Chapter 33. Electromagnetic Waves

Size: px
Start display at page:

Download "Chapter 33. Electromagnetic Waves"

Transcription

1 Chapter 33 Electromagnetic Waves Today s information age is based almost entirely on the physics of electromagnetic waves. The connection between electric and magnetic fields to produce light is own of the greatest achievements produced by physics, and electromagnetic waves are at the core of many fields in science and engineering. In this chapter we introduce fundamental concepts and explore the properties of electromagnetic waves. 33-1

2 Maxwell s Rainbow The wavelength/frequency range in which electromagnetic (EM) waves (light) are visible is only a tiny fraction of the entire electromagnetic spectrum Fig Fig

3 The Travelling Electromagnetic (EM) Wave, Qualitatively An LC oscillator causes currents to flow sinusoidally, which in turn produces oscillating electric and magnetic fields, which then propagate through space as EM waves Next slide Fig Oscillation Frequency: ω = 1 LC 33-3

4 The Travelling Electromagnetic (EM) Wave, Qualitatively EM fields at P looking back toward LC oscillator r r 1. Electric E and magnetic B fields always perpendicular to direction in which wave is travelling transverse wave (Ch. 16) r r 2. E always perpendicular to B r r 3. E B always gives direction of wave travel r r 4. E and B vary sinusoidally (in time and space) and are in phase (in step) with each other Fig

5 Mathematical Description of Travelling EM Waves Electric Field: E = E ( kx ωt) m sin Magnetic Field: B = B ( kx ωt) m sin Wave Speed: c = 1 µ ε All EM waves travel a c in vacuum EM Wave Simulation Wavenumber: k = Angular frequency: 2π λ ω = 2π τ Vacuum Permittivity: ε Fig Amplitude Ratio: Vacuum Permeability: µ Em c B = E( t) Magnitude Ratio: m B() t = c 33-5

6 A Most Curious Wave Unlike all the waves discussed in Chs. 16 and 17, EM waves require no medium through/along which to travel. EM waves can travel through empty space (vacuum)! Speed of light is independent of speed of observer! You could be heading toward a light beam at the speed of light, but you would still measure c as the speed of the beam! c = m/s 33-6

7 The Travelling EM Wave, Quantitatively Induced Electric Field Changing magnetic fields produce electric fields, Faraday s law of induction dφ B Eds r r Ñ g = dt E r r Ñ g d s = ( E + de) Eh = h de Φ B = ( B)( hdx) db de db hde= hdx = dt dx dt Fig E B = x t E B = kemcos kx t and = Bmcos x t kx t Em kemcos( kx ωt) = ωbmcos( kx ωt) = c B ( ω ) ω ( ω ) m 33-7

8 The Travelling EM Wave, Quantitatively Induced Magnetic Field Changing electric fields produce magnetic fields, Maxwell s law of induction Fig dφ E Bds r r Ñ g = µε ur dt B ds r Ñ g = ( B+ db) Bh= h db dφ E de Φ E = ( E)( h dx) = h dx dt dt db hdb= µε hdx dt B E = µε x t ( ω ) µεω cos( ω ) kb cos kx t = E kx t m ( ) Em = = = c c= B µε ω k µε c µ ε m m 33-8

9 Energy Transport and the Poynting Vector EM waves carry energy. The rate of energy transport in an EM wave is characterized by the Poynting vector S r Poynting Vector: r 1 r r S = E B µ The magnitude of S is related to the rate at which energy is transported by a wave across a unit area at any instant (inst). The unit for S is (W/m 2 ) energy/time power S = = area inst area inst The direction of S r at any point gives the wave's travel direction and the direction of energy transport at that point 33-9

10 Energy Transport and the Poynting Vector r r r r Since E B E B = EB Instantaneous 1 S = 1 E energy flow rate: S = EB and since B = µ c Note that S is a function of time. The time-averaged value for S, S avg is also called the intensity I of the wave. I energy/time power = Savg = = area area 1 1 = = = sin m ( ω ) I Savg E E kx t cµ avg cµ avg E 1 m 2 E rms = I = E rms 2 cµ B ue = εe = ε( cb) = ε B = = u µε 2µ avg avg cµ B EB 33-1

11 Variation of Intensity with Distance Consider a point source S that is emitting EM waves isotropically (equally in all directions) at a rate P S. Assume energy of waves is conserved as they spread from source. How does the intesnity (power/area) change with distance r? Fig I power P = = S area 4π r

12 Radiation Pressure EM waves have linear momentum as well as energy light can exert pressure S r incident p Total absorption: p = U c p r = I c S r reflected S r incident p F = t power I = = area U t = A p energy/time area Total reflection Back along path: r p = 2 U c U = IA t IA F = (total absorption) c 2IA F = (total reflection back along path) c F p = A Radiation Pressure p r = 2 I c 33-12

13 Polarization The polarization of light is describes how the electric field in the EM wave oscillates. Vertically plane-polarized (or linearly polarized) Fig

14 Polarized Light Unpolarized or randomly polarized light has its instantaneous polarization direction vary randomly with time Fig One can produce unpolarized light by the addition (superposition) of two perpendicularly polarized waves with randomly varying amplitudes. If the two perpendicularly polarized waves have fixed amplitudes and phases, one can produce different polarizations such as circularly or elliptically polarized light. Polarized Light Simulation 33-14

15 Polarizing Sheet I I Fig Only electric field component along polarizing direction of polarizing sheet is passed (transmitted), the perpendicular component is blocked (absorbed) 33-15

16 Intensity of Transmitted Polarized Light Intensity of transmitted light, unpolarized incident light: I = 1 2 I Since only the component of the incident electric field E parallel to the polarizing axis is transmitted Fig E = E = Ecosθ transmitted Intensity of transmitted light, polarized incident light: y 2 I = I cos θ For unpolarized light, θ varies randomly in time ( 2 ) ( 2 cos θ cos θ) I = I = I = I avg avg

17 Reflection and Refraction Although light waves spread as they move from a source, often we can approximate its travel as being a straight line geometrical optics What happens when a narrow beam of light encounters a glass surface? Law of Reflection θ ' = θ Reflection: 1 1 Fig Snell s Law n sinθ sinθ Refraction: sinθ n sinθ n2 n is the index of refraction of the material = = n 33-17

18 Sound Waves For light going from n 1 to n 2 n 2 = n 1 θ 2 = θ 1 n 2 > n 1 θ 2 <θ 1, light bent towards normal n 2 < n 1 θ 2 > θ 1, light bent away from normal Fig

19 Chromatic Dispersion The index of refraction n encountered by light in any medium except vacuum depends on the wavelength of the light. So if light consisting of different wavelengths enters a material, the different wavelengths will be refracted differently chromatic dispersion Fig Fig n 2blue >n 2red Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light) or bad (e.g., chromatic aberration in lenses) 33-19

20 Chromatic Dispersion Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light) prism Fig or bad (e.g., chromatic aberration in lenses) lens 33-2

21 Rainbows Sunlight consists of all visible colors and water is dispersive, so when sunlight is refracted as it enters water droplets, is reflected off the back surface, and again is refracted as it exits the water drops, the range of angles for the exiting ray will depend on the color of the ray. Since blue is refracted more strongly than red, only droplets that are closer the the rainbow center (A) will refract/reflect blue light to the observer (O). Droplets at larger angles will still refract/reflect red light to the observer. What happens for rays that reflect twice off the back surfaces of the droplets? Fig

22 Total Internal Reflection For light that travels from a medium with a larger index of refraction to a medium with a smaller medium of refraction n 1 >n 1 θ 2 >θ 1, as θ 1 increases, θ 2 will reach 9 o (the largest possible angle for refraction) before θ 1 does. n 2 n sinθ = n sin 9 = n 1 c 2 2 Critical Angle: θ c = sin n n n 1 Fig Total internal reflection can be used, for example, to guide/contain light along an optical fiber When θ 2 > θ c no light is refracted (Snell s Law does not have a solution!) so no light is transmitted Total Internal Reflection 33-22

23 Fig In which direction does light reflecting off a lake tend to be polarized? Polarization by Reflection When the refracted ray is perpendicular to the reflected ray, the electric field parallel to the page (plane of incidence) in the medium does not produce a reflected ray since there is no component of that field perpendicular to the reflected ray (EM waves are transverse). Applications 1. Perfect window: since parallel polarization is not reflected, all of it is transmitted 2. Polarizer: only the perpendicular component is reflected, so one can select only this component of the incident polarization Brewster s Law θb + θr = 9 n sinθ = n sinθ 1 B 2 r ( ) n sinθ = n sin 9 θ = n cosθ 1 n2 Brewster Angle: θ B = tan n 1 B 2 B 2 B

Electromagnetic Waves. Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)

Electromagnetic Waves. Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) PH 222-3A Spring 2007 Electromagnetic Waves Lecture 22 Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 33 Electromagnetic Waves Today s information age is based almost

More information

PH 222-2C Fall Electromagnetic Waves Lectures Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)

PH 222-2C Fall Electromagnetic Waves Lectures Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) PH 222-2C Fall 2012 Electromagnetic Waves Lectures 21-22 Chapter 33 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 33 Electromagnetic Waves Today s information age is based almost

More information

Chapter 1 - The Nature of Light

Chapter 1 - The Nature of Light David J. Starling Penn State Hazleton PHYS 214 Electromagnetic radiation comes in many forms, differing only in wavelength, frequency or energy. Electromagnetic radiation comes in many forms, differing

More information

Lecture 34: MON 13 APR Ch ,5

Lecture 34: MON 13 APR Ch ,5 Physics 2102 Jonathan Dowling James Clerk Maxwell (1831-1879) Lecture 34: MON 13 APR Ch.33.1 3,5 3,5 7: E&M Waves MT03 Avg: 65/100 Q1/P3 K. Schafer Office hours: MW 1:30-2:30 pm 222B Nicholson P1/Q2 J.

More information

Physics 214 Course Overview

Physics 214 Course Overview Physics 214 Course Overview Lecturer: Mike Kagan Course topics Electromagnetic waves Optics Thin lenses Interference Diffraction Relativity Photons Matter waves Black Holes EM waves Intensity Polarization

More information

Lecture 38: FRI 24 APR Ch.33 Electromagnetic Waves

Lecture 38: FRI 24 APR Ch.33 Electromagnetic Waves Physics 2113 Jonathan Dowling Heinrich Hertz (1857 1894) Lecture 38: FRI 24 APR Ch.33 Electromagnetic Waves Maxwell Equations in Empty Space: E da = 0 S B da = 0 S C C B ds = µ ε 0 0 E ds = d dt d dt S

More information

Chapter 34. Electromagnetic Waves

Chapter 34. Electromagnetic Waves Chapter 34 Electromagnetic Waves The Goal of the Entire Course Maxwell s Equations: Maxwell s Equations James Clerk Maxwell 1831 1879 Scottish theoretical physicist Developed the electromagnetic theory

More information

Chapter 33: ELECTROMAGNETIC WAVES 559

Chapter 33: ELECTROMAGNETIC WAVES 559 Chapter 33: ELECTROMAGNETIC WAVES 1 Select the correct statement: A ultraviolet light has a longer wavelength than infrared B blue light has a higher frequency than x rays C radio waves have higher frequency

More information

Electromagnetic fields and waves

Electromagnetic fields and waves Electromagnetic fields and waves Maxwell s rainbow Outline Maxwell s equations Plane waves Pulses and group velocity Polarization of light Transmission and reflection at an interface Macroscopic Maxwell

More information

EM Waves. From previous Lecture. This Lecture More on EM waves EM spectrum Polarization. Displacement currents Maxwell s equations EM Waves

EM Waves. From previous Lecture. This Lecture More on EM waves EM spectrum Polarization. Displacement currents Maxwell s equations EM Waves EM Waves This Lecture More on EM waves EM spectrum Polarization From previous Lecture Displacement currents Maxwell s equations EM Waves 1 Reminders on waves Traveling waves on a string along x obey the

More information

LECTURE 23: LIGHT. Propagation of Light Huygen s Principle

LECTURE 23: LIGHT. Propagation of Light Huygen s Principle LECTURE 23: LIGHT Propagation of Light Reflection & Refraction Internal Reflection Propagation of Light Huygen s Principle Each point on a primary wavefront serves as the source of spherical secondary

More information

Energy Carried by Electromagnetic Waves. Momentum and Radiation Pressure of an Electromagnetic Wave.

Energy Carried by Electromagnetic Waves. Momentum and Radiation Pressure of an Electromagnetic Wave. Today s agenda: Electromagnetic Waves. Energy Carried by Electromagnetic Waves. Momentum and Radiation Pressure of an Electromagnetic Wave. Maxwell s Equations Recall: EdA Eds q enclosed o d dt B Bds=μ

More information

LECTURE 23: LIGHT. Propagation of Light Huygen s Principle

LECTURE 23: LIGHT. Propagation of Light Huygen s Principle LECTURE 23: LIGHT Propagation of Light Reflection & Refraction Internal Reflection Propagation of Light Huygen s Principle Each point on a primary wavefront serves as the source of spherical secondary

More information

LC circuit: Energy stored. This lecture reviews some but not all of the material that will be on the final exam that covers in Chapters

LC circuit: Energy stored. This lecture reviews some but not all of the material that will be on the final exam that covers in Chapters Disclaimer: Chapter 29 Alternating-Current Circuits (1) This lecture reviews some but not all of the material that will be on the final exam that covers in Chapters 29-33. LC circuit: Energy stored LC

More information

Polarization. If the original light is initially unpolarized, the transmitted intensity I is half the original intensity I 0 :

Polarization. If the original light is initially unpolarized, the transmitted intensity I is half the original intensity I 0 : 33-4 33-4 Polarization Polarization Electromagnetic waves are polarized if their electric field vectors are all in a single plane, called the plane of oscillation. Light waves from common sources are not

More information

Class 30: Outline. Hour 1: Traveling & Standing Waves. Hour 2: Electromagnetic (EM) Waves P30-

Class 30: Outline. Hour 1: Traveling & Standing Waves. Hour 2: Electromagnetic (EM) Waves P30- Class 30: Outline Hour 1: Traveling & Standing Waves Hour : Electromagnetic (EM) Waves P30-1 Last Time: Traveling Waves P30- Amplitude (y 0 ) Traveling Sine Wave Now consider f(x) = y = y 0 sin(kx): π

More information

MCQs E M WAVES. Physics Without Fear.

MCQs E M WAVES. Physics Without Fear. MCQs E M WAVES Physics Without Fear Electromagnetic Waves At A Glance Ampere s law B. dl = μ 0 I relates magnetic fields due to current sources. Maxwell argued that this law is incomplete as it does not

More information

Exam 3: Tuesday, April 18, 5:00-6:00 PM

Exam 3: Tuesday, April 18, 5:00-6:00 PM Exam 3: Tuesday, April 18, 5:-6: PM Test rooms: Instructor Sections Room Dr. Hale F, H 14 Physics Dr. Kurter, N 15 CH Dr. Madison K, M 199 Toomey Dr. Parris J, L -1 ertelsmeyer Mr. Upshaw A, C, E, G G-3

More information

Electromagnetic Waves

Electromagnetic Waves Chapter 32 Electromagnetic Waves PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 32 To learn why a light

More information

Conceptual Physics. Luis A. Anchordoqui. Department of Physics and Astronomy Lehman College, City University of New York. Lesson VI October 3, 2017

Conceptual Physics. Luis A. Anchordoqui. Department of Physics and Astronomy Lehman College, City University of New York. Lesson VI October 3, 2017 Conceptual Physics Luis A. Anchordoqui Department of Physics and Astronomy Lehman College, City University of New York Lesson VI October 3, 2017 https://arxiv.org/abs/1711.07445 L. A. Anchordoqui (CUNY)

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Review Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 34! The speed of an electromagnetic wave can be expressed in terms of two fundamental constants related to electric fields and magnetic

More information

UNIT 102-6: ELECTROMAGNETIC WAVES AND POLARIZATION Approximate Time Three 100-minute Sessions

UNIT 102-6: ELECTROMAGNETIC WAVES AND POLARIZATION Approximate Time Three 100-minute Sessions Name St.No. - Date(YY/MM/DD) / / Section UNIT 102-6: ELECTROMAGNETIC WAVES AND POLARIZATION Approximate Time Three 100-minute Sessions Hey diddle diddle, what kind of riddle Is this nature of light? Sometimes

More information

PHYS 1444 Section 003 Lecture #23

PHYS 1444 Section 003 Lecture #23 PHYS 1444 Section 3 Lecture #3 Monday, Nov. 8, 5 EM Waves from Maxwell s Equations Speed of EM Waves Light as EM Wave Electromagnetic Spectrum Energy in EM Waves Energy Transport The epilogue Today s homework

More information

LECTURE 11 ELECTROMAGNETIC WAVES & POLARIZATION. Instructor: Kazumi Tolich

LECTURE 11 ELECTROMAGNETIC WAVES & POLARIZATION. Instructor: Kazumi Tolich LECTURE 11 ELECTROMAGNETIC WAVES & POLARIZATION Instructor: Kazumi Tolich Lecture 11 2 25.5 Electromagnetic waves Induced fields Properties of electromagnetic waves Polarization Energy of electromagnetic

More information

Chapter 29: Maxwell s Equation and EM Waves. Slide 29-1

Chapter 29: Maxwell s Equation and EM Waves. Slide 29-1 Chapter 29: Maxwell s Equation and EM Waves Slide 29-1 Equations of electromagnetism: a review We ve now seen the four fundamental equations of electromagnetism, here listed together for the first time.

More information

- 1 - θ 1. n 1. θ 2. mirror. object. image

- 1 - θ 1. n 1. θ 2. mirror. object. image TEST 5 (PHY 50) 1. a) How will the ray indicated in the figure on the following page be reflected by the mirror? (Be accurate!) b) Explain the symbols in the thin lens equation. c) Recall the laws governing

More information

CHAPTER 32: ELECTROMAGNETIC WAVES

CHAPTER 32: ELECTROMAGNETIC WAVES CHAPTER 32: ELECTROMAGNETIC WAVES For those of you who are interested, below are the differential, or point, form of the four Maxwell s equations we studied this semester. The version of Maxwell s equations

More information

Maxwell s equations and EM waves. From previous Lecture Time dependent fields and Faraday s Law

Maxwell s equations and EM waves. From previous Lecture Time dependent fields and Faraday s Law Maxwell s equations and EM waves This Lecture More on Motional EMF and Faraday s law Displacement currents Maxwell s equations EM Waves From previous Lecture Time dependent fields and Faraday s Law 1 Radar

More information

Waves & Oscillations

Waves & Oscillations Physics 42200 Waves & Oscillations Lecture 32 Electromagnetic Waves Spring 2016 Semester Matthew Jones Electromagnetism Geometric optics overlooks the wave nature of light. Light inconsistent with longitudinal

More information

: Imaging Systems Laboratory II. Laboratory 6: The Polarization of Light April 16 & 18, 2002

: Imaging Systems Laboratory II. Laboratory 6: The Polarization of Light April 16 & 18, 2002 151-232: Imaging Systems Laboratory II Laboratory 6: The Polarization of Light April 16 & 18, 22 Abstract. In this lab, we will investigate linear and circular polarization of light. Linearly polarized

More information

Oscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1

Oscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1 Oscillations and Electromagnetic Waves March 30, 2014 Chapter 31 1 Three Polarizers! Consider the case of unpolarized light with intensity I 0 incident on three polarizers! The first polarizer has a polarizing

More information

Clicker Question. Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no

Clicker Question. Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following equation a solution to the wave equation: y(x,t)=a sin(kx-ωt) (a) yes (b) no Is the following

More information

第 1 頁, 共 8 頁 Chap32&Chap33 1. Test Bank, Question 2 Gauss' law for magnetism tells us: the net charge in any given volume that the line integral of a magnetic around any closed loop must vanish the magnetic

More information

Light propagation. Ken Intriligator s week 7 lectures, Nov.12, 2013

Light propagation. Ken Intriligator s week 7 lectures, Nov.12, 2013 Light propagation Ken Intriligator s week 7 lectures, Nov.12, 2013 What is light? Old question: is it a wave or a particle? Quantum mechanics: it is both! 1600-1900: it is a wave. ~1905: photons Wave:

More information

Propagation of EM Waves in material media

Propagation of EM Waves in material media Propagation of EM Waves in material media S.M.Lea 09 Wave propagation As usual, we start with Maxwell s equations with no free charges: D =0 B =0 E = B t H = D t + j If we now assume that each field has

More information

Dispersion. f (increasing frequency)

Dispersion. f (increasing frequency) Dispersion The index of refraction n is usually a property of the medium but equally important, it also varies with the frequency f of light dispersion. n typically increases with increasing f. f (increasing

More information

Problem set 3. Electromagnetic waves

Problem set 3. Electromagnetic waves Second Year Electromagnetism Michaelmas Term 2017 Caroline Terquem Problem set 3 Electromagnetic waves Problem 1: Poynting vector and resistance heating This problem is not about waves but is useful to

More information

Skoog Chapter 6 Introduction to Spectrometric Methods

Skoog Chapter 6 Introduction to Spectrometric Methods Skoog Chapter 6 Introduction to Spectrometric Methods General Properties of Electromagnetic Radiation (EM) Wave Properties of EM Quantum Mechanical Properties of EM Quantitative Aspects of Spectrochemical

More information

Electromagnetic Waves Across Interfaces

Electromagnetic Waves Across Interfaces Lecture 1: Foundations of Optics Outline 1 Electromagnetic Waves 2 Material Properties 3 Electromagnetic Waves Across Interfaces 4 Fresnel Equations 5 Brewster Angle 6 Total Internal Reflection Christoph

More information

LECTURE 11 ELECTROMAGNETIC WAVES & POLARIZATION. Instructor: Kazumi Tolich

LECTURE 11 ELECTROMAGNETIC WAVES & POLARIZATION. Instructor: Kazumi Tolich LECTURE 11 ELECTROMAGNETIC WAVES & POLARIZATION Instructor: Kazumi Tolich Lecture 11 2 25.5 Electromagnetic waves Induced fields Properties of electromagnetic waves Polarization Energy of electromagnetic

More information

Impedance/Reactance Problems

Impedance/Reactance Problems Impedance/Reactance Problems. Consider the circuit below. An AC sinusoidal voltage of amplitude V and frequency ω is applied to the three capacitors, each of the same capacitance C. What is the total reactance

More information

Light Waves and Polarization

Light Waves and Polarization Light Waves and Polarization Xavier Fernando Ryerson Communications Lab http://www.ee.ryerson.ca/~fernando The Nature of Light There are three theories explain the nature of light: Quantum Theory Light

More information

Lecture 19 Optical MEMS (1)

Lecture 19 Optical MEMS (1) EEL6935 Advanced MEMS (Spring 5) Instructor: Dr. Huikai Xie Lecture 19 Optical MEMS (1) Agenda: Optics Review EEL6935 Advanced MEMS 5 H. Xie 3/8/5 1 Optics Review Nature of Light Reflection and Refraction

More information

Electromagnetic Waves Properties. The electric and the magnetic field, associated with an electromagnetic wave, propagating along the z=axis. Can be represented by E = E kˆ, = iˆ E = E ˆj, = ˆj b) E =

More information

1 Fundamentals of laser energy absorption

1 Fundamentals of laser energy absorption 1 Fundamentals of laser energy absorption 1.1 Classical electromagnetic-theory concepts 1.1.1 Electric and magnetic properties of materials Electric and magnetic fields can exert forces directly on atoms

More information

Topic 4: Waves 4.3 Wave characteristics

Topic 4: Waves 4.3 Wave characteristics Guidance: Students will be expected to calculate the resultant of two waves or pulses both graphically and algebraically Methods of polarization will be restricted to the use of polarizing filters and

More information

Lecture 1 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell

Lecture 1 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell Lecture 1 Notes, Electromagnetic Theory II Dr. Christopher S. Baird, faculty.uml.edu/cbaird University of Massachusetts Lowell 1. Overview of the Course - Last semester we covered electrostatics, magnetostatics,

More information

POLARISATION. We have not really discussed the direction of the Electric field other that that it is perpendicular to the direction of motion.

POLARISATION. We have not really discussed the direction of the Electric field other that that it is perpendicular to the direction of motion. POLARISATION Light is a transverse electromagnetic wave. We have not really discussed the direction of the Electric field other that that it is perpendicular to the direction of motion. If the E field

More information

Wave Phenomena Physics 15c. Lecture 15 Reflection and Refraction

Wave Phenomena Physics 15c. Lecture 15 Reflection and Refraction Wave Phenomena Physics 15c Lecture 15 Reflection and Refraction What We (OK, Brian) Did Last Time Discussed EM waves in vacuum and in matter Maxwell s equations Wave equation Plane waves E t = c E B t

More information

Physics Lecture 40: FRI3 DEC

Physics Lecture 40: FRI3 DEC Physics 3 Physics 3 Lecture 4: FRI3 DEC Review of concepts for the final exam Electric Fields Electric field E at some point in space is defined as the force divided by the electric charge. Force on charge

More information

Polarization of light

Polarization of light Laboratory#8 Phys4480/5480 Dr. Cristian Bahrim Polarization of light Light is a transverse electromagnetic wave (EM) which travels due to an electric field and a magnetic field oscillating in phase and

More information

Yell if you have any questions

Yell if you have any questions Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 Before Starting All of your grades should now be posted

More information

Light as a Transverse Wave.

Light as a Transverse Wave. Waves and Superposition (Keating Chapter 21) The ray model for light (i.e. light travels in straight lines) can be used to explain a lot of phenomena (like basic object and image formation and even aberrations)

More information

Electromagnetic wave energy & polarization

Electromagnetic wave energy & polarization Phys 0 Lecture 6 Electromagnetic wave energy & polarization Today we will... Learn about properties p of electromagnetic waves Energy density & intensity Polarization linear, circular, unpolarized Apply

More information

Wave Propagation in Uniaxial Media. Reflection and Transmission at Interfaces

Wave Propagation in Uniaxial Media. Reflection and Transmission at Interfaces Lecture 5: Crystal Optics Outline 1 Homogeneous, Anisotropic Media 2 Crystals 3 Plane Waves in Anisotropic Media 4 Wave Propagation in Uniaxial Media 5 Reflection and Transmission at Interfaces Christoph

More information

Today in Physics 218: Fresnel s equations

Today in Physics 218: Fresnel s equations Today in Physics 8: Fresnel s equations Transmission and reflection with E parallel to the incidence plane The Fresnel equations Total internal reflection Polarization on reflection nterference R 08 06

More information

in Electromagnetics Numerical Method Introduction to Electromagnetics I Lecturer: Charusluk Viphavakit, PhD

in Electromagnetics Numerical Method Introduction to Electromagnetics I Lecturer: Charusluk Viphavakit, PhD 2141418 Numerical Method in Electromagnetics Introduction to Electromagnetics I Lecturer: Charusluk Viphavakit, PhD ISE, Chulalongkorn University, 2 nd /2018 Email: charusluk.v@chula.ac.th Website: Light

More information

The Quantum Theory of Atoms and Molecules: Waves and Optics. Hilary Term Dr Grant Ritchie

The Quantum Theory of Atoms and Molecules: Waves and Optics. Hilary Term Dr Grant Ritchie The Quantum Theory of Atoms and Molecules: Waves and Optics Hilary Term 008 Dr Grant Ritchie Wave motion - travelling waves Waves are collective bulk disturbances, whereby the motion at one position is

More information

CHAPTER 9 ELECTROMAGNETIC WAVES

CHAPTER 9 ELECTROMAGNETIC WAVES CHAPTER 9 ELECTROMAGNETIC WAVES Outlines 1. Waves in one dimension 2. Electromagnetic Waves in Vacuum 3. Electromagnetic waves in Matter 4. Absorption and Dispersion 5. Guided Waves 2 Skip 9.1.1 and 9.1.2

More information

72. (30.2) Interaction between two parallel current carrying wires.

72. (30.2) Interaction between two parallel current carrying wires. 7. (3.) Interaction between two parallel current carrying wires. Two parallel wires carrying currents exert forces on each other. Each current produces a agnetic field in which the other current is placed.

More information

Electromagnetic Waves

Electromagnetic Waves Electromagnetic Waves As the chart shows, the electromagnetic spectrum covers an extremely wide range of wavelengths and frequencies. Though the names indicate that these waves have a number of sources,

More information

OPSE FINAL EXAM Fall 2016 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT.

OPSE FINAL EXAM Fall 2016 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. CLOSED BOOK. Equation Sheet is provided. YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED. (Except dimensionless units like

More information

Chapter 31. Faraday s Law

Chapter 31. Faraday s Law Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field B s II I d d μ o d μo με o o E ds E B Induction A loop of wire is connected to a sensitive ammeter

More information

Chapter 34. Electromagnetic Waves

Chapter 34. Electromagnetic Waves Chapter 34 Electromagnetic Waves Waves If we wish to talk about electromagnetism or light we must first understand wave motion. If you drop a rock into the water small ripples are seen on the surface of

More information

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Lesson 7 Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit Alternating Current Electromagnetic

More information

Summary of Beam Optics

Summary of Beam Optics Summary of Beam Optics Gaussian beams, waves with limited spatial extension perpendicular to propagation direction, Gaussian beam is solution of paraxial Helmholtz equation, Gaussian beam has parabolic

More information

SECTION 3 & 4 LIGHT WAVES & INFORMATION TRANSFER

SECTION 3 & 4 LIGHT WAVES & INFORMATION TRANSFER SECTION 3 & 4 LIGHT WAVES & INFORMATION TRANSFER Light Waves Light is a type of energy that travels as waves. Light is different than other waves because it does not need matter to travel. Light waves

More information

Chapter 9. Reflection, Refraction and Polarization

Chapter 9. Reflection, Refraction and Polarization Reflection, Refraction and Polarization Introduction When you solved Problem 5.2 using the standing-wave approach, you found a rather curious behavior as the wave propagates and meets the boundary. A new

More information

PHY2049 Fall11. Final Exam Solutions (1) 700 N (2) 350 N (3) 810 N (4) 405 N (5) 0 N

PHY2049 Fall11. Final Exam Solutions (1) 700 N (2) 350 N (3) 810 N (4) 405 N (5) 0 N Exam Solutions 1. Three charges form an equilateral triangle of side length d = 2 cm. The top charge is q3 = 3 μc, while the bottom two are q1 = q2 = - 6 μc. What is the magnitude of the net force acting

More information

ELECTROMAGNETIC WAVES

ELECTROMAGNETIC WAVES UNIT V ELECTROMAGNETIC WAVES Weightage Marks : 03 Displacement current, electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. Electromagnetic

More information

Lecture 14 (Poynting Vector and Standing Waves) Physics Spring 2018 Douglas Fields

Lecture 14 (Poynting Vector and Standing Waves) Physics Spring 2018 Douglas Fields Lecture 14 (Poynting Vector and Standing Waves) Physics 6-01 Spring 018 Douglas Fields Reading Quiz For the wave described by E E ˆsin Max j kz t, what is the direction of the Poynting vector? A) +x direction

More information

Class 15 : Electromagnetic Waves

Class 15 : Electromagnetic Waves Class 15 : Electromagnetic Waves Wave equations Why do electromagnetic waves arise? What are their properties? How do they transport energy from place to place? Recap (1) In a region of space containing

More information

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/3

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/3 Physics 201 p. 1/3 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/3 What are electromagnetic waves? Electromagnetic waves consist of electric fields and magnetic fields which

More information

Lab #13: Polarization

Lab #13: Polarization Lab #13: Polarization Introduction In this experiment we will investigate various properties associated with polarized light. We will study both its generation and application. Real world applications

More information

Electromagnetic Waves

Electromagnetic Waves Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 23 Electromagnetic Waves Marilyn Akins, PhD Broome Community College Electromagnetic Theory Theoretical understanding of electricity and magnetism

More information

Plane Waves Part II. 1. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when

Plane Waves Part II. 1. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when Plane Waves Part II. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when (a) The angle of incidence is equal to the Brewster angle with E field perpendicular

More information

Polarization of Light and Birefringence of Materials

Polarization of Light and Birefringence of Materials Polarization of Light and Birefringence of Materials Ajit Balagopal (Team Members Karunanand Ogirala, Hui Shen) ECE 614- PHOTONIC INFORMATION PROCESSING LABORATORY Abstract-- In this project, we study

More information

(a) Show that the amplitudes of the reflected and transmitted waves, corrrect to first order

(a) Show that the amplitudes of the reflected and transmitted waves, corrrect to first order Problem 1. A conducting slab A plane polarized electromagnetic wave E = E I e ikz ωt is incident normally on a flat uniform sheet of an excellent conductor (σ ω) having thickness D. Assume that in space

More information

Goal: The theory behind the electromagnetic radiation in remote sensing. 2.1 Maxwell Equations and Electromagnetic Waves

Goal: The theory behind the electromagnetic radiation in remote sensing. 2.1 Maxwell Equations and Electromagnetic Waves Chapter 2 Electromagnetic Radiation Goal: The theory behind the electromagnetic radiation in remote sensing. 2.1 Maxwell Equations and Electromagnetic Waves Electromagnetic waves do not need a medium to

More information

Light - electromagnetic radiation

Light - electromagnetic radiation Astronomy & Light Astronomy is a science In science we know by doing experiments When multiple experiments give the same results we develop theories and laws In astronomy many of the experiments are done

More information

16. More About Polarization

16. More About Polarization 16. More About Polarization Polarization control Wave plates Circular polarizers Reflection & polarization Scattering & polarization Birefringent materials have more than one refractive index A special

More information

Lecture 5: Polarization. Polarized Light in the Universe. Descriptions of Polarized Light. Polarizers. Retarders. Outline

Lecture 5: Polarization. Polarized Light in the Universe. Descriptions of Polarized Light. Polarizers. Retarders. Outline Lecture 5: Polarization Outline 1 Polarized Light in the Universe 2 Descriptions of Polarized Light 3 Polarizers 4 Retarders Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2016,

More information

Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation.

Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation. Use the following to answer question 1. Two point charges, A and B, lie along a line separated by a distance L. The point x is the midpoint of their separation. 1. Which combination of charges would yield

More information

Wave Phenomena Physics 15c

Wave Phenomena Physics 15c Wave Phenomena Physics 15c Lecture 15 lectromagnetic Waves (H&L Sections 9.5 7) What We Did Last Time! Studied spherical waves! Wave equation of isotropic waves! Solution e! Intensity decreases with! Doppler

More information

Yell if you have any questions

Yell if you have any questions Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 efore Starting All of your grades should now be posted

More information

Chapter 33 Nature and Propagation of Light. From vision to digital camera to rainbows to pictures of the early universe light is all around us

Chapter 33 Nature and Propagation of Light. From vision to digital camera to rainbows to pictures of the early universe light is all around us Chapter 33 Nature and Propagation of Light From vision to digital camera to rainbows to pictures of the early universe light is all around us Introduction A coating of oil on water or a delicate glass

More information

Exam 3 Solutions. The induced EMF (magnitude) is given by Faraday s Law d dt dt The current is given by

Exam 3 Solutions. The induced EMF (magnitude) is given by Faraday s Law d dt dt The current is given by PHY049 Spring 008 Prof. Darin Acosta Prof. Selman Hershfield April 9, 008. A metal rod is forced to move with constant velocity of 60 cm/s [or 90 cm/s] along two parallel metal rails, which are connected

More information

Interference. Gambar: Museum Victoria Australia

Interference. Gambar: Museum Victoria Australia Interference Gambar: Museum Victoria Australia Formulation of Interference Intensity Superposition between two waves (point sources) Two separate point sources S 1 (x 1 ) and S 2 (x 2 ) generate EM waves

More information

Electromagnetic Waves

Electromagnetic Waves Physics 102: Lecture 15 Electromagnetic Waves Energy & Polarization Physics 102: Lecture 15, Slide 1 Checkpoint 1.1, 1.2 y E x loop in xy plane loop in xz plane A B C Physics 102: Lecture 15, Slide 2 Propagation

More information

Chapter 31. Faraday s Law

Chapter 31. Faraday s Law Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field dφ B ( I I ) E d s = µ o + d = µ o I+ µ oεo ds E B 2 Induction A loop of wire is connected to a sensitive

More information

Measurements in Optics for Civil Engineers

Measurements in Optics for Civil Engineers Measurements in Optics for Civil Engineers I. FOCAL LENGTH OF LENSES The behavior of simplest optical devices can be described by the method of geometrical optics. For convex or converging and concave

More information

Vågrörelselära och optik

Vågrörelselära och optik Vågrörelselära och optik Harmonic oscillation: Experiment Experiment to find a mathematical description of harmonic oscillation Kapitel 14 Harmonisk oscillator 1 2 Harmonic oscillation: Experiment Harmonic

More information

Chapter 31 Maxwell s Equations and Electromagnetic Waves. Copyright 2009 Pearson Education, Inc.

Chapter 31 Maxwell s Equations and Electromagnetic Waves. Copyright 2009 Pearson Education, Inc. Chapter 31 Maxwell s Equations and Electromagnetic Waves Units of Chapter 31 Changing Electric Fields Produce Magnetic Fields; Ampère s Law and Displacement Current Gauss s Law for Magnetism Maxwell s

More information

Massachusetts Institute of Technology Physics 8.03 Practice Final Exam 3

Massachusetts Institute of Technology Physics 8.03 Practice Final Exam 3 Massachusetts Institute of Technology Physics 8.03 Practice Final Exam 3 Instructions Please write your solutions in the white booklets. We will not grade anything written on the exam copy. This exam is

More information

Electromagnetic Radiation. Physical Principles of Remote Sensing

Electromagnetic Radiation. Physical Principles of Remote Sensing Electromagnetic Radiation Physical Principles of Remote Sensing Outline for 4/3/2003 Properties of electromagnetic radiation The electromagnetic spectrum Spectral emissivity Radiant temperature vs. kinematic

More information

Electrodynamics I Final Exam - Part A - Closed Book KSU 2005/12/12 Electro Dynamic

Electrodynamics I Final Exam - Part A - Closed Book KSU 2005/12/12 Electro Dynamic Electrodynamics I Final Exam - Part A - Closed Book KSU 2005/12/12 Name Electro Dynamic Instructions: Use SI units. Short answers! No derivations here, just state your responses clearly. 1. (2) Write an

More information

Basics of electromagnetic response of materials

Basics of electromagnetic response of materials Basics of electromagnetic response of materials Microscopic electric and magnetic field Let s point charge q moving with velocity v in fields e and b Force on q: F e F qeqvb F m Lorenz force Microscopic

More information

EA Notes (Scen 101), Tillery Chapter 7. Light

EA Notes (Scen 101), Tillery Chapter 7. Light EA Notes (Scen 101), Tillery Chapter 7 Light Introduction Light is hard to study because you can't see it, you only see it's effects. Newton tried to explain the energy in a light beam as the KE of a particle

More information

CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter

CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter 1 Announcements Add to your notes of Chapter 1 Analytical sensitivity γ=m/s s Homework Problems 1-9, 1-10 Challenge

More information

CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter

CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter Announcements Add to your notes of Chapter 1 Analytical sensitivity γ=m/s s Homework Problems 1-9, 1-10 Challenge

More information