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Physics 273 - Fall 2006

Introductory Physics:
Waves and Optics

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Final exam:  Monday 12/18/06  8:00-10:00 AM

Course Evaluations On Line

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Syllabus Weekly Assignments
Solution Sets

Classroom Demonstrations

Course Description

Pre-requisites:  Phys 272 (fields) and Math 241 (multivariable calculus)
Co-requisites:  Math 246  or Math 414 (differential eqns)

Content:  Oscillations and AC circuits, Fourier series and integrals, waves on strings, sound; electromagnetic waves from Maxwell's equations in differential form; physical optics

Phys 273H - Students in 273H will be assigned one or two extra  problems on each problem set.



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Physics 273 - Introductory Physics:  Waves and Optics

Instructor:  Professor E. Williams  (http://www.physics.umd.edu/spg/)
Room 2332 Physics,
Phone 301-405-6156
course web page:   http://www.physics.umd.edu/courses/Phys273/williams06/index.html
e-mail:  edw@physics.umd.edu (include Phys 273 in subject line - otherwise e-mail may not be opened)
Office hours:  Mon, Tue 1-2 PM (or see me by appointment)

Teaching Assistant:  Yiwei Chen
e-mail:  Yiwei Chen <yiwei@mailfw1.umd.edu>

Class Location:

M Tu W Th  9:00 AM, Room 0405 Physics

Hirose and Langren, Introduction to Wave Phenomena, Krieger Publishing 2003
ISBN:  1-57524-231-1
Tipler and Mosca,  Physics for Scientists and Engineers, 5e, Vol. II, W.H. Freeman and Co.  2004.
ISBN:  0-7167-0810-8
You should also have an introductory Physics text (mechanics) for reference and review, for instance Volume I of Tipler and Mosca.

Course Outline:  We will be covering material in Ch. 1-14 of Hirose and Langren at approximately one chapter per week.  Not all material in each chapter will be covered.    Parallel material from Tipler and Mosca, chapters 25, 29 - 34 will be assigned as reading and in problem sets.   Material from Tipler Ch. 14-16 will be cited, as needed, as an example of material that can be found in your introductory Physics text. 

Aug. 30 -  Sept. 7      H&L Ch. 1,   reference example (Tipler, Ch. 14)
Sept.   7 -  Sept. 14    H&L Ch. 3,   Tipler Ch. 25, 29
Sept.  14 - Sept. 21    H&L Ch. 2 & 13,   reference example (Tipler Ch. 15)
Sept.  21 - Sept. 28    H&L Ch. 2, 4 & 13,  reference example (Tipler Ch. 15, 16)
    First Exam:  Oct. 3
Sept.  28 - Oct. 12      H&L Ch. 5, 7 & 8
Oct.   12 - Oct. 19      H&L Ch. 6 & 9
Oct.   19 - Oct. 26      H&L Ch. 9, Tipler Ch. 25
Oct.   26 - Nov.  2      H&L Ch. 9, Tipler Ch. 30
    Second Exam:  Nov. 7
Nov.    2 - Nov. 16     H&L  Ch. 11, Tipler Ch. 31
Nov.  16 - Nov. 28     H&L  Ch. 11, Tipler Ch. 33***   note Tuesday due date
Nov.  28 - Dec.   5      H&L  Ch. 12, Tipler Ch. 32***   note Tuesday due date
Dec.    5 -  Dec. 13     H&L  Ch. 12, Tipler Ch. 32***    note Tuesday due date
    Final Exam
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1. Problem sets, 1 set per week, due Thursday at or before the beginning of class.
Typically 6 - 8 problems assigned from the text books. 
STAPLE your multi-page homework solutions. 
2. On-line "Quizzes",  1 per week.  These will be  WebAssign problems chosen to encourage study of the basic concepts.
3. Exams:   October 3,  Nov. 7
4. Final Exam:  Cumulative examination with an emphasis on material after exam #2.
Monday, December 18, 8:00-10:00 AM
Use of a calculator is allowed and expected on examinations, quizzes and problem sets.  Please remember to bring your own to exams.

Accommodations for Students with Disabilities:

The University has a legal obligation to provide appropriate accommodations for students with documented disabilities.   In order to ascertain what accommodations may need to be provided, students with disabilities should inform me of their needs in the first week of the semester. 

Online "Quizzes" - 10%
Problem sets:          25%  
Exams     Exam 1:  20%
                Exam 2:  20%
                Final:      25%
Regular attendance and class participation is expected, and will serve as a differentiator for borderline grades.  Examples and demonstrations presented in class will be included in the material covered by examinations.  You should keep a well-organized class notebook and bring it with you when you need to discuss course material with the instructor or TA.  

Partial credit will be assigned on problem set and exam problems where work is clearly presented. 

Missed assignments or exams

Late problem sets or quizzes will not be accepted.  The two lowest problem set scores and quiz scores will be dropped.   This is your insurance policy for unforeseen events - don't intentionally skip two assignments and then find yourself without an option when the dog eats your homework. 

 Makeup examinations will only be given for those with a valid documented excuse (doctor's note, accident report, certifiable religious observance,  etc.).  If you know ahead of time that you will miss an exam, you must notify me before the exam.   If you miss an exam due to an emergency, let me know as soon as possible afterwards.   I consider requests for make-ups or any other special consideration to be governed by the precepts of academic honesty. 

Academic Honesty

Working together on assignments is encouraged.  However, each student is expected to do the assigned problems and write the problem sets independently, and hand in his or her own work for grading.  Examinations are closed book and are expected to be worked totally independently.   I consider requests for make-ups or any other special consideration to be governed by the precepts of academic honesty.  

For any questions about academic honesty, see University policies at:


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Assignment 12

Reading:  H&L:   Chapter 12, sections 6 - 9
                Tipler:   Chapter 32, Sections 2, 4

WebAssign Quiz # 12: Due Monday, December 11, 9 AM

Problem Set # 12
Due:  Tuesday Dec. 12

Phys 273 and 273H:    Problem 1  (see below)
                                    Tipler Ch 32 # 49, 54,  61, 76, 90, 99, 102

Phys 273H:                 H&L Ch. 12 # 16 and 19

Problem 1:  (From last year's final)
A thin lens lens is found to create a virtual image at I1 = -75cm when the object distance is O1 = 25cm. 
a)  Find the focal length f1 of the lens.  Carefully draw the ray diagram demonstrating the image formation.
b)  A second lens is place a distance t = 0.5 cm after the first lens.  A real image is formed at a distance I2 = 2.5 cm.  Find the focal length of the second lens.  Carefully draw the ray diagram demonstrating the image formation.
c)  Find the height of the image if the original object height is 20cm. 
d)  If the light entering the second lens is limited by an aperture of diameter a = 0.1mm, what is the smallest separation Δh of two objects at s2 = O2 = 75.5 cm that can be resolved with light of wavelength 500 nm?  (ignore lens 1 for this problem)

ray diagram for aperture-limited lens

Assignment 11

Reading:  H&L:   Chapter 12, section 4
                            Tipler Ch. 32 Section 1

WebAssign Quiz # 11: Due Monday, December 4, 9 AM

Problem Set # 11
Due:  Tuesday Dec. 5

Phys 273 and 273H:    Problems 1-3  (see below)
                                    H&L Ch. 11 #  17
                                    Tipler Ch 33 # 74
                                    Tipler Ch 32 # 28,  37, 39

Phys 273H:                 H&L Ch. 12 # 10
                                    Tipler Ch. 33 # 75

Problem 1:  a)  A plane wave is normally incident on a plane with two parallel slits.  Find the ratio of the slit width to the wavelenth (a/λ) and the slit spacing to the wavelength  (d/ λ) given the intensity of the light at the detector as a function of detector angle as shown in the figure. 

intensity profile for two-slits of finite width

Problem 2:   
For a single slit of width 3.000µm and a normally incident plane wave of wavelength λ = 600.0 nm,  find the angle at which the diffracted intensity  is I/I0 = 0.2500.  Prove clearly that your answer is accurate to within 0.1%. 

Problem 3:   Make a careful plot of image distance vs. object distance, normalized to focal length (e.g. plot I/f vs. O/f), for
 a) a concave mirror of focal length f, and
 b) a convex mirror of focal length f. 

Assignment 10

Reading:  H&L:   Chapter 11, section1 1-7
                            Tipler Ch. 33 Sections 1-4 and  7-8

WebAssign Quiz # 10: Due Monday, November 27, 9 AM

Problem Set # 10
Due:  Tuesday Nov. 28

Phys 273 and 273H:    Problems 1-2  (see below)
                                    H&L Ch. 11 # 3, 11
                                    Tipler Ch 33 # 34, 42, 50, 59, 72

Phys 273H:                 H&L Ch. 11 # 13 - repeat the problem for wavelength       
                                    Tipler Ch. 33 # 86
                                    H&L Ch. 12 #21 post-poned from PS 10 - notes)

Problem 1:  The amplitude of the electromagnetic field for the superposition of N coherent electromagnetic waves that differ in phase by equal multiples of angle φ is:   equation for diffracted electric field.
Find the expressions for the complex conjugate E*, and the intensity of the superposition  I=εcE*E.

Make a careful plot of I vs. φ for N = 6.

Problem 2: 
An electron has wave-like behavior that allows it to act like a plane wave of wavelength  equation for wavelength of an electron
(An angstrom Å is 0.1 nm.)  An electron that scatters off a crystalline surface gives rise to a diffraction pattern due to scattering from the periodic array of atoms on the surface.  (The first people to observe and correctly interpret this behavior were Davisson and Germer;  Davisson won the 1937 Physics Nobel prize for the discovery.)  The diffraction angles follow the same relationship as for a grating (for normal incidence), nλ = dsinθ, where d is the distance between the atoms. 

Find the wavelength of electrons accelerated through a potential of 120V (these electrons have energy 120 eV).
Find the angles for first and second order diffraction (n = ±1, n = ±2) when these electrons are scattered from a surface where the distance between atoms is 3Å.

Assignment 9  Nov. 2 - Nov.  16

Reading:  H&L:   Chapter 9 section 5;  Ch. 12 sections 2,3;  Ch. 11 sections 11.2 and 11.5
                            Tipler Ch. 31 and Ch. 33 Sections 1-2

WebAssign Quiz # 9: Due Tuesday, November 14, 9 AM

Problem Set # 9
Due:  Tuesday Nov. 21

Phys 273 and 273H:    Problem 1  (see below)
                                    H&L Ch. 11 # 5, 7
                                    Tipler Ch 31  # 37, 39, 40,  59, 70
                                    Tipler Ch 33 # 23
equations relating refractive index and impedance
Phys 273H:                 Ch 12 # 5 and 21  (postpone #21 to PS 10 - notes)

Problem 1:  The relationship between the impedance of a dielectric medium and the refractive index n is given in the first formula to the right.

Show that when light traveling in free space (refractive index n = 1) is normally incident on the surface of a dielectric of refractive index n, the reflected intensity is Ir and the transmitted intensity  It are given by the 2d and 3d equations to the right.

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Assignment 8  Oct. 26 - Nov. 2

Reading:  H&L:   Chapter 9 sections 5, 6
                            Tipler Ch. 30

WebAssign Quiz # 8: Due Tuesday, October 31, 9 AM

Problem Set # 8
Due:  Thursday Nov. 2

Phys 273 and 273H:    Problems 1 & 2  (see below)
                                    H&L Ch. 9 #  9, 10, 13
                                    Tipler Ch 30  #31, 44, 45, 56

Phys 273H:                 Ch 9 # 17,   Ch. 30 # 67

Problem 1:   Wave Reflection 1

Use a graphing program such as Excel and make two graphs to show the properties of EM wave reflection and transmission in a transmission line with a junction between regions of impedance Z1and Z2 as a function of  Z1/Z2.  Assume the permeability and the geometric factor for the transmission line are the same on both sides of the junction. Use values both greater than and less than 1 for Z1/Z2, and extend the range  as far as seems interesting and physically reasonable. 
a)  The first graph should show the ratios   Vref/Vinc, Vtrans/Vinc and  λ12 as a function of Z1/Z2
b)  The second graph should show the ratios  Iref/Iinc,  Itrans/Iinc  and  λ12  as a function of Z1/Z2.

Problem 2:   Wave Reflection 2    SpreadsheetWaveReflection.doc   WaveReflection.xls

Assignment 7  Oct. 19 - Oct. 26

Reading:  H&L:   Chapter 9 sections 1-5, Ch. 13 Example 4
                            Tipler Ch. 24 section 3,  Ch 28 section 7  (for WebAssign problems)

WebAssign Quiz # 7: Due Tuesday, October 24, 9 AM

Problem Set #7
Due:  Thursday October 26

Phys 273 and 273H:    Problem 1 and 2 (see below)
                                    Ch. 9 # 1,2,4,5,6,7

Phys 273H:                 Ch 9 # 3 and Problem 3 (see below)

Problem 1:   Amplitude modulation - Use the Excel spreadsheet AMwave.xls to show that the waveforms generated using the two functions:

        f(t) = A(1+acos(ωat))sin(ωct)
        g(t) = A sin(ωct)+0.5aA[sin((ωca)t)+sin((ωca)t)]

are identical. Use an acoustic frequency of fa=440Hz and a carrier frequency of fc= 6800Hz (a realistic carrier frequency for AM  radio would be 680kHz, but that is too tedious to graph), and A = 1.0, a = 0.5 in arbitrary units. 

In the spreadsheet you should calculate the appropriate values in the labeled columns to generate three graphs, which you will print out and turn in for this problem.  The first graph should show f(t), sin(ωct) and 1+acos(ωat)) on the same axes.  The second graph should show g(t), sin((ωca)t) and sin((ωca)t)] on the same axes.  The third graph should show g(t)-f(t), with the vertical axis expanded x100. 

For the second graph, explain how the sum of the three waves causes the maxima and minima in amplitude to occur.  What frequencies will appear in the fourier spectrum of the amplitude modulated wave?   (see Ch. 13, example 4 in H&L).

Problem 2: 
Use complex variables in polar form to derive the trigonometric identity:

            cos(A+B) = cos(A)cos(B)-sin(A)sin(B).

Problem 3: 
Use complex variables in polar form to derive the trigonometric identity:

            cos(A) + cos(B) =2cos[(A+B)/2]cos[(A-B)/2].

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Assignment 6   Oct. 12 - Oct 19

Reading:  H&L Chapter 6; Chapter 9, sections 1-2

WebAssign Quiz # 6: Due Tuesday, October 17, 9 AM

Problem Set #6
Due:  Thursday October 19

Phys 273 and 273H:  Problem 1:   ImaginaryWorksheet.pdf
                                  Problem 2:   SpreadsheetWaveSum1.doc  &  SumWaves1.xls
                                  Problem 3:   SpreadsheetWaveSum2.doc &   SumWaves2.xls
                                  Problem 4:   see below
                                  Problems 5-8:  H&L Ch. 6 # 1,  6, 10, 11

Phys 273H:                Problem 9:   see below
                                   Problem 10:  see below

Problem 4:  Standing acoustic waves are formed in a tube of length l, with a particle displacement form:  ξ(x,t) = (Acoskx+Bsinkx)sinωt.  Sketch the first three harmonics for each of the two cases:

a)  Both ends of the tube open, boundary conditions:  both right and left side ∂ξ/∂x = 0

b)  Left end of tube open, boundary condition, ∂ξ/∂x = 0; right end closed, boundary condition ξ = 0.

Problem 9:  The displacement of a wave on a string which is fixed at both ends is given by:   y(x,t) = Acos(ωt – kx) + rAcos(ωt+kx),   where r is the coefficient of amplitude reflection.  Show that this may be expressed as a sum of two standing waves:  
y(x,t) = B(cosωt)(coskx) + C(sinωt)(sinkx), and find expressions for B and C in terms of A and r.

Problem 10:  Show that z = Aexp(i{ωt - (k1x+k2y)} where k2 =  ω2/c2 = k12+k22 is a solution of the two dimensional wave equation:

            ∂2z/∂x2 + ∂2z/∂y2 = (1/c2)( ∂2z/∂t2). 

Assignment 5  Sept. 28 - Oct. 12

Reading:  H&L Chapter 5; Chapter 7, sections 1-3; Chapter 8

WebAssign Quiz # 5: Due Tuesday, October 10, 9 AM

Problem Set #5
Due:  Thursday October 12

Phys 273 and 273H:  H&L Ch. 5 # 4, 6, 7, 9;
                                   H&L Ch. 7 # 1, 2, 3
                                   H&L Ch. 8 # 1, 4, 7
Phys 273H:                H&L Ch 5 #  11; Ch 7 # 7; Ch 8 # 8

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Assignment 4 -  Sept.  21 - Sept. 28

Reading:  H&S  Chapter 4, omit section 5; 
                          Chapter 13, sections 1-4

WebAssign  Quiz #4:  Due Tuesday, Sept. 26, 9 AM

Problem Set #4
Due:  Thursday, September 28 at the beginning of class

Phys 273 and 273H:   H&L Ch. 4 # 1,3, 4a&b, 9, 10 ;   Ch. 13 # 2, 3
Phys 273H:                H&L Ch. 4 # 13;  Ch. 13 # 4
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Assignment 3 -  Sept.  14 - Sept. 21

Reading:  H&S  Chapter 2, omit section 2.6 ; 
                          Chapter 13, sections 1-3

WebAssign  Quiz #3:  Due Tuesday, Sept. 19, 9 AM

Problem Set #3
Due:  Thursday, September 21 at the beginning of class

Phys 273 and 273H:  H&L Ch. 2 #   3, 4, 5, 7, 9, 11
Phys 273H:                H&L Ch. 2 # 12  (see section 2.6)

Assignment 2 -  Sept.  7 - Sept. 14

Reading:  H&S  Chapter 1, sections 5-7;  Chapter 3
                Tipler, Chapter 25, sections 5&6; Chapter 29
WebAssign  Quiz #2:  Due Tuesday, Sept. 12, 9 AM

Problem Set #2
Due:  Thursday, September 14 at the beginning of class

Problem # 1:  Complete the derivation, using the complex numbers approach, as oulined in class (Sept. 7) for a forced, damped harmonic oscillator:   ma + bv + kx = Focos(wDt).  Demonstrate that the solution is identical to the solution given in class (Sept. 5). 

Problem # 2:  Given the complex number z = 0.9659 +0.2588i,
a)  express the number in polar representation including numerical values of the magnitude and phase angle. 
b)  find the cube roots of z. 

Phys 273 and 273H:  H&L Ch.1 #  11, 12; 
                                   H&L Ch. 3 #2; 
                                   Tipler Ch. 29 # 63
Phys 273H:                Tipler Ch. 29 # 96, 100

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Assignment 1
-  Aug. 30- Sept.  7

Reading:  H&S  Chapter 1;  Review material on oscillations, such as Tipler Ch. 14

Required WebAssign :  Intro to WebAssign 2006,   Due Monday,  Sept. 4,  9AM
WebAssign  Quiz #1:  Due Tuesday, Sept. 5, 9 AM

Problem Set #1
Due:  Thursday, September 7 at the beginning of class

Problem # 1:  Derive the values of beta and omega-prime for a damped harmonic oscillator as discussed in class in terms of the physical parameters m (the mass), k (the spring constant) and b (the damping constant). 

Phys 273 and 273H:  H&L Ch.1 # 2, 4, 5, 7, 8
Phys 273H:                H&L Ch.1 # 15, 17

7: The moment of inertia of the hoop when rotating around one of the points on the hoop is 2ma^2.
8: At the bottom of the bowl, the marble is essentially moving in the x direction. Set up Newton's equation along the direction of motion.The force along the direction of motion can be calculated as mg sin(theta), with tan(theta) = dy/dx. When theta is small, sin(theta) ~ tan(theta) ~theta.

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Classroom Demonstrations

I will occasionally use classroom demonstrations to illustrate ideas in the course.  You should not treat these demonstrations as  opportunities for a nap - the material presented will be included in the material covered on examinations (often a demo gives me an idea for an exam problem).   If you're interested in looking at the demonstration descriptions (and finding some references describing them, you can go to the Lecture Demonstration web site:  http://www.physics.umd.edu/deptinfo/facilities/lecdem/services/demos/mainindex.htm 

Demonstrations to date

Week of  Sept. 5:
               Takoma Narrows video
               Barton's Pendulums (pendula of different length with external driver)  G2-12
               Forced Harmonic Motion with damping (spring suspended mass, eddy current damper, moving mount point) G2-02

Week of Sept. 11:
                Eddy-current damped pendulum
                Waves on a slinky
                Wave-driven bumper-jack (waves transmit energy)

Week of September 25:
       Addition of two waves of different frequency:  Small and larger frequency difference, beats
       Fourier synthesis:  Addition of waves that have integer multiples of base frequency
Week of October 2:
                  Beaker breaker (sound waves tuned to resonance of vibration of beaker)
                  Speaker and candle  

Week of October 9:      
                   Doppler ball and spectrum analyzer
                    Sound meter (dB)
                   Shive machine (visual demonstration of wave reflection)
                   Sound into a tube with adjustable length (demo by W. Stem)  Resonance Tube Demonstration.xls
Week of October 16:    
                    Three wires of different length with a mechanical oscillation
                    Tuning forks and plastic tube
                    Twirling plastic tube with for increasing pitch with speed
                    Shive machine demonstration of partial reflections and impedance matching
                    Radiowaves in a wire revealed by a fluorescent sensor

Week of October 23:
                    Electromagnetic wave model (orthogonal E and B fields)
                    Pulse in transmission lines (time required for reflection, and sign of reflection)
                    Microwaves in tubular waveguide

Week of October 30
                   Amplitude Modulation (C. Mehta)
                   Polarization intensity as a function of angle between crossed polarizers

Week of November 13
                Refraction on optical board.  Rectangular and triangular blocks.
                Total internal reflection:  laser waterfall, fiber optics tree and communication line
                Interference in mica thin film and soap bubble
                Michelson interferometer
Week of November 20
                Refraction and total internal reflection using microwaves (W. Stem)
                Interference from two slits with variable spacing and slit width

Week of November 27
                Laser diffraction: finite aperture width, slit and circle (C. Mehta)
                                              multiple slits of variable width and spacing

Week of December 4: 
                Optical Board:  image formation with concave mirror

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Solution Sets and Handouts
these are downloadable files
or web links

   Some Wave History:  Acoustics History.pdf

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WebAssign Instructions

The "quizzes" will be delivered and graded online via WebAssign.  The problems are set to allow 10 tries each, with a different set of numbers each time.    You will also be able to access your homework and exam scores on-line through WebAssign. 

1. Go to http://www.webassign.net/ and hit "login" or directly to https://www.webassign.net/login.html

2. Enter your username, institution, and password. If you have problems, contact me personally, and I will tell you the username and password.
3. You need to pay for access by Tuesday, Sept. 12, at 12:00 noon.  Do not delay payment. The price is about $9.95. There are two ways to pay:
4. WebAssign Student Guide is available at https://www.webassign.net/info/guide/index.html

Copyright (2006) University of Maryland, College Park. All rights reserved. 
Permission to redistribute the contents without alteration is granted to
educational institutions for non-profit administrative
or educational purposes if proper credit is given to
the University of Maryland, College Park as the source.