β 1 = 2 π and the path length difference is δ 1 = λ. The small angle approximation gives us y 1 L = tanθ 1 θ 1 sin θ 1 = δ 1 y 1
|
|
- Antonia Barnett
- 6 years ago
- Views:
Transcription
1 rgsdle (zdr8) HW13 ditmire (58335) 1 This print-out should hve 1 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. 001 (prt 1 of ) 10.0 points Consider the setup of single slit experiment. The wvelength of the incident light is λ 0 nm. The slit width nd the distnce between the slit nd the is specified in the figure. β 1 π nd the pth length difference is δ 1 λ. The smll ngle pproximtion gives us y 1 tn 1 1 sin 1 δ 1, or y 1 δ 1 λ mm. 00 (prt of ) 10.0 points Denote the intensity on the t y mm by I nd the intensity on the t y 0 by I µm S 8. m y 1 60 µm S 8. m mm Find the position y y 1 of the first intensity minimum. Use smll ngle pproximtion sin tn. Correct nswer: mm. Find the intensity rtio I I 0. Correct nswer: I I 0 [ ] sin(β/). β/ et : λ 0 nm, 8. m, 60 µm. nd 1 0 π π π or 360 β S [ y δ sin ] y 1 For single slit diffrction, destructive interference occurs when, sin λ, or simply when, δ sin λ. Thus, between the two end rys which correspond to the first minimum, the phse ngle difference is 0 1 et: δ λ β π δ λ sin λ R y mm y mm λ y (1) 0.59, ()
2 where y 1 is the position of the first intensity minimum. From Eq. (1), rgsdle (zdr8) HW13 ditmire (58335) β π y [ λ ] π (60 µm) (3.075 mm) 0 nm (8. m) rd 1., in greement with the bove digrm Following is the lterntive method. From Eq. (1) nd (), we hve R β β 1 δ δ 1 y y 1. β Rβ 1 (0.59) π rd (since β 1 π), the intensity rtio t ny point on the is I I 0 sin ( β β ) [ ] sin(rπ) Rπ [ sin(0.59π) 0.59π 0.681, in greement with the intensity digrm in the question points Hint: Use smll ngle pproximtion; e.g., sin tn nd cos 1. Consider the setup of double-slit experiment in the schemtic drwing below. Note: As cn be seen in the figure below, one of the double-slit interference mxim is locted t the first single-slit diffrction minimum. ] d S y Determine the rtio d ; i.e., the slit seprtion d compred to the slit width. 1. d correct. d 6 3. d 5. d 7 5. d 9 6. d d 5 8. d 9. d d 3 At y there is minimum for single-slit diffrction nd mxim for double-slit interference, s noted in the question. The first minimum for single-slit diffrction occurs when sin λ, (1)
3 rgsdle (zdr8) HW13 ditmire (58335) 3 nd the mxim for double-slit interference occur when sin (m) λ d. () The first diffrction minimum for single-slit diffrction nd the fourth double-slit interference mximum (m ) occur t the sme position y, s seen in the figure below. Figure: The dshed curve on the left of the is due to single slit interference. The dshed curve on the right of the is due to double slit interference. The position is zero mplitude nd the positive direction is reflected on either side of the. Since the single-slit diffrction minimum msks the fourth double-slit interference mxim, one must estimte where the fourth double-slit mxim occurs using the spcing between the double-slit interference pttern shown on the right-hnd side of the, s seen in the figure bove. Using Eq. 1 nd, we hve keywords: sin λ 1 (m) 1 d d (). 0 m /* If you use ny of these, fix the comment symbols points The lines in grting re uniformly spced t 1530 nm. Clculte the ngulr seprtion of the second order bright fringes between light of wvelength 600 nm nd nm. Correct nswer: mrd. The eqution for the n th bright fringe is d sin n λ, for n 0, ±1, ±,, where is the ngulr displcement describing the n th fringe. Hence the ngulr difference between the second bright fringe (n ) of two different wvelengths (λ nd λ 1 ) of light is ( ) ( ) λ λ1 1 rcsin rcsin d d [ ( ] m) rcsin m [ ( ] m) rcsin m rd mrd points ight of wvelength 56 nm from mercury rc flls on diffrction grting ruled with 7700 lines/in. Wht is the ngulr seprtion between the first-order imges on either side of the centrl mximum? (Cution: do not use smll ngle pproximtion here.) Correct nswer: For double-slit,.5 cm/in d 7700 lines/in nm sin 1 λ d (56 nm) ( nm) ,
4 rgsdle (zdr8) HW13 ditmire (58335) so Since we re sked for the ngulr seprtion between first-order imges to either side of the centrl mximum, it should be points A bem of light is diffrcted by single slit. The distnce between the positions of zero intensity (m ±1) is.1 mm mm S.119 m.05 mm Estimte the wvelength of the lser light. Use smll ngle pproximtion sin tn. Correct nswer: nm. tn m y m. In the smll ngle pproximtion, when is in rdins sin tn y m mλ y m mλ. The spcing between the minim m 1 nd m 1 is equl to b y 1 λ λ b m ( m).119 m 109 nm m nm points An unpolrized light bem with intensity of I 0 psses through polrizers shown in the picture. Unpolrized light Polrizer et :.119 m, y.05 mm, mm. nd Trnsmission xis E0 Polrized lihgt Anlyzer E0cos S y The distnce y m from the m th minimum to the center of the first-order mximum cn be clculted from the formule sin m mλ, If 30,wht is the bem intensity fter the second polrizer? 1. I 5 8 I 0. I 9 3. I 5. I 1 8 I 0 5. I 3 8 I 0 correct
5 rgsdle (zdr8) HW13 ditmire (58335) 5 6. I 3 7. I 1 I 0 8. I 7 9. I I 1 I 0 The bem intensity fter the first polrizer is I 1 I 0. We use the formul for the intensity of the trnsmitted (polrized) light. Thus the bem intensity fter the second polrizer is I I 1 cos I 0 cos (30 ) 3 I (prt 1 of ) 10.0 points Consider 3 polrizers #1, #, nd #3 ordered sequentilly. The incident light is unpolrized with intensity I 0. The intensities fter the light psses through the subsequent polrizers re lbeled s I 1, I, nd I 3, respectively (see the sketch). I 0 I 1 I I 3 #1 # #3 Polrizers #1 nd #3 re crossed such tht their trnsmission xes re perpendiculr to ech other. Polrizer # is plced between the polrizers #1 nd #3 with its trnsmission xis t 60 with respect to the trnsmission xis of the polrizer #1 (see the sketch). #1 60 # #3 After pssing through polrizer # the intensity I (in terms of the intermedite intensity I 1 ) is 1. I I 1 correct. None of these. 3. I I 1 ( ) 3. I I 1 5. I I 1 6. I I I I 1 3 When the light psses through the polrizer #1 it is polrized verticlly. Thus the ngle between its polriztion nd the orienttion of polrizer # is 60. Thus the trnsmitted intensity is I I 1 cos I 1 cos (60 ) 1 I 1. When polrized light psses through polrizer, the trnsmitted intensity is I I 1 cos, where is the ngle between the polriztion of the light (of I 1 ) nd the orienttion of the polrizer #. Thus I I (prt of ) 10.0 points Wht is the finl intensity I 3? 1. I 3 3
6 rgsdle (zdr8) HW13 ditmire (58335) 6. I I 0 3. I 3 1 I 0. I 3 1 I 0 et : λ m d m. Applying Ryleigh s criterion, nd 5. I I I I 0 correct 8. I I 0 After the polrizer #1 I 1 I 0. After the polrizer # I I 1 cos (60 ) After the polrizer #3 I 1. I 3 I cos (90 60 ) ( ) 3 I ( ) ( ) 3 1 I 1 ( ) ( ) ( ) I I points If we were to send ruby lser bem (wvelength 55 nm) outwrd from the brrel of telescope whose dimeter is 3.6 m, wht would be the dimeter of the big red spot when the bem hit the Moon km wy? Neglect tmospheric dispersion. Correct nswer: m. min r D 1. λ d, where r is the rdius of the spot. So, for the dimeter x of the spot we obtin x r 1. λ D d (1.) ( m)( m) (3.6 m) m points On the night of April 18, 1775, signl ws to be sent from the Old North Church steeple to Pul Revere, who ws.3 mi wy: One if by lnd, two if by se. Assume tht Pul Revere s pupils hd dimeter of.93 mm t night, nd tht the lntern light hd predominnt wvelength of 685 nm. At wht minimum seprtion did the sexton hve to set the lnterns so tht Revere could receive the correct messge? One mile is pproximtely equl to km. Correct nswer: m. The ngle of resolution for the Pul Revere s pupils is Therefore min 1. λ D d. d 1. λ D (685 nm) (.3 mi) mm 1. ( m) ( m) m m.
7 rgsdle (zdr8) HW13 ditmire (58335) points Consider the setup of single slit experiment. Hint: Use smll ngle pproximtion; e.g., sin tn. S 10 y3 Determine the height y 3, where the third minimum occurs. 1. y 3 λ. y 3 5 λ 3. y 3 3 λ. y 3 λ 5. y 3 5 λ 6. y 3 9 λ 7. y 3 λ 8. y 3 λ 9. y 3 3 λ correct 10. y 3 7 λ The third minimum occurs t β 6 π, which corresponds to pth difference between two end rys: b 3 β k ( 6 π ) π λ 3 λ b 3 y 3 y 3 b 3 3 λ points A converging lens with dimeter of 9.9 cm forms n imge of stellite pssing overhed. The stellite hs two green lights (wvelength 505 nm) spced 1 m prt. If the lights cn just be resolved ccording to the Ryleigh criterion, wht is the ltitude of the stellite? Correct nswer: km. Given : d 1 m, D 9.9 cm 0.99 m, nd λ 505 nm m. The ngulr resolution is m 1. λ D Thus the ltitude is h d m 0.99 m rd. 1 m rd km. 1 km m points A binry str system in the constelltion Orion hs n ngulr seprtion between the two strs of rd. If the wvelength is 70 nm, wht is the smllest dimeter telescope cn hve nd
8 just resolve the two strs? Correct nswer: cm. et : λ 70 nm. rgsdle (zdr8) HW13 ditmire (58335) 8 1. λ D, D 1. λ 70 nm rd 10 cm 10 9 nm cm.
Diffraction. Diffraction and Polarization. Diffraction. Diffraction. Diffraction I. Angular Spread: θ ~ λ/a
1 nd Polriztion Chpter 38 Rleigh s Criterion Polriztion n geometricl optics, we modeled rs like this! n fct wht hppens is this... A sphericl wve propgtes out from the perture. All wves do this.. For double
More informationragsdale (zdr82) HW2 ditmire (58335) 1
rgsdle (zdr82) HW2 ditmire (58335) This print-out should hve 22 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. 00 0.0 points A chrge of 8. µc
More informationData Provided: A formula sheet and table of physical constants are attached to this paper.
PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts re ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT
More informationGraduate Students do all problems. Undergraduate students choose three problems.
OPTI 45/55 Midterm Due: Februr, Grdute Students do ll problems. Undergrdute students choose three problems.. Google Erth is improving the resolution of its globl mps with dt from the SPOT5 stellite. The
More informationPhysics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011
Physics 9 Fll 0 Homework - s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you
More informationto calculate the angular position θ of the first minimum. The minima are located by EXECUTE:
DIFFRACTIO 36 36 IDETIFY: Use y = xtnθ to clculte the ngulr position θ of the first minimum The minim re locted by m Eq(36): sin θ =, m =±, ±, First minimum mens m = nd sin θ = / nd = sin θ Use this eqution
More informationData Provided: A formula sheet and table of physical constants is attached to this paper.
PHY15-B PHY47 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 009-010 ASTRONOMY DEPARTMENT
More informationData Provided: A formula sheet and table of physical constants are attached to this paper.
PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts re ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT
More informationCorrect answer: 0 m/s 2. Explanation: 8 N
Version 001 HW#3 - orces rts (00223) 1 his print-out should hve 15 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Angled orce on Block 01 001
More informationChapter 36. a λ 2 2. (minima-dark fringes) Diffraction and the Wave Theory of Light. Diffraction by a Single Slit: Locating the Minima, Cont'd
Chpter 36 Diffrction In Chpter 35, we sw how light bes pssing through ifferent slits cn interfere with ech other n how be fter pssing through single slit flres-iffrcts- in Young's experient. Diffrction
More informationDIFFRACTION OF LIGHT
DIFFRACTION OF LIGHT The phenomenon of bending of light round the edges of obstcles or nrrow slits nd hence its encrochment into the region of geometricl shdow is known s diffrction. P Frunhofer versus
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time allowed Two hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time llowed Two hours (Plus 5 minutes reding time) DIRECTIONS TO CANDIDATES Attempt ALL questions ALL questions
More informationHigher Checklist (Unit 3) Higher Checklist (Unit 3) Vectors
Vectors Skill Achieved? Know tht sclr is quntity tht hs only size (no direction) Identify rel-life exmples of sclrs such s, temperture, mss, distnce, time, speed, energy nd electric chrge Know tht vector
More informationQUB XRD Course. The crystalline state. The Crystalline State
QUB XRD Course Introduction to Crystllogrphy 1 The crystlline stte Mtter Gseous Stte Solid stte Liquid Stte Amorphous (disordered) Crystlline (ordered) 2 The Crystlline Stte A crystl is constructed by
More informationIn-Class Problems 2 and 3: Projectile Motion Solutions. In-Class Problem 2: Throwing a Stone Down a Hill
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Physics Physics 8T Fll Term 4 In-Clss Problems nd 3: Projectile Motion Solutions We would like ech group to pply the problem solving strtegy with the
More informationWave Phenomena Physics 15c
Wve Phenomen Physics 15c Lecture Diffrction (H&L Chpter 11) Wht We Did Lst Time! Studied interference! or more wves overlp " Amplitudes dd up " Intensity = (mplitude) does not dd up! Thin-film interference!
More informationName Solutions to Test 3 November 8, 2017
Nme Solutions to Test 3 November 8, 07 This test consists of three prts. Plese note tht in prts II nd III, you cn skip one question of those offered. Some possibly useful formuls cn be found below. Brrier
More information- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.
- 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked. - 6 - QUESTION 1 [Mrks 22] A thin non-conducting
More informationCALCULATED POWDER X-RAY DIFFRACTION LINE PROFILES VIA ABSORPTION
16 17 CALCULATED POWDER X-RAY DFFRACTON LNE PROFLES VA ABSORPTON Keji Liu nd Heifen Chen School of Mteril Science nd Engineering, Shnghi nstitute of Technology, Shnghi, Chin 2233 ABSTRACT We hve clculted
More informationPHY 140A: Solid State Physics. Solution to Midterm #1
PHY 140A: Solid Stte Physics Solution to Midterm #1 TA: Xun Ji 1 October 24, 2006 1 Emil: jixun@physics.ucl.edu Problem #1 (20pt)Clculte the pcking frction of the body-centered cubic lttice. Solution:
More informationTrigonometric Functions
Exercise. Degrees nd Rdins Chpter Trigonometric Functions EXERCISE. Degrees nd Rdins 4. Since 45 corresponds to rdin mesure of π/4 rd, we hve: 90 = 45 corresponds to π/4 or π/ rd. 5 = 7 45 corresponds
More informationPhys 4321 Final Exam December 14, 2009
Phys 4321 Finl Exm December 14, 2009 You my NOT use the text book or notes to complete this exm. You nd my not receive ny id from nyone other tht the instructor. You will hve 3 hours to finish. DO YOUR
More informationPhysics 2135 Exam 3 April 21, 2015
Em Totl hysics 2135 Em 3 April 21, 2015 Key rinted Nme: 200 / 200 N/A Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. C Two long stright
More informationPhysicsAndMathsTutor.com
1. A uniform circulr disc hs mss m, centre O nd rdius. It is free to rotte bout fixed smooth horizontl xis L which lies in the sme plne s the disc nd which is tngentil to the disc t the point A. The disc
More informationAlg. Sheet (1) Department : Math Form : 3 rd prep. Sheet
Ciro Governorte Nozh Directorte of Eduction Nozh Lnguge Schools Ismili Rod Deprtment : Mth Form : rd prep. Sheet Alg. Sheet () [] Find the vlues of nd in ech of the following if : ) (, ) ( -5, 9 ) ) (,
More informationProblems for HW X. C. Gwinn. November 30, 2009
Problems for HW X C. Gwinn November 30, 2009 These problems will not be grded. 1 HWX Problem 1 Suppose thn n object is composed of liner dielectric mteril, with constnt reltive permittivity ɛ r. The object
More informationIMPORTANT. Read these directions carefully:
Physics 208: Electricity nd Mgnetism Finl Exm, Secs. 506 510. 7 My. 2004 Instructor: Dr. George R. Welch, 415 Engineering-Physics, 845-7737 Print your nme netly: Lst nme: First nme: Sign your nme: Plese
More informationThis final is a three hour open book, open notes exam. Do all four problems.
Physics 55 Fll 27 Finl Exm Solutions This finl is three hour open book, open notes exm. Do ll four problems. [25 pts] 1. A point electric dipole with dipole moment p is locted in vcuum pointing wy from
More informationProblem Set 3 Solutions
Chemistry 36 Dr Jen M Stndrd Problem Set 3 Solutions 1 Verify for the prticle in one-dimensionl box by explicit integrtion tht the wvefunction ψ ( x) π x is normlized To verify tht ψ ( x) is normlized,
More informationLight and Optics Propagation of light Electromagnetic waves (light) in vacuum and matter Reflection and refraction of light Huygens principle
Light nd Optics Propgtion of light Electromgnetic wves (light) in vcuum nd mtter Reflection nd refrction of light Huygens principle Polristion of light Geometric optics Plne nd curved mirrors Thin lenses
More informationNOT TO SCALE. We can make use of the small angle approximations: if θ á 1 (and is expressed in RADIANS), then
3. Stellr Prllx y terrestril stndrds, the strs re extremely distnt: the nerest, Proxim Centuri, is 4.24 light yers (~ 10 13 km) wy. This mens tht their prllx is extremely smll. Prllx is the pprent shifting
More informationTime : 3 hours 03 - Mathematics - March 2007 Marks : 100 Pg - 1 S E CT I O N - A
Time : hours 0 - Mthemtics - Mrch 007 Mrks : 100 Pg - 1 Instructions : 1. Answer ll questions.. Write your nswers ccording to the instructions given below with the questions.. Begin ech section on new
More informationThe Properties of Stars
10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product
More informationR(3, 8) P( 3, 0) Q( 2, 2) S(5, 3) Q(2, 32) P(0, 8) Higher Mathematics Objective Test Practice Book. 1 The diagram shows a sketch of part of
Higher Mthemtics Ojective Test Prctice ook The digrm shows sketch of prt of the grph of f ( ). The digrm shows sketch of the cuic f ( ). R(, 8) f ( ) f ( ) P(, ) Q(, ) S(, ) Wht re the domin nd rnge of
More informationExam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B
PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere
More information1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?
Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt
More information25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?
PhysicsndMthsTutor.com 25 Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? 972//M/J/2 frequency speed (in vcuum) decreses
More informationA LEVEL TOPIC REVIEW. factor and remainder theorems
A LEVEL TOPIC REVIEW unit C fctor nd reminder theorems. Use the Fctor Theorem to show tht: ) ( ) is fctor of +. ( mrks) ( + ) is fctor of ( ) is fctor of + 7+. ( mrks) +. ( mrks). Use lgebric division
More informationES 111 Mathematical Methods in the Earth Sciences Lecture Outline 1 - Thurs 28th Sept 17 Review of trigonometry and basic calculus
ES 111 Mthemticl Methods in the Erth Sciences Lecture Outline 1 - Thurs 28th Sept 17 Review of trigonometry nd bsic clculus Trigonometry When is it useful? Everywhere! Anything involving coordinte systems
More informationSOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014
SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 014 Mrk Scheme: Ech prt of Question 1 is worth four mrks which re wrded solely for the correct nswer.
More information2.57/2.570 Midterm Exam No. 1 March 31, :00 am -12:30 pm
2.57/2.570 Midterm Exm No. 1 Mrch 31, 2010 11:00 m -12:30 pm Instructions: (1) 2.57 students: try ll problems (2) 2.570 students: Problem 1 plus one of two long problems. You cn lso do both long problems,
More information1 ST ROUND, SOLUTIONS
ST ROUND, SOLUTIONS Problem (Lithuni) Self destructing pper ( points) Solution ( ) ( ) ( ) [Al HO OH ) ph pk lg [Al H O ( ) ( ) [Al H O OH [Al ( ).9 [Al H O.9.47 [Al ( ) ( ) ( ) [Al H O OH.9 pk ph lg.
More informationVersion 001 HW#6 - Circular & Rotational Motion arts (00223) 1
Version 001 HW#6 - Circulr & ottionl Motion rts (00223) 1 This print-out should hve 14 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Circling
More informationPhysics 1B: Review for Final Exam Solutions
Physics B: eview for Finl Exm s Andrew Forrester June 6, 2008 In this worksheet we review mteril from the following chpters of Young nd Freedmn plus some dditionl concepts): Chpter 3: Periodic Motion Chpter
More informationProf. Anchordoqui. Problems set # 4 Physics 169 March 3, 2015
Prof. Anchordoui Problems set # 4 Physics 169 Mrch 3, 15 1. (i) Eight eul chrges re locted t corners of cube of side s, s shown in Fig. 1. Find electric potentil t one corner, tking zero potentil to be
More informationLecture Outline. Dispersion Relation Electromagnetic Wave Polarization 8/7/2018. EE 4347 Applied Electromagnetics. Topic 3c
Course Instructor Dr. Rymond C. Rumpf Office: A 337 Phone: (915) 747 6958 E Mil: rcrumpf@utep.edu EE 4347 Applied Electromgnetics Topic 3c Wve Dispersion & Polriztion Wve Dispersion These notes & Polriztion
More informationStudent Session Topic: Particle Motion
Student Session Topic: Prticle Motion Prticle motion nd similr problems re on the AP Clculus exms lmost every yer. The prticle my be prticle, person, cr, etc. The position, velocity or ccelertion my be
More informationLoudoun Valley High School Calculus Summertime Fun Packet
Loudoun Vlley High School Clculus Summertime Fun Pcket We HIGHLY recommend tht you go through this pcket nd mke sure tht you know how to do everything in it. Prctice the problems tht you do NOT remember!
More informationPhysics 2135 Exam 1 February 14, 2017
Exm Totl / 200 Physics 215 Exm 1 Ferury 14, 2017 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the est or most nerly correct nswer. 1. Two chrges 1 nd 2 re seprted
More informationVersion 087 EX4 ditmire (58335) 1
Version 087 EX4 ditmire (58335) This print-out should have 3 questions. Multiple-choice questions ma continue on the next column or page find all choices before answering. 00 (part of ) 0.0 points A material
More information200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes
PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write
More informationMATH 253 WORKSHEET 24 MORE INTEGRATION IN POLAR COORDINATES. r dr = = 4 = Here we used: (1) The half-angle formula cos 2 θ = 1 2
MATH 53 WORKSHEET MORE INTEGRATION IN POLAR COORDINATES ) Find the volume of the solid lying bove the xy-plne, below the prboloid x + y nd inside the cylinder x ) + y. ) We found lst time the set of points
More information(See Notes on Spontaneous Emission)
ECE 240 for Cvity from ECE 240 (See Notes on ) Quntum Rdition in ECE 240 Lsers - Fll 2017 Lecture 11 1 Free Spce ECE 240 for Cvity from Quntum Rdition in The electromgnetic mode density in free spce is
More information#6A&B Magnetic Field Mapping
#6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by
More informationSupplementary Information for Directional Reflective Surface Formed via Gradient- Impeding Acoustic Meta-surfaces
Supplementry Informtion for Directionl Reflective Surfce Formed vi Grdient- Impeding Acoustic Met-surfces Kyungjun Song 1*, Jedo Kim 2, Hur Shin 1, Jun-Hyuk Kwk 1, Seong-Hyun Lee 3,Tesung Kim 4 1 Deprtment
More informationPhysics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:
Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You
More informationPhysics 3323, Fall 2016 Problem Set 7 due Oct 14, 2016
Physics 333, Fll 16 Problem Set 7 due Oct 14, 16 Reding: Griffiths 4.1 through 4.4.1 1. Electric dipole An electric dipole with p = p ẑ is locted t the origin nd is sitting in n otherwise uniform electric
More informationinteratomic distance
Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule
More informationWMAP satellite. 16 Feb Feb Feb 2012
16 Feb 2012 21 Feb 2012 23 Feb 2012 è Announcements è Problem 5 (Hrtle 18.3). Assume V * is nonreltivistic. The reltivistic cse requires more complicted functions. è Outline è WMAP stellite è Dipole nisotropy
More informationOn the diagram below the displacement is represented by the directed line segment OA.
Vectors Sclrs nd Vectors A vector is quntity tht hs mgnitude nd direction. One exmple of vector is velocity. The velocity of n oject is determined y the mgnitude(speed) nd direction of trvel. Other exmples
More informationMath 113 Exam 2 Practice
Mth 3 Exm Prctice Februry 8, 03 Exm will cover 7.4, 7.5, 7.7, 7.8, 8.-3 nd 8.5. Plese note tht integrtion skills lerned in erlier sections will still be needed for the mteril in 7.5, 7.8 nd chpter 8. This
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 999 MATHEMATICS UNIT (ADDITIONAL) Time llowed Three hours (Plus 5 minutes reding time) DIRECTIONS TO CANDIDATES Attempt ALL questions ALL questions re of equl vlue
More informationSULIT /2 3472/2 Matematik Tambahan Kertas 2 2 ½ jam 2009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING
SULIT 1 347/ 347/ Mtemtik Tmbhn Kerts ½ jm 009 SEKOLAH-SEKOLAH MENENGAH ZON A KUCHING PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 009 MATEMATIK TAMBAHAN Kerts Du jm tig puluh minit JANGAN BUKA KERTAS
More informationLog1 Contest Round 3 Theta Individual. 4 points each 1 What is the sum of the first 5 Fibonacci numbers if the first two are 1, 1?
008 009 Log1 Contest Round Thet Individul Nme: points ech 1 Wht is the sum of the first Fiboncci numbers if the first two re 1, 1? If two crds re drwn from stndrd crd deck, wht is the probbility of drwing
More informationSAINT IGNATIUS COLLEGE
SAINT IGNATIUS COLLEGE Directions to Students Tril Higher School Certificte 0 MATHEMATICS Reding Time : 5 minutes Totl Mrks 00 Working Time : hours Write using blue or blck pen. (sketches in pencil). This
More informationThe Fundamental Theorem of Calculus, Particle Motion, and Average Value
The Fundmentl Theorem of Clculus, Prticle Motion, nd Averge Vlue b Three Things to Alwys Keep In Mind: (1) v( dt p( b) p( ), where v( represents the velocity nd p( represents the position. b (2) v ( dt
More informationk ) and directrix x = h p is A focal chord is a line segment which passes through the focus of a parabola and has endpoints on the parabola.
Stndrd Eqution of Prol with vertex ( h, k ) nd directrix y = k p is ( x h) p ( y k ) = 4. Verticl xis of symmetry Stndrd Eqution of Prol with vertex ( h, k ) nd directrix x = h p is ( y k ) p( x h) = 4.
More informationTest , 8.2, 8.4 (density only), 8.5 (work only), 9.1, 9.2 and 9.3 related test 1 material and material from prior classes
Test 2 8., 8.2, 8.4 (density only), 8.5 (work only), 9., 9.2 nd 9.3 relted test mteril nd mteril from prior clsses Locl to Globl Perspectives Anlyze smll pieces to understnd the big picture. Exmples: numericl
More informationMinnesota State University, Mankato 44 th Annual High School Mathematics Contest April 12, 2017
Minnesot Stte University, Mnkto 44 th Annul High School Mthemtics Contest April, 07. A 5 ft. ldder is plced ginst verticl wll of uilding. The foot of the ldder rests on the floor nd is 7 ft. from the wll.
More informationPhys 6321 Final Exam - Solutions May 3, 2013
Phys 6321 Finl Exm - Solutions My 3, 2013 You my NOT use ny book or notes other thn tht supplied with this test. You will hve 3 hours to finish. DO YOUR OWN WORK. Express your nswers clerly nd concisely
More informationPHYSICS 211 MIDTERM I 21 April 2004
PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of
More informationThat reminds me must download the test prep HW. adapted from (nz118.jpg)
Tht reminds me must downlod the test prep HW. dpted from http://www.neringzero.net (nz118.jpg) Em 1: Tuesdy, Feb 14, 5:00-6:00 PM Test rooms: Instructor Sections Room Dr. Hle F, H 104 Physics Dr. Kurter
More informationfiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics
Solid Stte Physics JEST-0 Q. bem of X-rys is incident on BCC crystl. If the difference between the incident nd scttered wvevectors is K nxˆkyˆlzˆ where xˆ, yˆ, zˆ re the unit vectors of the ssocited cubic
More informationJUST THE MATHS UNIT NUMBER INTEGRATION APPLICATIONS 12 (Second moments of an area (B)) A.J.Hobson
JUST THE MATHS UNIT NUMBE 13.1 INTEGATION APPLICATIONS 1 (Second moments of n re (B)) b A.J.Hobson 13.1.1 The prllel xis theorem 13.1. The perpendiculr xis theorem 13.1.3 The rdius of grtion of n re 13.1.4
More informationProblem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are:
(x + y ) = y + (x + y ) = x + Problem Set 9 Discussion: Nov., Nov. 8, Nov. (on probbility nd binomil coefficients) The nme fter the problem is the designted writer of the solution of tht problem. (No one
More informationJUST THE MATHS SLIDES NUMBER INTEGRATION APPLICATIONS 12 (Second moments of an area (B)) A.J.Hobson
JUST THE MATHS SLIDES NUMBER 13.12 INTEGRATION APPLICATIONS 12 (Second moments of n re (B)) b A.J.Hobson 13.12.1 The prllel xis theorem 13.12.2 The perpendiculr xis theorem 13.12.3 The rdius of grtion
More informationPartial Derivatives. Limits. For a single variable function f (x), the limit lim
Limits Prtil Derivtives For single vrible function f (x), the limit lim x f (x) exists only if the right-hnd side limit equls to the left-hnd side limit, i.e., lim f (x) = lim f (x). x x + For two vribles
More information1.2 What is a vector? (Section 2.2) Two properties (attributes) of a vector are and.
Homework 1. Chpters 2. Bsis independent vectors nd their properties Show work except for fill-in-lnks-prolems (print.pdf from www.motiongenesis.com Textooks Resources). 1.1 Solving prolems wht engineers
More informationMTH 4-16a Trigonometry
MTH 4-16 Trigonometry Level 4 [UNIT 5 REVISION SECTION ] I cn identify the opposite, djcent nd hypotenuse sides on right-ngled tringle. Identify the opposite, djcent nd hypotenuse in the following right-ngled
More information13.3 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS
33 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS As simple ppliction of the results we hve obtined on lgebric extensions, nd in prticulr on the multiplictivity of extension degrees, we cn nswer (in
More informationMathematics of Motion II Projectiles
Chmp+ Fll 2001 Dn Stump 1 Mthemtics of Motion II Projectiles Tble of vribles t time v velocity, v 0 initil velocity ccelertion D distnce x position coordinte, x 0 initil position x horizontl coordinte
More informationu( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.
nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $
More informationVorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen
Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:
More informationVersion 001 HW#6 - Electromagnetic Induction arts (00224) 1 3 T
Version 001 HW#6 - lectromgnetic Induction rts (00224) 1 This print-out should hve 12 questions. Multiple-choice questions my continue on the next column or pge find ll choices efore nswering. AP 1998
More informationTHE KENNESAW STATE UNIVERSITY HIGH SCHOOL MATHEMATICS COMPETITION PART I MULTIPLE CHOICE NO CALCULATORS 90 MINUTES
THE 08 09 KENNESW STTE UNIVERSITY HIGH SHOOL MTHEMTIS OMPETITION PRT I MULTIPLE HOIE For ech of the following questions, crefully blcken the pproprite box on the nswer sheet with # pencil. o not fold,
More informationProblem 1. Solution: a) The coordinate of a point on the disc is given by r r cos,sin,0. The potential at P is then given by. r z 2 rcos 2 rsin 2
Prolem Consider disc of chrge density r r nd rdius R tht lies within the xy-plne. The origin of the coordinte systems is locted t the center of the ring. ) Give the potentil t the point P,,z in terms of,r,
More informationUNIT 3 Indices and Standard Form Activities
UNIT 3 Indices nd Stndrd Form Activities Activities 3.1 Towers 3.2 Bode's Lw 3.3 Mesuring nd Stndrd Form 3.4 Stndrd Inde Form Notes nd Solutions (1 pge) ACTIVITY 3.1 Towers How mny cubes re needed to build
More informationScientific notation is a way of expressing really big numbers or really small numbers.
Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific
More informationSimple Harmonic Motion I Sem
Simple Hrmonic Motion I Sem Sllus: Differentil eqution of liner SHM. Energ of prticle, potentil energ nd kinetic energ (derivtion), Composition of two rectngulr SHM s hving sme periods, Lissjous figures.
More informationMath 116 Final Exam April 26, 2013
Mth 6 Finl Exm April 26, 23 Nme: EXAM SOLUTIONS Instructor: Section:. Do not open this exm until you re told to do so. 2. This exm hs 5 pges including this cover. There re problems. Note tht the problems
More informationYear 12 Mathematics Extension 2 HSC Trial Examination 2014
Yer Mthemtics Etension HSC Tril Emintion 04 Generl Instructions. Reding time 5 minutes Working time hours Write using blck or blue pen. Blck pen is preferred. Bord-pproved clcultors my be used A tble of
More informationhttp:dx.doi.org1.21611qirt.1994.17 Infrred polriztion thermometry using n imging rdiometer by BALFOUR l. S. * *EORD, Technion Reserch & Development Foundtion Ltd, Hif 32, Isrel. Abstrct This pper describes
More informationT M S C A M I D D L E S C H O O L M A T H E M A T I C S R E G I O N A L T E S T M A R C H 9,
T M S C A M I D D L E S C H O O L M A T H E M A T I C S R E G I O N A L T E S T M A R C H 9, 0 GENERAL DIRECTIONS. Aout this test: A. You will e given 0 minutes to tke this test. B. There re 0 prolems
More informationr 0 ( ) cos( ) r( )sin( ). 1. Last time, we calculated that for the cardioid r( ) =1+sin( ),
Wrm up Recll from lst time, given polr curve r = r( ),, dx dy dx = dy d = (r( )sin( )) d (r( ) cos( )) = r0 ( )sin( )+r( ) cos( ) r 0 ( ) cos( ) r( )sin( ).. Lst time, we clculted tht for crdioid r( )
More informationLevel I MAML Olympiad 2001 Page 1 of 6 (A) 90 (B) 92 (C) 94 (D) 96 (E) 98 (A) 48 (B) 54 (C) 60 (D) 66 (E) 72 (A) 9 (B) 13 (C) 17 (D) 25 (E) 38
Level I MAML Olympid 00 Pge of 6. Si students in smll clss took n em on the scheduled dte. The verge of their grdes ws 75. The seventh student in the clss ws ill tht dy nd took the em lte. When her score
More informationLecture 13 - Linking E, ϕ, and ρ
Lecture 13 - Linking E, ϕ, nd ρ A Puzzle... Inner-Surfce Chrge Density A positive point chrge q is locted off-center inside neutrl conducting sphericl shell. We know from Guss s lw tht the totl chrge on
More informationCoimisiún na Scrúduithe Stáit State Examinations Commission
M 30 Coimisiún n Scrúduithe Stáit Stte Exmintions Commission LEAVING CERTIFICATE EXAMINATION, 005 MATHEMATICS HIGHER LEVEL PAPER ( 300 mrks ) MONDAY, 3 JUNE MORNING, 9:30 to :00 Attempt FIVE questions
More informationB.Sc. in Mathematics (Ordinary)
R48/0 DUBLIN INSTITUTE OF TECHNOLOGY KEVIN STREET, DUBLIN 8 B.Sc. in Mthemtics (Ordinry) SUPPLEMENTAL EXAMINATIONS 01 Numericl Methods Dr. D. Mckey Dr. C. Hills Dr. E.A. Cox Full mrks for complete nswers
More informationKai Sun. University of Michigan, Ann Arbor
Ki Sun University of Michign, Ann Arbor How to see toms in solid? For conductors, we cn utilize scnning tunneling microscope (STM) to see toms (Nobel Prize in Physics in 1986) Limittions: (1) conductors
More informationBME 207 Introduction to Biomechanics Spring 2018
April 6, 28 UNIVERSITY O RHODE ISAND Deprtment of Electricl, Computer nd Biomedicl Engineering BME 27 Introduction to Biomechnics Spring 28 Homework 8 Prolem 14.6 in the textook. In ddition to prts -e,
More information