Fraunhofer Diffraction


 Lesley Cobb
 5 years ago
 Views:
Transcription
1 Physics 334 Spring 1 Purpose Fraunhofer Diffraction The experiment will test the theory of Fraunhofer diffraction at a single slit by comparing a careful measurement of the angular dependence of intensity of diffracted laser light with predictions of the theory. A qualitative overview of interference and diffraction phenomena will round off the experiment. Light waves are known to be transversely polarized waves. Unfortunately, the majority of diffraction problems of practical interest can be solved only for the simpler case of waves in a scalar field. The lack of a sound fundamental basis for diffraction theory emphasizes the need for experimental tests of its ability to correctly predict optical phenomena. Introduction "Diffraction" refers to the spreading of waves and appearance of fringes that occur when a wave front is constricted by an aperture in a screen that is otherwise opaque. The light pattern changes as you move away from the aperture, being characterized by three regions. Plane waves Intensity profiles X θμιν Z OA Intensity Aperture Shadow Fresnel Diffraction Z ~ a /λ Fraunhofer Diffraction Figure 3.1 Diffraction of plane waves at an aperture. 1. In the shadow region, close to the aperture, the boundary of the transmitted light is sharp and resembles the aperture in shape.. As you move away into the Fresnel region, the beam width remains comparable to that in the aperture, but narrow fringes appear at the edges. 3. Far away, in the Fraunhofer region, the beam spreads to a width much greater than that of the aperture and is flanked by many weaker fringes. Fraunhofer Diffraction 3.1 Spring 1
2 The Fraunhofer region is chosen for the experiment because the broader fringes are easier to measure with an optical detector of finite aperture, and the calculations are more straightforward than in region. y x R r P(x,y) x y Z axis Incident waves Aperture da Figure 3.. Geometry for the KirchoffFresnel diffraction integral. z Observation plane The HuygensFresnel principle governs diffraction phenomena: "Every unobstructed element of a wavefront acts as a source of spherical waves with the same frequency as the primary wave. The amplitude of the optical field beyond is a superposition of all these wavelets taking account of their amplitudes and phases." The KirchoffFresnel diffraction integral gives quantitative expression to these ideas. Consider plane waves incident on an aperture from the left, as shown in Figure 3.. The incident field is described via: ikz ( ωt) E z, t = E e INC ( ) The field in the aperture i.e., where z=, is then INC (, ) G the wave front of area da' and at position r = ( x, y,) E t E e ω i t =. A typical element of then acts as a source of Huygens wavelets. Our light detector sits at a point P in the observation screen, at a vector distance, R, from the origin of the aperture. Note that the distance of the detector, P, from the element da', is given by: G G r = R r The field at P due to the element da' is then equal to: iωt ikr Ee e de ( P) = da λ r = Source strength Huygens spherical wave ( ) ( ) The field at P due to the entire aperture is then a superposition of the wavelets from all the elemental areas: Fraunhofer Diffraction 3. Spring 1
3 ( ) E P Aperture Area iωt ikr Ee e = da λ r The detector measures the light intensity at P, rather than the electric field strength. Intensity is given by the magnitude of the time averaged Poynting vector, S G = E G B G µ = E Z z. Therefore, the detector measures: ˆ ( ) = ( ) I P E P Z Where Z = µ ε = 377Ω is the characteristic impedance (the ratio of the electric field magnitude to the magnetic field magnitude) of free space. In the present experiment, the aperture is a slit of width, a, while the detector is a photodiode at position, P. Evaluation of the KirchoffFresnel integral for the slit gives the following prediction for the diffracted intensity: xa sin π a z I( P( x, z) ) λ = I INC λz xa π λ z This prediction is subject to the condition that the observation point is far enough away so that z a λ. From a practical perspective, z 1a λ is sufficiently far away for the theory to be quite accurate. Notice that the formula applies to a situation in which plane waves of uniform intensity are incident normal to a long narrow slit of uniform width. The rays from different parts of the slit to a given observing point are effectively parallel (the Fraunhofer condition). The design of the experiment must mimic these conditions as closely as is possible. The condition on parallelism of rays is adequately satisfied at a distance of z 1a λ or more, since the error depends on the square of this quantity. The general form of the intensity equation as a function of detector position, x, at a fixed distance, z, from the slit is sketched below on linear and logarithmic scales. For the range of intensities that you are likely to measure, only the log scale can represent the weaker high order fringes. You should plot the data on 5 cycle loglinear graph paper. If you use a plotting program to display the data, again, be sure to use a logarithmic intensity scale. Fraunhofer Diffraction 3.3 Spring 1
4 Apparatus A beam expander increases the diameter of the laser beam so that the light is uniform over the width of the diffracting slit. The intensity of the diffracted light is measured with a photodiode. The photocurrent is determined from the voltage developed across a load resistor, using a digital multimeter. An analyzing slit of width, w, restricts the effective aperture of the photodiode so that the detailed shape of the diffraction pattern can be discerned. The photodiode and analyzing slit can be moved horizontally (the xdirection) by a calibrated translation stage driven by tuning a lead screw of pitch 1 mm. The revolution counter indicates the integral number of mm. Each small division on the calibrated knob represents.1 mm. Be sure to disengage the worm drive by tuning the lifting screw before use. diffracting analyzing R 9V slit slit Lx1 Lx I(x,z) HeNe laser Beam expander a Photodiode Calibrated translation stage Figure 3.3 Experimental arrangement for Fraunhofer Diffraction. DMM lead screw (1mm pitch) Fraunhofer Diffraction 3.4 Spring 1
5 Outline of the Experiment 1. Set up the apparatus Make up the diffraction and analyzing slits from razor blades. Measure the width of each with the measuring microscope to % if possible. On the optic bench, set up the laser, beam expander, diffracting slit, and calibrated translator. Mount the photodiode with analyzing slit on the translator. With the laser on, check that all the light passing through the analyzing slit also enters the detector for all positions of the translator. Draw the appearance of the fringes. Connect the photodiode circuit. Check that the output is not saturated when the detector is at the center of the central maximum.. Measurements Test the symmetry. Measure the intensities and positions for all the measurable maxima and minima on both sides of the center. The theory predicts that the pattern should be symmetric about the center. If it is not symmetric, then either the experiment has problems or the theory is wrong (or both!). If there is an asymmetry, assume that it is the experiment. Fix the problem before you go ahead. It is most likely a combination of nonuniform slit width, tilted slit, and detector at the wrong height. For the main data run, measure intensity versus detector position with about 5 points per peak. Make a stepwise scan from the x= position, to the maximum positive x; then return stepwise through the x= position and out to the greatest negative x. Then return to zero. Why is this procedure necessary? Do you need to improve on the procedure? Graph your results on 5cycle loglinear paper. Compare the intensity of the full laser beam with the intensity at the center of the central maximum. 3. Compare you data with the following predictions of the KirchoffFresnel singleslit formula. For the zeros of intensity, the position of the nth zero should satisfy: λz xn = n n = ± 1, ±, ± 3, " a Graph the quantity ax n /z versus n for the various zeros. This plot should give a line with a slope of λ. Calculate the value of λ and compare it to the result you found from the Ronchi grating in the Projection Microscope laboratory. For maxima of intensity, the relative intensity of the nth subsidiary maximum is predicted to be approximately: Fraunhofer Diffraction 3.5 Spring 1
6 I n 1 = n = ± 1, ±, ± 3, " I( x = ) 1 π n + I Graph n 1 versus n + on loglog paper. We expect a slope of . I( x = ) The intensity at the central maximum is predicted to be: I( x = ) a = I λz 4. Overview of interference and diffraction. INC In your experimental kit, you will find two transparency slides with several frames of circular apertures. Slide A has four rows and three columns with single circular and rectangular apertures (rows 14 in column A) and pairs of apertures with different separations (rows 14 in columns b and c). Slide B has single apertures and several arrays of apertures. You can use the inspection microscope to examine the slides. Examine the diffraction patterns produced with the transparencies and interpret what you see. Illuminate each frame separately, using an aperture to restrict the size of the laser beam. Change the frame by moving the transparency over the aperture. Stick some magnetic tape on the slide and use a steel aperture plate so that the magnetic force holds the slide in position. Shown below are some pictures of several of the patterns you should be able to find. Slide A 1a Slide A a Slide B 1b Slide B a Slide B 3b Fraunhofer Diffraction 3.6 Spring 1
7 Problems 1. Verify that the equations of part 3) in the experiment do indeed follow from the Kirchoff Fresnel formula for single slit diffraction. Slit widths What is the maximum width, a, of the diffracting slit if it is to satisfy the condition for Fraunhofer diffraction when the detector is 1 meter away from the slit, assuming that the wavelength is.6 microns? Calculate the width, w, of the scanning slit such that it samples only one tenth of the width of a subsidiary fringe. This width is needed so that you can properly map the shape of each fringe. 3. Laser beam. What is the minimum diameter needed for the expanded laser beam if the intensity is to be uniform to within 5% over the width of the diffracting slit? In other words, what is the minimum diameter needed so that: I x = I x = a ( ) ( ) I( x = ) =.5 Assume that the beam has a Gaussian intensity distribution: I /e () r I r I e R = I 5% a 4. Geometric problems in setting up the experiment. D r a. If the diffracting slit is tapered instead of being uniform in width, what would the diffraction pattern look like? Sketch the fringes. What effect would it have on the intensity distribution observed with the photodiode? b. If the slit is uniform, but slightly off the vertical position, how would the diffraction pattern be changed? Suppose the detector is correctly positioned for the central fringe, due to the nonvertical slit and is constrained to move horizontally, how would the apparent intensities of the fringes be changed? Sketch roughly the logarithmic graphs for the correct and incorrect geometries. Fraunhofer Diffraction 3.7 Spring 1
Diffraction of a Circular Aperture
Diffraction of a Circular Aperture Diffraction can be understood by considering the wave nature of light. Huygen's principle, illustrated in the image below, states that each point on a propagating wavefront
More informationInterference. Physics 102 Workshop #3. General Instructions
Interference Physics 102 Workshop #3 Name: Lab Partner(s): Instructor: Time of Workshop: General Instructions Workshop exercises are to be carried out in groups of three. One report per group is due by
More informationLab 9: The AcoustoOptic Effect
Lab 9: The AcoustoOptic Effect Incoming Laser Beam Travelling Acoustic Wave (longitudinal wave) O A 1st order diffracted laser beam A 1 Introduction qb d O 2qb rarefractions compressions Refer to Appendix
More informationINTERFERENCE OF SOUND WAVES
1/2016 Sound 1/8 INTERFERENCE OF SOUND WAVES PURPOSE: To measure the wavelength, frequency, and propagation speed of ultrasonic sound waves and to observe interference phenomena with ultrasonic sound waves.
More informationDiffraction and Young s Single Slit Experiment
Diffraction and Young s Single Slit Experiment Developers AB Overby Objectives Preparation Background The objectives of this experiment are to observe Fraunhofer, or farfield, diffraction through a single
More informationInterference and Diffraction
Chapter 14 nterference and Diffraction 14.1 Superposition of Waves... 1414. Young s DoubleSlit Experiment... 144 Example 14.1: DoubleSlit Experiment... 147 14.3 ntensity Distribution... 148 Example
More informationInterferometers. OBJECTIVES To examine the operation of several kinds of interferometers. d sin = n (1)
Interferometers The true worth of an experimenter consists in his pursuing not only what he seeks in his experiment, but also what he did not seek. Claude Bernard (18131878) OBJECTIVES To examine the
More informationElectrical Resonance
Electrical Resonance (RLC series circuit) APPARATUS 1. RLC Circuit board 2. Signal generator 3. Oscilloscope Tektronix TDS1002 with two sets of leads (see Introduction to the Oscilloscope ) INTRODUCTION
More informationwith functions, expressions and equations which follow in units 3 and 4.
Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model
More informationPolarization of Light
Polarization of Light References Halliday/Resnick/Walker Fundamentals of Physics, Chapter 33, 7 th ed. Wiley 005 PASCO EX997A and EX999 guide sheets (written by Ann Hanks) weight Exercises and weights
More information6) How wide must a narrow slit be if the first diffraction minimum occurs at ±12 with laser light of 633 nm?
Test IV Name 1) In a single slit diffraction experiment, the width of the slit is 3.1 105 m and the distance from the slit to the screen is 2.2 m. If the beam of light of wavelength 600 nm passes through
More informationUsing light scattering method to find The surface tension of water
Experiment (8) Using light scattering method to find The surface tension of water The aim of work: The goals of this experiment are to confirm the relationship between angular frequency and wave vector
More informationPhysics 41, Winter 1998 Lab 1  The Current Balance. Theory
Physics 41, Winter 1998 Lab 1  The Current Balance Theory Consider a point at a perpendicular distance d from a long straight wire carrying a current I as shown in figure 1. If the wire is very long compared
More informationAP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light
AP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light Name: Period: Date: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Reflection,
More informationWAVELENGTH OF LIGHT  DIFFRACTION GRATING
PURPOSE In this experiment we will use the diffraction grating and the spectrometer to measure wavelengths in the mercury spectrum. THEORY A diffraction grating is essentially a series of parallel equidistant
More informationMagnetic Field of a Circular Coil Lab 12
HB 112607 Magnetic Field of a Circular Coil Lab 12 1 Magnetic Field of a Circular Coil Lab 12 Equipment coil apparatus, BK Precision 2120B oscilloscope, Fluke multimeter, Wavetek FG3C function generator,
More informationDOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS RAYLEIGHSOMMERFELD DIFFRACTION INTEGRAL OF THE FIRST KIND
DOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS RAYLEIGHSOMMERFELD DIFFRACTION INTEGRAL OF THE FIRST KIND THE THREEDIMENSIONAL DISTRIBUTION OF THE RADIANT FLUX DENSITY AT THE FOCUS OF A CONVERGENCE BEAM
More informationE/M Experiment: Electrons in a Magnetic Field.
E/M Experiment: Electrons in a Magnetic Field. PRELAB You will be doing this experiment before we cover the relevant material in class. But there are only two fundamental concepts that you need to understand.
More informationDiffraction of Laser Light
Diffraction of Laser Light No Prelab Introduction The laser is a unique light source because its light is coherent and monochromatic. Coherent light is made up of waves, which are all in phase. Monochromatic
More informationA Guide to AcoustoOptic Modulators
A Guide to AcoustoOptic Modulators D. J. McCarron December 7, 2007 1 Introduction Acoustooptic modulators (AOMs) are useful devices which allow the frequency, intensity and direction of a laser beam
More informationELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES
ELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES The purpose of this lab session is to experimentally investigate the relation between electric field lines of force and equipotential surfaces in two dimensions.
More informationEXPERIMENT O6. Michelson Interferometer. Abstract. References. PreLab
EXPERIMENT O6 Michelson Interferometer Abstract A Michelson interferometer, constructed by the student, is used to measure the wavelength of HeNe laser light and the index of refraction of a flat transparent
More informationExperiment 7: Forces and Torques on Magnetic Dipoles
MASSACHUSETTS INSTITUTE OF TECHNOLOY Department of Physics 8. Spring 5 OBJECTIVES Experiment 7: Forces and Torques on Magnetic Dipoles 1. To measure the magnetic fields due to a pair of currentcarrying
More informationModern Classical Optics
Modern Classical Optics GEOFFREY BROOKER Department of Physics University of Oxford OXPORD UNIVERSITY PRESS Contents 1 Electromagnetism and basic optics 1 1.1 Introduction 1 1.2 The Maxwell equations 1
More information4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet
4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet Required: READ Hamper pp 115134 SL/HL Supplemental: Cutnell and Johnson, pp 473477, 507513 Tsokos, pp 216242 REMEMBER TO. Work through all
More information3.5.4.2 One example: Michelson interferometer
3.5.4.2 One example: Michelson interferometer mirror 1 mirror 2 light source 1 2 3 beam splitter 4 object (n object ) interference pattern we either observe fringes of same thickness (parallel light) or
More informationDIFFRACTION AND INTERFERENCE
DIFFRACTION AND INTERFERENCE In this experiment you will emonstrate the wave nature of light by investigating how it bens aroun eges an how it interferes constructively an estructively. You will observe
More informationReflection and Refraction
Equipment Reflection and Refraction Acrylic block set, planeconcaveconvex universal mirror, cork board, cork board stand, pins, flashlight, protractor, ruler, mirror worksheet, rectangular block worksheet,
More informationThe purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.
260 171 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this
More informationINTERFERENCE OF SOUND WAVES
2011 Interference  1 INTERFERENCE OF SOUND WAVES The objectives of this experiment are: To measure the wavelength, frequency, and propagation speed of ultrasonic sound waves. To observe interference phenomena
More informationAP1 Waves. (A) frequency (B) wavelength (C) speed (D) intensity. Answer: (A) and (D) frequency and intensity.
1. A fire truck is moving at a fairly high speed, with its siren emitting sound at a specific pitch. As the fire truck recedes from you which of the following characteristics of the sound wave from the
More informationExperiment 8: Undriven & Driven RLC Circuits
Experiment 8: Undriven & Driven RLC Circuits Answer these questions on a separate sheet of paper and turn them in before the lab 1. RLC Circuits Consider the circuit at left, consisting of an AC function
More informationSection 5.0 : Horn Physics. By Martin J. King, 6/29/08 Copyright 2008 by Martin J. King. All Rights Reserved.
Section 5. : Horn Physics Section 5. : Horn Physics By Martin J. King, 6/29/8 Copyright 28 by Martin J. King. All Rights Reserved. Before discussing the design of a horn loaded loudspeaker system, it is
More informationLab E1: Introduction to Circuits
E1.1 Lab E1: Introduction to Circuits The purpose of the this lab is to introduce you to some basic instrumentation used in electrical circuits. You will learn to use a DC power supply, a digital multimeter
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationOptical Fibres. Introduction. Safety precautions. For your safety. For the safety of the apparatus
Please do not remove this manual from from the lab. It is available at www.cm.ph.bham.ac.uk/y2lab Optics Introduction Optical fibres are widely used for transmitting data at high speeds. In this experiment,
More informationAntenna Properties and their impact on Wireless System Performance. Dr. Steven R. Best. Cushcraft Corporation 48 Perimeter Road Manchester, NH 03013
Antenna Properties and their impact on Wireless System Performance Dr. Steven R. Best Cushcraft Corporation 48 Perimeter Road Manchester, NH 03013 Phone (603) 6277877 FAX: (603) 6271764 Email: sbest@cushcraft.com
More informationMeasuring index of refraction
Grzegorz F. Wojewoda Zespół Szkół Ogólnokształcących nr 1 Bydgoszcz, Poland Logo designed by Armella Leung, www.armella.fr.to Translation: Małgorzata Czart Measuring index of refraction The advent of lowcost
More informationExperiment 5. Lasers and laser mode structure
Northeastern University, PHYS5318 Spring 2014, 1 1. Introduction Experiment 5. Lasers and laser mode structure The laser is a very important optical tool that has found widespread use in science and industry,
More informationPennsylvania System of School Assessment
Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read
More informationPhysics 41 Chapter 38 HW Key
Physics 41 Chapter 38 HW Key 1. Helium neon laser light (63..8 nm) is sent through a 0.300mmwide single slit. What is the width of the central imum on a screen 1.00 m from the slit? 7 6.38 10 sin θ.11
More informationINTERFERENCE OBJECTIVES PRELECTURE. Aims
53 L4 INTERFERENCE Aims OBJECTIVES When you have finished this chapter you should understand how the wave model of light can be used to explain the phenomenon of interference. You should be able to describe
More informationPHYS 39a Lab 3: Microscope Optics
PHYS 39a Lab 3: Microscope Optics Trevor Kafka December 15, 2014 Abstract In this lab task, we sought to use critical illumination and Köhler illumination techniques to view the image of a 1000 linesperinch
More informationPHYA2. General Certificate of Education Advanced Subsidiary Examination June 2010. Mechanics, Materials and Waves
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 2 For this paper you must have: a ruler a calculator a Data and Formulae Booklet.
More informationPhysics 111 Homework Solutions Week #9  Tuesday
Physics 111 Homework Solutions Week #9  Tuesday Friday, February 25, 2011 Chapter 22 Questions  None MultipleChoice 223 A 224 C 225 B 226 B 227 B 229 D Problems 227 In this double slit experiment we
More informationO6: The Diffraction Grating Spectrometer
2B30: PRACTICAL ASTROPHYSICS FORMAL REPORT: O6: The Diffraction Grating Spectrometer Adam Hill Lab partner: G. Evans Tutor: Dr. Peter Storey 1 Abstract The calibration of a diffraction grating spectrometer
More informationphysics 1/12/2016 Chapter 20 Lecture Chapter 20 Traveling Waves
Chapter 20 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 20 Traveling Waves Chapter Goal: To learn the basic properties of traveling waves. Slide
More informationε: Voltage output of Signal Generator (also called the Source voltage or Applied
Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and
More informationFriday 18 January 2013 Morning
Friday 18 January 2013 Morning AS GCE PHYSICS B (ADVANCING PHYSICS) G492/01 Understanding Processes / Experimentation and Data Handling *G411640113* Candidates answer on the Question Paper. OCR supplied
More informationForce on Moving Charges in a Magnetic Field
[ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after
More informationSample Questions for the AP Physics 1 Exam
Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiplechoice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each
More informationv = fλ PROGRESSIVE WAVES 1 Candidates should be able to :
PROGRESSIVE WAVES 1 Candidates should be able to : Describe and distinguish between progressive longitudinal and transverse waves. With the exception of electromagnetic waves, which do not need a material
More informationEfficiency of a Light Emitting Diode
PHYSICS THROUGH TEACHING LABORATORY VII Efficiency of a Light Emitting Diode RAJESH B. KHAPARDE AND SMITHA PUTHIYADAN Homi Bhabha Centre for Science Education Tata Institute of Fundamental Research V.
More informationDevelopment of Optical Wave Microphone Measuring Sound Waves with No Diaphragm
Progress In Electromagnetics Research Symposium Proceedings, Taipei, March 5 8, 3 359 Development of Optical Wave Microphone Measuring Sound Waves with No Diaphragm Yoshito Sonoda, Takashi Samatsu, and
More informationExperiment 7: Familiarization with the Network Analyzer
Experiment 7: Familiarization with the Network Analyzer Measurements to characterize networks at high frequencies (RF and microwave frequencies) are usually done in terms of scattering parameters (S parameters).
More informationIntroduction to Optics
Second Edition Introduction to Optics FRANK L. PEDROTTI, S.J. Marquette University Milwaukee, Wisconsin Vatican Radio, Rome LENO S. PEDROTTI Center for Occupational Research and Development Waco, Texas
More informationPhysics 221 Experiment 5: Magnetic Fields
Physics 221 Experiment 5: Magnetic Fields August 25, 2007 ntroduction This experiment will examine the properties of magnetic fields. Magnetic fields can be created in a variety of ways, and are also found
More informationMeasurement of ChargetoMass (e/m) Ratio for the Electron
Measurement of ChargetoMass (e/m) Ratio for the Electron Experiment objectives: measure the ratio of the electron chargetomass ratio e/m by studying the electron trajectories in a uniform magnetic
More informationPHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator.
PHYS 222 Spring 2012 Final Exam Closed books, notes, etc. No electronic device except a calculator. NAME: (all questions with equal weight) 1. If the distance between two point charges is tripled, the
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson AddisonWesley.
Chapter 20. Traveling Waves You may not realize it, but you are surrounded by waves. The waviness of a water wave is readily apparent, from the ripples on a pond to ocean waves large enough to surf. It
More informationAP1 Oscillations. 1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More informationPhysics 25 Exam 3 November 3, 2009
1. A long, straight wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what would be the the magnitude of the magnetic field at a distance d/3 from the wire,
More informationAlgebra 2 Chapter 1 Vocabulary. identity  A statement that equates two equivalent expressions.
Chapter 1 Vocabulary identity  A statement that equates two equivalent expressions. verbal model A word equation that represents a reallife problem. algebraic expression  An expression with variables.
More informationGRID AND PRISM SPECTROMETERS
FYSA230/2 GRID AND PRISM SPECTROMETERS 1. Introduction Electromagnetic radiation (e.g. visible light) experiences reflection, refraction, interference and diffraction phenomena when entering and passing
More informationGeorgia Standards of Excellence Curriculum Map. Mathematics. GSE 8 th Grade
Georgia Standards of Excellence Curriculum Map Mathematics GSE 8 th Grade These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. GSE Eighth Grade
More informationUnderstanding Poles and Zeros
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.14 Analysis and Design of Feedback Control Systems Understanding Poles and Zeros 1 System Poles and Zeros The transfer function
More informationExperiment 3 Lenses and Images
Experiment 3 Lenses and Images Who shall teach thee, unless it be thine own eyes? Euripides (480?406? BC) OBJECTIVES To examine the nature and location of images formed by es. THEORY Lenses are frequently
More informationPHYSICS PAPER 1 (THEORY)
PHYSICS PAPER 1 (THEORY) (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) 
More informationUsing the Impedance Method
Using the Impedance Method The impedance method allows us to completely eliminate the differential equation approach for the determination of the response of circuits. In fact the impedance method even
More informationAPPLICATION NOTE ULTRASONIC CERAMIC TRANSDUCERS
APPLICATION NOTE ULTRASONIC CERAMIC TRANSDUCERS Selection and use of Ultrasonic Ceramic Transducers The purpose of this application note is to aid the user in the selection and application of the Ultrasonic
More informationP R E A M B L E. Facilitated workshop problems for class discussion (1.5 hours)
INSURANCE SCAM OPTICS  LABORATORY INVESTIGATION P R E A M B L E The original form of the problem is an Experimental Group Research Project, undertaken by students organised into small groups working as
More informationThe PointSlope Form
7. The PointSlope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationExperiment #9, Magnetic Forces Using the Current Balance
Physics 182  Fall 2014  Experiment #9 1 Experiment #9, Magnetic Forces Using the Current Balance 1 Purpose 1. To demonstrate and measure the magnetic forces between current carrying wires. 2. To verify
More informationPHYSICS EXPERIMENTS (SOUND)
PHYSICS EXPERIMENTS (SOUND) In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself often more valuable than
More informationExamples of Uniform EM Plane Waves
Examples of Uniform EM Plane Waves Outline Reminder of Wave Equation Reminder of Relation Between E & H Energy Transported by EM Waves (Poynting Vector) Examples of Energy Transport by EM Waves 1 Coupling
More informationMAG Magnetic Fields revised July 24, 2012
MAG Magnetic Fields revised July 24, 2012 (You will do two experiments; this one (in Rock 402) and the Magnetic Induction experiment (in Rock 403). Sections will switch rooms and experiments halfway through
More informationEpisode 126: Capacitance and the equation C =Q/V
Episode 126: Capacitance and the equation C =Q/V Having established that there is charge on each capacitor plate, the next stage is to establish the relationship between charge and potential difference
More informationSolution Derivations for Capa #14
Solution Derivations for Capa #4 ) An image of the moon is focused onto a screen using a converging lens of focal length (f = 34.8 cm). The diameter of the moon is 3.48 0 6 m, and its mean distance from
More informationRFMicrowaves formulas  1port systems
RFMicrowaves formulas  port systems sparameters: Considering a voltage source feeding into the DUT with a source impedance of. E i E r DUT The voltage into the DUT is composed of 2 parts, an incident
More informationAntenna Deployment Technical Brief
ProCurve Networking Antenna Deployment Technical Brief Introduction... 2 Antenna types... 2 Omni directional antennas... 2 Directional antennas... 2 Diversity antennas... 3 High gain directional antennas...
More informationFrequency response: Resonance, Bandwidth, Q factor
Frequency response: esonance, Bandwidth, Q factor esonance. Let s continue the exploration of the frequency response of circuits by investigating the series circuit shown on Figure. C + V  Figure The
More information6 J  vector electric current density (A/m2 )
Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J  vector electric current density (A/m2 ) M  vector magnetic current density (V/m 2 ) Some problems
More informationHeliumNeon Laser. Figure 1: Diagram of optical and electrical components used in the HeNe laser experiment.
HeliumNeon Laser Experiment objectives: assemble and align a 3mW HeNe laser from readily available optical components, record photographically the transverse mode structure of the laser output beam,
More informationSimple Harmonic Motion
Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights
More informationPhysics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6. Instructions: 1. In the formula F = qvxb:
Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6 Signature Name (Print): 4 Digit ID: Section: Instructions: Answer all questions 24 multiple choice questions. You may need to do some calculation.
More informationRutgers Analytical Physics 750:228, Spring 2016 ( RUPHY228S16 )
1 of 13 2/17/2016 5:28 PM Signed in as Weida Wu, Instructor Help Sign Out Rutgers Analytical Physics 750:228, Spring 2016 ( RUPHY228S16 ) My Courses Course Settings University Physics with Modern Physics,
More informationAcceleration levels of dropped objects
Acceleration levels of dropped objects cmyk Acceleration levels of dropped objects Introduction his paper is intended to provide an overview of drop shock testing, which is defined as the acceleration
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT 4 Understand singlephase alternating current (ac) theory Single phase AC
More informationQ1. The graph below shows how a sinusoidal alternating voltage varies with time when connected across a resistor, R.
Q1. The graph below shows how a sinusoidal alternating voltage varies with time when connected across a resistor, R. (a) (i) State the peaktopeak voltage. peaktopeak voltage...v (1) (ii) State the
More informationBasic Optics System OS8515C
40 50 30 60 20 70 10 80 0 90 80 10 20 70 T 30 60 40 50 50 40 60 30 C 70 20 80 10 90 90 0 80 10 70 20 60 50 40 30 Instruction Manual with Experiment Guide and Teachers Notes 01209900B Basic Optics System
More informationAC CIRCUITS  CAPACITORS AND INDUCTORS
EXPRIMENT#8 AC CIRCUITS  CAPACITORS AND INDUCTORS NOTE: Two weeks are allocated for this experiment. Before performing this experiment, review the Proper Oscilloscope Use section of Experiment #7. Objective
More informationWhat does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
PRIMARY CONTENT MODULE Algebra  Linear Equations & Inequalities T37/H37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of
More informationRec. ITUR F.6995 1 RECOMMENDATION ITUR F.6995 *
Rec. ITUR F.6995 1 RECOMMENATION ITUR F.6995 * REFERENCE RAIATION PATTERNS FOR LINEOFSIGHT RAIORELAY SYSTEM ANTENNAS FOR USE IN COORINATION STUIES AN INTERFERENCE ASSESSMENT IN THE FREQUENCY RANGE
More information1051232 Imaging Systems Laboratory II. Laboratory 4: Basic Lens Design in OSLO April 2 & 4, 2002
05232 Imaging Systems Laboratory II Laboratory 4: Basic Lens Design in OSLO April 2 & 4, 2002 Abstract: For designing the optics of an imaging system, one of the main types of tools used today is optical
More informationExample SECTION 131. XAXIS  the horizontal number line. YAXIS  the vertical number line ORIGIN  the point where the xaxis and yaxis cross
CHAPTER 13 SECTION 131 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants XAXIS  the horizontal
More informationChapter 22: Electric Flux and Gauss s Law
22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we
More informationELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON
ELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON M.A.Shapiro, C.P.Moeller, and R.J.Temkin Plasma Science and Fusion Ceer, Massachusetts Institute of Technology,
More informationElectron Charge to Mass Ratio Matthew Norton, Chris Bush, Brian Atinaja, Becker Steven. Norton 0
Electron Charge to Mass Ratio Matthew Norton, Chris Bush, Brian Atinaja, Becker Steven Norton 0 Norton 1 Abstract The electron charge to mass ratio was an experiment that was used to calculate the ratio
More informationToday. next two weeks
Today Temporal and spatial coherence Spatially incoherent imaging The incoherent PSF The Optical Transfer Function (OTF) and Modulation Transfer Function (MTF) MTF and contrast comparison of spatially
More informationPrelab Quiz/PHYS 224 Magnetic Force and Current Balance. Your name Lab section
Prelab Quiz/PHYS 224 Magnetic Force and Current Balance Your name Lab section 1. What do you investigate in this lab? 2. Two straight wires are in parallel and carry electric currents in opposite directions
More information