1 W14D1: EM Waves, Dipole Radiation, Polarization and Interference Today’s Reading Course Notes: Sections 13.8, 13.10,

Announcements Math Review Week 14 Tuesday 9-11 pm in PS 10 due Week 14 Tuesday at 9 pm in boxes outside or Next Reading Assignment W14D2 Course Notes: Sections

3 Outline Generating Plane EM Waves Generating Electric Dipole EM Waves Microwaves Polarization Interference

4 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

5 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

6 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?

7 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 35&show=0

8 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.

9 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

10 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

11 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.up 2.down 3.zero 4.cannot tell, depends on past history

12 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.

13 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:

14 Generating Electric Dipole Radiation Applet

15 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.Up or down 2.Left or right 3.Cannot tell, depends on past history

16 Concept Q. Ans: Generating Plane Waves The 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.

17 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.

18 Lecture Demonstration: Polarization of Microwaves K3 Some materials can absorb waves with the electric field aligned in a particular direction (for example, sunglasses) 3&show=0

19 Lecture Demonstration: Polarization of Radio Waves Dipole Antenna K4 4&show=0

20 Spark Gap Generator: An LC Oscillator This is what Hertz did in 1886

21 Our spark gap antenna 1) Charging time scale (RC) 2)Oscillation after breakdown! (LC) 3) Repeat

22 Spark Gap Antenna Accelerated charges are the source of EM waves. Most common example: Electric Dipole Radiation. t = 0t = T/4t = T/2t = T

23 Spark Gap Antenna

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

25 Interference

26 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

27 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

28 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:

29 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 constructivedestructive

30 Extra Path Length

31 Extra Path Length

32 Phase Shift = Extra Path? What is exact relationship between extra path length and phase shift?

33 Demonstration: Microwave Interference Two Transmitters 4&show=0

34 Microwave Interference

35 Microwave Interference

36 Two In-Phase Sources: Geometry

37 Interference for Two Sources in Phase Constructive: Destructive:

38 Concept Question Two Slits with Width

39 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

41 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

42 The Light Equivalent: Two Slits

43 Lecture Demonstration: Double Slit 10&show=0

44 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!

45 Young’s Double-Slit Experiment Bright Fringes: Constructive interference Dark Fringes: Destructive interference

46 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. ABAB 1.Frequency in A is larger than in frequency B 2.Frequency in A is smaller than infrequency B 3.Frequency in A is equal to frequency in B

47 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 ABAB