge is

11

concept q ans generating plane waves
Concept Q. Ans: Generating Plane Waves

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.

When you are pulling the charged plane down, the radiation electric field right at the position of the plane of charge is

12

generating electric dipole em waves

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:

generating electric dipole radiation applet

Generating Electric Dipole Radiation Applet

http://web.mit.edu/viz/EM/simulations/radiationcharge.jnlp

concept q generating plane waves1
Concept Q.: Generating Plane Waves

Up or down

Left or right

Cannot tell, depends on past history

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

15

concept q ans generating plane waves1
Concept Q. Ans: Generating Plane Waves

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.

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

16

state of polarization

State of Polarization:

Describes how the direction of the electric field

in an EM wave changes at a point in space.

  • Linear polarization
  • Circular polarization
  • Elliptical polarization
lecture demonstration polarization of microwaves k3

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

lecture demonstration polarization of radio waves dipole antenna k4

Lecture Demonstration: Polarization of Radio Waves Dipole Antenna K4

http://tsgphysics.mit.edu/front/?page=demo.php&letnum=K 4&show=0

our spark gap antenna

Oscillation after

  • breakdown! (LC)

Our spark gap antenna

1) Charging time scale (RC)

3) Repeat

spark gap antenna
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

spark gap antenna1
Spark Gap Antenna

http://web.mit.edu/viz/EM/movies/light/hiResAntenna.avi

http://youtu.be/SV4kTSbFWRc

experiment 5 spark gap generator find the angular distribution of radiation and its polarization

Experiment 5Spark Gap Generator:Find the Angular Distribution of Radiation, and its Polarization

interference the difference between waves and particles
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

26

interference1
Interference

Interference: Combination of two or more waves to form composite wave – use superposition principle.

Waves can add constructively or destructively

  • Conditions for interference:
  • Coherence: the sources must maintain a constant phase with respect to each other
  • Monochromaticity: the sources consist of waves of a single wavelength

27

interference phase shift
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

28

interference phase shift1
Interference – Phase Shift

constructive

destructive

What can introduce a phase shift?

  • From different, out of phase sources
  • Sources in phase, but travel different distances because they come from different locations

29

phase shift extra path
Phase Shift = Extra Path?

What is exact relationship between extra path length

and phase shift?

32

demonstration microwave interference two transmitters

Demonstration:Microwave InterferenceTwo Transmitters

http://tsgphysics.mit.edu/front/?page=demo.php&letnum=P 4&show=0

33

microwave interference
Microwave Interference

http://youtu.be/-O8V2QHkaLI

http://web.mit.edu/viz/EM/movies/light/distant.avi

34

microwave interference1
Microwave Interference

http://youtu.be/SkEdqP86hmUhttp://web.mit.edu/viz/EM/movies/light/close.avi

35

interference for two sources in phase
Interference for Two Sources in Phase

Constructive:

Destructive:

37

concept question double slit
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

  • d sin θ
  • L sin θ
  • d cos θ
  • L cos θ

39

concept q answer double slit
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).

group problem lecture demo

The distance to the interference minima are given by

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?

lecture demonstration double slit

Lecture Demonstration:Double Slit

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

measure 1 10 000 of a cm
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!

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

young s double slit experiment
Young’s Double-Slit Experiment

Bright Fringes: Constructive interference

Dark Fringes: Destructive interference

concept q two slit interference
Concept Q.: Two Slit Interference

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

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.

46

con q answer two slit interference
Con. Q. Answer: Two Slit Interference

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

A B

Two ways to see this:

First: By eye, ; ;

Second:

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

47