2. Do Not use the laser without getting instructions from the demonstrator.


 Luke Nash
 1 years ago
 Views:
Transcription
1 EXPERIMENT 3 Diffraction Pattern Measurements using a Laser Laser Safety The Helium Neon lasers used in this experiment and are of low power (0.5 milliwatts) but the narrow beam of light is still of high intensity. Consequently, 1. Never look directly into the unexpanded laser beam or at its reflection from a mirror surface.. Do Not use the laser without getting instructions from the demonstrator. Introduction Physical optics predicts the angular position θ of the Fraunhofer diffraction fringe minima produced by monochromatic light of wavelength λ passing through a single slit of width b to be given by mλ = b sin θ m (3.1) where θm is the angle between the central maximum and mth dark fringe. Theory also predicts that the fringe intensity is given by where I = I o sin β β = I o sinc β (3.) β = π b sin θ λ and Io is the intensity of the central maximum at θ = 0. Thus the Fraunhofer pattern for a single narrow slit has the form shown in Fig The pattern consists of a broad intensely illuminated central band accompanied by a series of more weakly illuminated narrow fringes all parallel to the slit and located on either side of it. 31 (3.3)
2 Experimental Arrangement A photodiode detector interfaced to a PC facilitates the plotting of a graph of diffraction fringe intensity as a function of position for single and multiple slits. The Fresnel diffraction pattern formed by a horizontal laser beam passing through a narrow vertical single slit is arranged to fall on a movable detector (Fig. 3.). Note that while Eq. 3.1 and 3. are derived for Fraunhofer diffraction, these equations are approximately correct when θ is small i.e. when the distance between the slit and detector is large compared with the fringe spacing. Fig. 3. illustrates the apparatus used to facilitate intensity measurements in the diffraction pattern. The detector is a photodiode mounted on a steel rod which can be moved horizontally along that rod in order to investigate the nature of the fringe pattern. The horizontal position of the detector and the light intensity are recorded automatically by the computer as the detector is driven along the horizontal rod. The light intensity and the detector position are recorded 56 times during a scan through the diffraction pattern. Figure 3.1: Fraunhofer diffraction pattern for a single narrow slit Procedure You must calibrate the horizontal axis by recording the detector position in centimetres and noting the corresponding xaxis value on the computer screen at a series of points along the scan. Before taking any measurements, the positions of the single slit at the laser and the detector must be adjusted so that the detector receives laser light throughout the entire scan of the diffraction pattern. A: The Single Slit The width of the single slit provided can be adjusted by turning the control on the side of the slit. You are required to record the intensity pattern for three different slit widths. In order to determine the slit width b with precision, the distance y between the two 4th order minima must be measured. 3
3 From Eq λ = b sin θ 4 b = 4λ 4λ sin θ 4 θ 4 since y D = tan θ 4 θ 4 (3.4) where D is the detector  slit distance meters. It follows that b = 4 λ y D = 8D λ y Using the HeNe laser with λ = 638Å, adjust the slit width to give a wellseparated diffraction pattern in the plane of the detector. Because the central maximum is about 0 times more intense than the next bright fringe on either side, it is necessary to adjust the intensity of the laser using a neutral density filter. You must adjust the filter so that the intensity reading on the detector when placed at the central maximum position is less than 56 (use Setup). The photodiode is then moved through the fringe pattern by setting the motion control to computer whilst executing the program supplied. The demonstrator will help you to set up the program. The readings of the position and intensity then automatically appear on the screen. When the scan is completed, a printout can be obtained by pressing the SHIFT and PRTSC keys together. Remove the neutral density filter and repeat the procedure. The detector will now be saturated when passing through the central peak but at least four maxima should be observed on either side of the central maximum. Check when you remove the filter that the diffraction pattern falls on the detector throughout its horizontal scan. Determine the slit width using Eq Obtain the diffraction patterns for two additional slit widths, ensuring in each case that the intensity reading in the central maximum position is less than 56. Apply the following analysis to your diffraction patterns. 1. Find using β the location of both the minima and subsidiary maxima in the diffraction pattern. Extrema (i.e. maxima and minima) of I θ = I o sin β which di θ dβ = I o sin β β (3.5) = I o sinc β correspond to values of β for (β cos β sin β) β 3 = 0 Minima occur when sin β = 0 and β 0, i.e. when β = ± m π with m = 1,, Confirm the values of β at the first three minima by measuring the distance between corresponding minima on each side, obtaining θ from Eq. 3.4 and substituting for θ in Eq Subsidiary maxima occur for nonzero β satisfying the relationship β cos β sin β = 0 33
4 D Laser Filter Computer Printer Single / Double slit Moveable Photodiode Figure 3.: Experimental Arrangement which can be arranged to give: tan β = β The last equation is most simply solved graphically by superimposing the straight line f 1 (β) = β on the curves f (β) = tan β. The points of intersection, other than the origin (Fig. 3.3), locate the subsidiary maxima at β = ±1.4303π, ±.459π, ±3.4707π etc. Note that these peaks are not quite midway between the minima, but are displaced towards the centre of the pattern by an amount which decreases with increasing value of m.. Determine the intensity of the first three or more maxima in terms of I o, the principal peak value. To evaluate I o for the second plot, where the main maximum is off scale, we can use the ratio of I 1 I from the first plot because I 1 o I is constant. o We know that secondary peaks occur at β 1 = 1.43, β =.46 and β 3 = 3.47 and that I θ = I o sinc β and so to measure the β values, we need only calculate the sinc function in the Appendix to find sinc β 1 which should be ( 0.17) = sinc β which should be (0.18) = and sinc β 3 which should be ( 0.091) = The desired values shown should then be compared with your measured values and with those obtained previously. 3. The approximate expression for the angular width at half maximum of the central peak of the diffraction pattern is obtained as follows 34
5 Figure 3.3: Graphs of f 1 (β) = β and f (β) = tan θ superimposed We must determine the value of θ for which the intensity is one half the peak intensity or i.e. I 1 I o = sinc β = 1 sincβ = The sinc function shows the intensity to have its half maximum value at β 1 Fig. 3.1). = 1.39 radians (see Since β 1 β = πb sin θ λ = 1.39 πb λ θ 1 the total angular width, θ is θ 1 This is usually rounded off to and θ 1 = 0.44 λ b and hence θ = λ b. θ = λ b Check that the width of the diffraction pattern varies inversely with the width of the slit using the three graphs plotted with the neutral density filter and measure the halfwidth of the main maximum in each case. Calibrate the horizontal axis of the pattern and hence evaluate the actual slit widths used in each case. 35
6 B: The Double Slit Replace the single slit with the double slit and record the intensity pattern. From the intensity pattern determine the width of the slits and their separation. The equation of the intensity pattern can be found in various optics books and is I(θ) = 4 I o sinc β cos α where πa sin θ α = λ and a is the separation between the centres of the two slits. The peak I o is that of a single slit at θ = 0 and I(0) = 4I o. Fig. 3.4 shows the intensity variation across the pattern for a = 3b. The first term in the above equation gives the intensity distribution in the Fraunhofer pattern for a single slit and gives the slowly varying envelope within which lie the fringes given by the second term. The cos fringes are characteristic of the interference between two point or line sources separated by a distance a. The second term represents the effect of interference between disturbances from the two slits and the first term the result of diffraction at each individual slit (see Eq. 3.1). The bright band of order n in the interference pattern for two slits is said to be suppressed or missing when it is coincident with a null in the diffraction envelope. Maxima in the interference pattern occur when a sin θ = nλ(n = 0, ±1, ±,...). Minima in the single slit diffraction pattern result when b sin θ = m(m = ±1, ±...). When both of these equations are satisfied a b = n m In Fig. 3.4 the first missing order corresponds to n = 3 where m = 1 and accordingly a = 3b. The second missing order results when n = 6 and m =. If we include the two half fringes at the missing orders, there are m n bright bands within the central diffraction peak. Apply the above considerations to your intensity pattern. C: Babinet s Principle Babinet s principle states that the diffraction patterns produced by two complementary objects (e.g. slit and wire of the same diameter) are identical. This principle can be used here to estimate the diameter of human hair. Stretch a hair across the empty slideholder provided and tape the ends to secure it in position. Mount the hair in place of the usual single or double slit and record the resulting diffraction pattern. The width of the hair may be obtained simply by comparing the width of the central maximum with that obtained for a single slit. Questions 1. Sketch and explain briefly the diffraction pattern of a straight edge. Can such a pattern be measured with this experimental arrangement?. Sketch and explain briefly the diffraction pattern of a circular aperture. 36
7 Figure 3.4: Fraunhofer diffraction pattern for a double slit of width b and separation a where a = 3b 3. Briefly what did you learn from this experiment? References 1. Optics, Hecht & Zajac. Fundamentals of Optics, Jenkins & White WWW : Particle Size Analysis with Laser Diffraction  ID=158 Diffraction in Medicine
Interference. 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 informationFraunhofer Diffraction
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
More informationDiffraction 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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A single slit forms a diffraction pattern, with the first minimum at an angle of 40 from
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 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 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 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 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 informationRESOLVING POWER OF A READING TELESCOPE
96 Lab Experiments Experiment255 RESOLVING POWER OF A READING TELESCOPE S Dr Jeethendra Kumar P K KamalJeeth Instrumentation & Service Unit, No60, TATA Nagar, Bangalore560 092, INDIA. Email:jeeth_kjisu@rediffmail.com
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 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 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 informationPhysics Spring Experiment #8 1 Experiment #8, Magnetic Forces Using the Current Balance
Physics 182  Spring 2012  Experiment #8 1 Experiment #8, Magnetic Forces Using the Current Balance 1 Purpose 1. To demonstrate and measure the magnetic forces between current carrying wires. 2. To verify
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 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 informationAnswer: b. Answer: a. Answer: d
Practice 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
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 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 informationPHYS2212 LAB Coulomb s Law and the Force between Charged Plates
PHYS2212 LAB Coulomb s Law and the Force between Charged Plates Objectives To investigate the electrostatic force between charged metal plates and determine the electric permittivity of free space, ε
More informationThe HeNe Laser * HeNe Laser System. Power supply and ballast. interatomic collision. 1E7 sec
The HeNe Laser * I. Introduction The HeNe laser (Figure 1) uses a low pressure (ca. 1 Torr He, 0.1 Torr Ne) mixture excited by a dc electric discharge. A ballast resistor is placed in series with the
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 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 informationLAUE DIFFRACTION INTRODUCTION CHARACTERISTICS X RAYS BREMSSTRAHLUNG
LAUE DIFFRACTION INTRODUCTION Xrays are electromagnetic radiations that originate outside the nucleus. There are two major processes for Xray production which are quite different and which lead to different
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 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 informationATOMIC SPECTRA. Apparatus: Optical spectrometer, spectral tubes, power supply, incandescent lamp, bottles of dyed water, elevating jack or block.
1 ATOMIC SPECTRA Objective: To measure the wavelengths of visible light emitted by atomic hydrogen and verify the measured wavelengths against those predicted by quantum theory. To identify an unknown
More informationHeliumNeon Laser. 1 Introduction. 2 Background. 2.1 HeliumNeon Gain Medium. 2.2 Laser Cavity. 2.3 HermiteGaussian or tranverse Modes
HeliumNeon Laser 1 Introduction The HeliumNeon Laser, short HeNeLaser, is one of the most common used laser for allignement, reference laser and optics demonstrations. Its most used wavelength is at
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 informationLab M1: The Simple Pendulum
Lab M1: The Simple Pendulum Introduction. The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are usually regarded as the beginning of
More informationLecture 12: Fraunhofer diffraction by a single slit
Lecture 12: Fraunhofer diffraction y a single slit Lecture aims to explain: 1. Diffraction prolem asics (reminder) 2. Calculation of the diffraction integral for a long slit 3. Diffraction pattern produced
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 #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 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 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 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 informationBohr s Model and Emission Spectra of Hydrogen and Helium
PHYS01 LAB03 Bohr s Model and Emission Spectra of Hydrogen and Helium 1. Objective The objective of this experiment is to study the emission spectrum of hydrogen and to understand its origin in terms
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 informationExperiment P007: Acceleration due to Gravity (Free Fall Adapter)
Experiment P007: Acceleration due to Gravity (Free Fall Adapter) EQUIPMENT NEEDED Science Workshop Interface Clamp, right angle Base and support rod Free fall adapter Balls, 13 mm and 19 mm Meter stick
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 informationTHE BOHR QUANTUM MODEL
THE BOHR QUANTUM MODEL INTRODUCTION When light from a lowpressure gas is subject to an electric discharge, a discrete line spectrum is emitted. When light from such a lowpressure gas is examined with
More informationMATH SOLUTIONS TO PRACTICE FINAL EXAM. (x 2)(x + 2) (x 2)(x 3) = x + 2. x 2 x 2 5x + 6 = = 4.
MATH 55 SOLUTIONS TO PRACTICE FINAL EXAM x 2 4.Compute x 2 x 2 5x + 6. When x 2, So x 2 4 x 2 5x + 6 = (x 2)(x + 2) (x 2)(x 3) = x + 2 x 3. x 2 4 x 2 x 2 5x + 6 = 2 + 2 2 3 = 4. x 2 9 2. Compute x + sin
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 informationBasic Physical Optics
F UNDAMENTALS OF PHOTONICS Module 1.4 Basic Physical Optics Leno S. Pedrotti CORD Waco, Texas In Module 13, Basic Geometrical Optics, we made use of light rays to demonstrate reflection and refraction
More informationLab 5: Conservation of Energy
Lab 5: Conservation of Energy Equipment SWS, 1meter stick, 2meter stick, heavy duty bench clamp, 90cm rod, 40cm rod, 2 double clamps, brass spring, 100g mass, 500g mass with 5cm cardboard square
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 informationG(θ) = max{g 1 (θ), G 2 (θ)}
Rec. ITUR F.1336 1 RECOMMENDATION ITUR F.1336* Rec. ITUR F.1336 REFERENCE RADIATION PATTERNS OF OMNIDIRECTIONAL AND OTHER ANTENNAS IN POINTTOMULTIPOINT SYSTEMS FOR USE IN SHARING STUDIES (Question
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 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 informationFTIR Instrumentation
FTIR Instrumentation Adopted from the FTIR lab instruction by H.N. Hsieh, New Jersey Institute of Technology: http://wwwec.njit.edu/~hsieh/ene669/ftir.html 1. IR Instrumentation Two types of instrumentation
More informationCORNU S SPIRAL. Such diffraction is called Fraunhofer diffraction.
CORNU S SPIRAL If a parallel beam of light from a distant source encounters an obstacle, the shadow of the obstacle is not a simple geometric shadow but is, rather, a diffraction pattern. For example,
More informationRoots and Coefficients of a Quadratic Equation Summary
Roots and Coefficients of a Quadratic Equation Summary For a quadratic equation with roots α and β: Sum of roots = α + β = and Product of roots = αβ = Symmetrical functions of α and β include: x = and
More informationIMPORTANT NOTE ABOUT WEBASSIGN:
Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
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 informationGEOMETRICAL OPTICS. Lens Prism Mirror
GEOMETRICAL OPTICS Geometrical optics is the treatment of the passage of light through lenses, prisms, etc. by representing the light as rays. A light ray from a source goes in a straight line through
More informationENGINEERING METROLOGY
ENGINEERING METROLOGY ACADEMIC YEAR 9293, SEMESTER ONE COORDINATE MEASURING MACHINES OPTICAL MEASUREMENT SYSTEMS; DEPARTMENT OF MECHANICAL ENGINEERING ISFAHAN UNIVERSITY OF TECHNOLOGY Coordinate Measuring
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 informationSection 1.8 Coordinate Geometry
Section 1.8 Coordinate Geometry The Coordinate Plane Just as points on a line can be identified with real numbers to form the coordinate line, points in a plane can be identified with ordered pairs of
More informationCinema Projection Distortion
This paper was presented at: The 141st SMPTE Technical Conference and Exhibition Displays for the Theater and Home Session November 20, 1999 Cinema Projection Distortion Ronald A. Petrozzo Stuart W. Singer
More informationChapter 2 Laser Diode Beam Propagation Basics
Chapter 2 Laser Diode Beam Propagation Basics Abstract Laser diode beam propagation characteristics, the collimating and focusing behaviors and the M 2 factor are discussed using equations and graphs.
More informationMechanics. Determining the gravitational constant with the gravitation torsion balance after Cavendish. LD Physics Leaflets P1.1.3.1.
Mechanics Measuring methods Determining the gravitational constant LD Physics Leaflets P1.1.3.1 Determining the gravitational constant with the gravitation torsion balance after Cavendish Measuring the
More informationCHARGE TO MASS RATIO OF THE ELECTRON
CHARGE TO MASS RATIO OF THE ELECTRON In solving many physics problems, it is necessary to use the value of one or more physical constants. Examples are the velocity of light, c, and mass of the electron,
More informationFRICTION, WORK, AND THE INCLINED PLANE
FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle
More informationAcceleration Due to Gravity
Activity 5 PS2826 Acceleration Due to Gravity Kinematics: linear motion, acceleration, free fall, graphing GLX setup file: free fall Qty Equipment and Materials Part Number 1 PASPORT Xplorer GLX PS2002
More informationInstytut Fizyki Doświadczalnej Wydział Matematyki, Fizyki i Informatyki UNIWERSYTET GDAŃSKI
Instytut Fizyki Doświadczalnej Wydział Matematyki, Fizyki i Informatyki UNIWERSYTET GDAŃSKI I. Background theory. 1. Electromagnetic waves and their properties. 2. Polarisation of light: a) unpolarised
More informationGrazing incidence wavefront sensing and verification of Xray optics performance
Grazing incidence wavefront sensing and verification of Xray optics performance Timo T. Saha, Scott Rohrbach, and William W. Zhang, NASA Goddard Space Flight Center, Greenbelt, Md 20771 Evaluation of
More informationPRACTICE EXAM IV P202 SPRING 2004
PRACTICE EXAM IV P202 SPRING 2004 1. In two separate double slit experiments, an interference pattern is observed on a screen. In the first experiment, violet light (λ = 754 nm) is used and a secondorder
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 informationAnnouncements. Dry Friction
Announcements Dry Friction Today s Objectives Understand the characteristics of dry friction Draw a FBD including friction Solve problems involving friction Class Activities Applications Characteristics
More informationCH205: Fluid Dynamics
CH05: Fluid Dynamics nd Year, B.Tech. & Integrated Dual Degree (Chemical Engineering) Solutions of Mid Semester Examination Data Given: Density of water, ρ = 1000 kg/m 3, gravitational acceleration, g
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 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 informationOPTICAL FIBERS INTRODUCTION
OPTICAL FIBERS References: J. Hecht: Understanding Fiber Optics, Ch. 13, Prentice Hall N.J. 1999 D. R. Goff: Fiber Optic Reference Guide (2 nd ed.) Focal Press 1999 Projects in Fiber Optics (Applications
More informationCHAPTER 28 THE CIRCLE AND ITS PROPERTIES
CHAPTER 8 THE CIRCLE AND ITS PROPERTIES EXERCISE 118 Page 77 1. Calculate the length of the circumference of a circle of radius 7. cm. Circumference, c = r = (7.) = 45.4 cm. If the diameter of a circle
More informationFIBER OPTICS. Prof. R.K. Shevgaonkar. Department of Electrical Engineering. Indian Institute of Technology, Bombay. Lecture: 09
FIBER OPTICS Prof. R.K. Shevgaonkar Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture: 09 Analysis of Signal Distortion in Optical Fiber Fiber Optics, Prof. R.K. Shevgaonkar,
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationCharge and Discharge of a Capacitor
Charge and Discharge of a Capacitor INTRODUCTION Capacitors 1 are devices that can store electric charge and energy. Capacitors have several uses, such as filters in DC power supplies and as energy storage
More informationTriple Stage Raman spectrograph/spectrometer Raman system with scanning microscopy attachment: QTY: One
Specifications: Triple Stage Raman spectrograph/spectrometer Raman system with scanning microscopy attachment: QTY: One A. Triple Stage Raman spectrograph/spectrometer: 1. Spectral range : UV_Vis_NIR :
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 informationMeasure the Distance Between Tracks of CD and DVD
University of Technology Laser & Optoelectronics Engineering Department Laser Eng Branch Laser application Lab. The aim of work: Experiment (9) Measure the Distance Between Tracks of CD and DVD 1measure
More informationStudy Guide and Review for Electricity and Light Lab Final
Study Guide and Review for Electricity and Light Lab Final This study guide is provided to help you prepare for the lab final. The lab final consists of multiplechoice questions, usually two for each unit,
More information0.1 Dielectric Slab Waveguide
0.1 Dielectric Slab Waveguide At high frequencies (especially optical frequencies) the loss associated with the induced current in the metal walls is too high. A transmission line filled with dielectric
More informationTHREE DIMENSIONAL GEOMETRY
Chapter 11 THREE DIMENSIONAL GEOMETRY 111 Overview 1111 Direction cosines of a line are the cosines of the angles made by the line with positive directions of the coordinate axes 111 If l, m, n are the
More informationHow can I tell what the polarization axis is for a linear polarizer?
How can I tell what the polarization axis is for a linear polarizer? The axis of a linear polarizer determines the plane of polarization that the polarizer passes. There are two ways of finding the axis
More informationThermal Diffusivity, Specific Heat, and Thermal Conductivity of Aluminum Oxide and Pyroceram 9606
Report on the Thermal Diffusivity, Specific Heat, and Thermal Conductivity of Aluminum Oxide and Pyroceram 9606 This report presents the results of phenol diffusivity, specific heat and calculated thermal
More informationHooke s Law and Simple Harmonic Motion
Hooke s Law and Simple Harmonic Motion OBJECTIVE to measure the spring constant of the springs using Hooke s Law to explore the static properties of springy objects and springs, connected in series and
More informationHarmonic oscillation springs linked in parallel and in series
Harmonic oscillation TEP Principle The spring constant k for different springs and connections of springs is determined. For different experimental setups and suspended mass the oscillation period is
More informationColor holographic 3D display unit with aperture field division
Color holographic 3D display unit with aperture field division Weronika Zaperty, Tomasz Kozacki, Malgorzata Kujawinska, Grzegorz Finke Photonics Engineering Division, Faculty of Mechatronics Warsaw University
More informationTHE CONSERVATION OF ENERGY  PENDULUM 
THE CONSERVATION OF ENERGY  PENDULUM  Introduction The purpose of this experiment is to measure the potential energy and the kinetic energy of a mechanical system and to quantitatively compare the two
More information3D Scanner using Line Laser. 1. Introduction. 2. Theory
. Introduction 3D Scanner using Line Laser Di Lu Electrical, Computer, and Systems Engineering Rensselaer Polytechnic Institute The goal of 3D reconstruction is to recover the 3D properties of a geometric
More informationFigure 1 Different parts of experimental apparatus.
Objectives Determination of center of buoyancy Determination of metacentric height Investigation of stability of floating objects Apparatus The unit shown in Fig. 1 consists of a pontoon (1) and a water
More informationExample 1. Example 1 Plot the points whose polar coordinates are given by
Polar Coordinates A polar coordinate system, gives the coordinates of a point with reference to a point O and a half line or ray starting at the point O. We will look at polar coordinates for points
More informationChapter 24 Physical Pendulum
Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...
More information1 One Dimensional Horizontal Motion Position vs. time Velocity vs. time
PHY132 Experiment 1 One Dimensional Horizontal Motion Position vs. time Velocity vs. time One of the most effective methods of describing motion is to plot graphs of distance, velocity, and acceleration
More informationRevision problem. Chapter 18 problem 37 page 612. Suppose you point a pinhole camera at a 15m tall tree that is 75m away.
Revision problem Chapter 18 problem 37 page 612 Suppose you point a pinhole camera at a 15m tall tree that is 75m away. 1 Optical Instruments Thin lens equation Refractive power Cameras The human eye Combining
More informationMaking Better Medical Devices with Multisensor Metrology
Making Better Medical Devices with Multisensor Metrology by Nate J. Rose, Chief Applications Engineer, Optical Gaging Products (OGP) Multisensor metrology is becoming a preferred quality control technology
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 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 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 informationDetermination of Acceleration due to Gravity
Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two
More information