# FRAUNHOFER AND FRESNEL DIFFRACTION IN ONE DIMENSION

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 FRAUNHOFER AND FRESNEL DIFFRACTION IN ONE DIMENSION Revised November 15, 2017 INTRODUCTION The simplest and most commonly described examples of diffraction and interference from two-dimensional apertures are those for which the light incident on the apertures and the light after passage through the apertures can be described as plane waves. In this limit the diffraction is described as Fraunhofer or far field diffraction. If one of the aperture dimensions is very small compared to the other an example would be a slit with a width small compared to its length the intensity of the light transmitted through the aperture and observed some distance away will vary in a direction perpendicular to the slit width and the light beam, but will be constant in a direction along the slit. Thus the variation in the pattern can be described by only a single dimension and it is called one-dimensional. Fraunhofer diffraction has a particularly simple mathematical description. The amplitude of the diffracted wave can be described as the Fourier transform of the aperture function (For this experiment a suitable aperture function is one that is a constant equal to 1 over the aperture and 0 elsewhere). It is, of course, the intensity that is observed. Because it is most convenient to treat the amplitude as a complex quantity, the intensity or irradiance is proportional to the amplitude times its complex conjugate. For many examples of diffraction, the light source and the point of observation are sufficiently far from the diffracting aperture that both the incident and diffracted light can be treated as plane waves. If these conditions are met the diffraction is described as Fraunhofer or far field diffraction. If the condition that the light source and point of observation are far from the diffracting aperture is not met, so that one cannot employ the approximation of plane waves, then the curvature of the wavefront must be considered in deriving the diffraction pattern. This diffraction is described as Fresnel or near-field diffraction. (Fresnel is pronounced Fray-NEL.) The mathematics involved in Fresnel diffraction is not as simple as the Fourier transforms of far-field diffraction. However, a description has been developed in terms of what are called Fresnel zones, that will yield understandable, qualitative results. If more quantitative answers are needed, special integrals called Fresnel integrals must be evaluated. This can either be done numerically or graphically with the aid of a Cornu spiral. In this experiment, you will first observe far-field diffraction by the use of a lens which will collimate the light so that it hits the diffracting aperture as an approximate plane wave. Then you will remove the lens, and study near-field diffraction. REFERENCES 1. Hecht, Optics (4th or 5th ed.), Section 10.2, Fraunhofer diffraction. 2. Hecht, Optics (4th or 5th ed.), Section 10.3, Fresnel diffraction; Section , the Cornu spiral. APPARATUS and INITIAL SETUP The light source is a helium-neon laser (λ = nm). A spatial filter consisting of a microscope objective and a 25µ pinhole with three micrometer positioning screws is used to clean up the beam. In the Fraunhofer diffraction part, the spatial filter is followed by a long focal length collimating lens. A high-resolution detector is used to record the diffraction pattern. The detector is a Hamamatsu S3923 MOS linear image sensor. It consists of 1024 photodetector elements called pixels 0.5 mm high and arrayed along a line with a separation of 25 µm between the centers of adjacent pixels. It is important to align the array so that the entire diffraction pattern falls on the detector array and the plane of the array is perpendicular to the light beam. 1

3 pinhole position on the light pattern: by slightly moving the horizontal or vertical micrometers, the bright disk should not move but should be extinguished. If the blob appears to move (up or down, left or right) the position of the microscope lens is not yet correct. Detector Alignment First place the polarizer in the beam between the laser and spatial filter (refer to Figure 1). Rotate the polarizer using the small handle and notic what it does to the light intensity. At one setting the laser light should appear quite dim, and at another, nearly as bright as it was without the polarizer. Set the polarizer to transmit maximum light. Now, position the linear array so that the front of the array housing is approximately cm from the front of the spatial-filter pinhole. Orient the base to that the track is perpendicular to the beam path and clamp the array assembly in place with the magnetic base. Turn on the array controller box and press the RESET switch so that the green LED labeled ACQ. (ACQuire) is on. Turn on the oscilloscope used to monitor the array output, and adjust it, if necessary, to obtain a trace. Without any other object in the beam, you should see a broad hump on the oscilloscope screen. If the beam is too bright, the detector pixels may saturate. If this happens, move the polarizer into place between the laser and spatial filter, and adjust the polarizer angle to reduce the beam intensity. Center the hump in the detector by moving it horizontally along the track. Once it is centered, clamp the detector in place. FRAUNHOFER DIFFRACTION In this part you will obtain the intensity pattern for laser light after it has passed through a single slit, sets of double slits with different ratios of slit width to slit separation, and a multiple slit pattern of either 3, 4, or 5 slits. The detector will give you digital values for the integrated (over time) intensity of the diffracted light at 1024 points in the diffraction pattern. You will acquire the data electronically and plot it out using a program of your choice (such as Excel). From the plots, you will manually extract the relevant experimental parameters and their uncertainties. LASER POLARIZER SPATIAL FILTER ASSEMBLY MICROSCOPE OBJECTIVE PINHOLE 135 mm CAMERA LENS IRIS SLIT HOLDER SLIDE TILT ADJUST LINEAR CCD ARRAY CABLE TO CONTROL BOX & COMPUTER MICROMETERS 30 cm cm DETECTOR HEIGHT ADJUST cm Figure 1: Setup for Fraunhofer diffraction. Distances are approximate. Procedure for Fraunhofer diffraction A camera lens is used to bring the laser light from the pinhole to simulate plane-wave propagation as it passes through the diffraction apertures. The lens thus enables a practical (tabletop) realization of Fraunhofer diffraction. [Note for the curious: This setup is not quite the arrangement depicted in Fig of Hecht, in that the waves which impinge on the diffraction aperture in our experiment are not plane waves, but are converging toward the focus point on the screen. It can be shown, however, that our setup is optically equivalent to 3

5 Single slit diffraction 1. Obtain separate diffraction patterns for two single slits with different widths and record the data on the computer. 2. Record the necessary additional information you will need in order to analyze the patterns you obtain. You will need additional distances and the wavelength of the laser light (see the paragraph below). 3. Use the computer program to plot the data, or download the data set (a simple two-column text file) and plot it using your plotting program of choice (such as Excel). Then obtain the physical parameters from the graph directly. There is no need to make a computer fit to the pattern; indeed the physics is better understood by measuring the graph by hand with a ruler. For one slit, you should find (from the graph) information that you may use to calculate the slit width and its associated error. The width of the central peak and the location of the minima on either side should both be used to obtain your results. You will need a number of experimental parameters, such as the wavelength of the laser, the slit-to-array distance and the horizontal scale of the detector. The laser wavelength and the horizontal scale (pixel to pixel spacing) have already been given. Use a tape measure to measure the distance from the slits to the detector. Be careful to avoid any contact with the front of the detector. Use standard propagation-of-error techniques to determine the error on the slit width. Comment on the agreement between your derived values and the actual values of the slit width (available in the lab). Double slit diffraction 4. Select two sets of double slits with different ratios of slit width to slit separation. Obtain and record data sets for each. 5. Using the same techniques as above, obtain the slit widths and slit separations from the plotted data; comment on the agreement with the actual values. Multiple slit diffraction 6. Select at least one from the 3, 4, or 5 slit apertures. Obtain and record a data set for the aperture of your choice. 7. Using the same technique as above, obtain the slit widths, separation, and number of slits from the plotted data. (The slit number can be obtained by measuring the width of the fringes and comparing it to the fringe separation, rounding off to nearest integral value.) Comment on the agreement with the actual values. FRESNEL DIFFRACTION In this part two examples of Fresnel diffraction will be observed and compared to theory: diffraction from a single slit (illustrating the transition from Fresnel to Fraunhofer diffraction), and diffraction from a straight edge. Procedure for Fresnel diffraction The apparatus is essentially the same as that used for Fraunhofer diffraction. In fact, the first objective is to study how the Fraunhofer pattern for a single slit becomes Fresnel-like as you widen the slit. 5

6 LASER POLARIZER SPATIAL FILTER ASSEMBLY MICROSCOPE OBJECTIVE PINHOLE VARIABLE SLIT LINEAR CCD ARRAY CABLE TO CONTROL BOX & COMPUTER MICROMETERS 10 cm 30 cm cm DETECTOR HEIGHT ADJUST Figure 2: Setup for Fresnel diffraction. Remove the camera lens and iris used in the Fraunhofer diffraction part of the experiment and set it gently aside. Slide the slit holder on its track so that it is no longer in the beam. Check the position of the linear array so that the front of the array housing is approximately cm from the pinhole on the spatial filter. The light which will hit the aperture is no longer traveling in (approximate) plane waves, but has wave fronts whose curvature depend on the focal length of the microscope objective and the distance between the pinhole and the slit. (Here, we will only use a single slit or straight edge.) Place the variable slit approximately 10 cm in front of the pinhole (see Figure 2), and adjust its position so the slit is uniformly illuminated and the diffraction pattern is the right size to fill the array. To prevent saturation of the array (indicated by a flat line at the top of the readout) it may be necessary to reduce the light intensity with the polarizer. With all the optics in good alignment and with the desired diffraction pattern displayed on the scope, you are now ready to record the diffraction pattern on the computer. Single slit diffraction 1. First determine where the transition from Fraunhofer to Fresnel diffraction occurs as you change the slit width with the micrometer on the variable slit. (Hint: the Fraunhofer pattern is the square of a sinc function [sin(x)/x]: the the minima are all zero. These minima change when the slit is opened enough to require a Fresnel interpretation). Record the approximate slit width when this transition takes place and later determine whether it agrees with the theory. Obtain a 1024 point readout of the intensity pattern using the LabVIEW program. Carefully record all relevant distances and dimensions. In this case, you need to have the numbers necessary to calculate the reduced slit width u (or v); see Hecht section for definitions and an explanation. 2. Next, reduce the slit width to the Fraunhofer regime and use the techniques described in the Fraunhofer write-up to determine the slit width. The pattern should include the central maximum plus three secondary maxima on both sides. Obtain a 1024 point readout of the intensity pattern using the LabVIEW program. Carefully record all relevant distances and dimensions, as before. 3. Finally, starting from the Fraunhofer regime, increase the slit width and note that there are a number of discrete widths (in the Fresnel regime) where the central point in the intensity pattern goes through a minimum. Record the slit widths for the first two or three of these minima and obtain a 1024 point readout of the pattern for each one. The analysis will use the Cornu spiral. Figure in Hecht gives a labeled graph which can be used (Fig in 4th ed.). From your knowledge of the connection between the Cornu spiral and the intensity plot, it should be fairly obvious how one obtains the approximate slit widths corresponding to these minima. 6

7 This procedure is approximate; the error estimate should involve an educated guess of how well one can obtain the data from the graph. Be sure to convert the Fresnel units back to laboratory units using the formulas in the book or notes. Diffraction by a straight edge 4. Widen the slit further and notice how the pattern approaches that for a single edge. Replace the slit with the thin, straight-edged piece of metal shim stock provided. It is on another stand and magnetic base. BE CAREFUL: the metal edge is sharp and can cut! Obtain a 1024 point readout of the intensity pattern. Carefully record all relevant distances and dimensions. 7

### Experiment 1: Fraunhofer Diffraction of Light by a Single Slit

Experiment 1: Fraunhofer Diffraction of Light by a Single Slit Purpose 1. To understand the theory of Fraunhofer diffraction of light at a single slit and at a circular aperture; 2. To learn how to measure

### OPTICS I LENSES AND IMAGES

APAS Laboratory Optics I OPTICS I LENSES AND IMAGES If at first you don t succeed try, try again. Then give up- there s no sense in being foolish about it. -W.C. Fields SYNOPSIS: In Optics I you will learn

### Physics 3340 Spring Fourier Optics

Physics 3340 Spring 011 Purpose Fourier Optics In this experiment we will show how the Fraunhofer diffraction pattern or spatial Fourier transform of an object can be observed within an optical system.

### PHY 431 Homework Set #5 Due Nov. 20 at the start of class

PHY 431 Homework Set #5 Due Nov. 0 at the start of class 1) Newton s rings (10%) The radius of curvature of the convex surface of a plano-convex lens is 30 cm. The lens is placed with its convex side down

### Will contain image distance after raytrace Will contain image height after raytrace

Name: LASR 51 Final Exam May 29, 2002 Answer all questions. Module numbers are for guidance, some material is from class handouts. Exam ends at 8:20 pm. Ynu Raytracing The first questions refer to the

### Option G 4:Diffraction

Name: Date: Option G 4:Diffraction 1. This question is about optical resolution. The two point sources shown in the diagram below (not to scale) emit light of the same frequency. The light is incident

### Experimental Question 2: An Optical Black Box

Experimental Question 2: An Optical Black Box TV and computer screens have advanced significantly in recent years. Today, most displays consist of a color LCD filter matrix and a uniform white backlight

### Diffraction. Interference with more than 2 beams. Diffraction gratings. Diffraction by an aperture. Diffraction of a laser beam

Diffraction Interference with more than 2 beams 3, 4, 5 beams Large number of beams Diffraction gratings Equation Uses Diffraction by an aperture Huygen s principle again, Fresnel zones, Arago s spot Qualitative

### Lab 12 Microwave Optics.

b Lab 12 Microwave Optics. CAUTION: The output power of the microwave transmitter is well below standard safety levels. Nevertheless, do not look directly into the microwave horn at close range when the

### Chapter 36: diffraction

Chapter 36: diffraction Fresnel and Fraunhofer diffraction Diffraction from a single slit Intensity in the single slit pattern Multiple slits The Diffraction grating X-ray diffraction Circular apertures

### Basic Optics System OS-8515C

40 50 30 60 20 70 10 80 0 90 80 10 20 70 T 30 60 40 50 50 40 60 30 70 20 80 90 90 80 BASIC OPTICS RAY TABLE 10 0 10 70 20 60 50 40 30 Instruction Manual with Experiment Guide and Teachers Notes 012-09900B

### The diffraction of light

7 The diffraction of light 7.1 Introduction As introduced in Chapter 6, the reciprocal lattice is the basis upon which the geometry of X-ray and electron diffraction patterns can be most easily understood

### Physics 476LW. Advanced Physics Laboratory - Microwave Optics

Physics 476LW Advanced Physics Laboratory Microwave Radiation Introduction Setup The purpose of this lab is to better understand the various ways that interference of EM radiation manifests itself. However,

### MICHELSON INTERFEROMETER & FOURIER TRANSFORM SPECTROMETRY

MICHELSON INTERFEROMETER & FOURIER TRANSFORM SPECTROMETRY REFERENCES Revised October 18, 217. 1. Hecht, Optics (4th ed.), Fourier transforms and coherence basics, pp. 39 316; Michelson interferometer and

### LECTURE 13 DIFFRACTION. Instructor: Kazumi Tolich

LECTURE 13 DIFFRACTION Instructor: Kazumi Tolich Lecture 13 2 Reading chapter 33-4 & 33-6 to 33-7 Single slit diffraction Two slit interference-diffraction Fraunhofer and Fresnel diffraction Diffraction

### Holography. Introduction

Holography Introduction Holography is the technique of using monochromatic light sources to produce 3D images on photographic film or specially designed plates. In this experiment you will learn about

### 3B SCIENTIFIC PHYSICS

3B SCIENTIFIC PHYSICS Equipment Set for Wave Optics with Laser U17303 Instruction sheet 10/08 Alf 1. Safety instructions The laser emits visible radiation at a wavelength of 635 nm with a maximum power

### Lab Report 3: Speckle Interferometry LIN PEI-YING, BAIG JOVERIA

Lab Report 3: Speckle Interferometry LIN PEI-YING, BAIG JOVERIA Abstract: Speckle interferometry (SI) has become a complete technique over the past couple of years and is widely used in many branches of

### Polarization Experiments Using Jones Calculus

Polarization Experiments Using Jones Calculus Reference http://chaos.swarthmore.edu/courses/physics50_2008/p50_optics/04_polariz_matrices.pdf Theory In Jones calculus, the polarization state of light is

### Diffraction of a Circular Aperture

DiffractionofaCircularAperture 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

### Physics 1520, Spring 2013 Quiz 2, Form: A

Physics 1520, Spring 2013 Quiz 2, Form: A Name: Date: Section 1. Exercises 1. The index of refraction of a certain type of glass for red light is 1.52. For violet light, it is 1.54. Which color of light,

### E X P E R I M E N T 12

E X P E R I M E N T 12 Mirrors and Lenses Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics II, Exp 12: Mirrors and Lenses

### HOLOGRAPHY EXPERIMENT 25. Equipment List:-

EXPERIMENT 25 HOLOGRAPHY Equipment List:- (a) (b) (c) (d) (e) (f) (g) Holography camera and plate holders Laser/beam lamp and assembly Shutter on stand Light meter Objects to make holographs of Holographic

### OPTICS LENSES AND TELESCOPES

ASTR 1030 Astronomy Lab 97 Optics - Lenses & Telescopes OPTICS LENSES AND TELESCOPES SYNOPSIS: In this lab you will explore the fundamental properties of a lens and investigate refracting and reflecting

### Week IX: INTERFEROMETER EXPERIMENTS

Week IX: INTERFEROMETER EXPERIMENTS Notes on Adjusting the Michelson Interference Caution: Do not touch the mirrors or beam splitters they are front surface and difficult to clean without damaging them.

### Exam 4. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: Class: Date: Exam 4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Mirages are a result of which physical phenomena a. interference c. reflection

### Diffraction Single-slit Double-slit Diffraction grating Limit on resolution X-ray diffraction. Phys 2435: Chap. 36, Pg 1

Diffraction Single-slit Double-slit Diffraction grating Limit on resolution X-ray diffraction Phys 2435: Chap. 36, Pg 1 Single Slit New Topic Phys 2435: Chap. 36, Pg 2 Diffraction: bending of light around

### Lab 10: Lenses & Telescopes

Physics 2020, Fall 2010 Lab 8 page 1 of 6 Circle your lab day and time. Your name: Mon Tue Wed Thu Fri TA name: 8-10 10-12 12-2 2-4 4-6 INTRODUCTION Lab 10: Lenses & Telescopes In this experiment, you

### Image Formation. Light from distant things. Geometrical optics. Pinhole camera. Chapter 36

Light from distant things Chapter 36 We learn about a distant thing from the light it generates or redirects. The lenses in our eyes create images of objects our brains can process. This chapter concerns

### AP B Webreview ch 24 diffraction and interference

Name: Class: _ Date: _ AP B Webreview ch 24 diffraction and interference Multiple Choice Identify the choice that best completes the statement or answers the question.. In order to produce a sustained

### The Wave Nature of Light

The Wave Nature of Light Physics 102 Lecture 7 4 April 2002 Pick up Grating & Foil & Pin 4 Apr 2002 Physics 102 Lecture 7 1 Light acts like a wave! Last week we saw that light travels from place to place

### Experiment 19. Microwave Optics 1

Experiment 19 Microwave Optics 1 1. Introduction Optical phenomena may be studied at microwave frequencies. Using a three centimeter microwave wavelength transforms the scale of the experiment. Microns

### Chapter 7. Optical Measurement and Interferometry

Chapter 7 Optical Measurement and Interferometry 1 Introduction Optical measurement provides a simple, easy, accurate and reliable means for carrying out inspection and measurements in the industry the

### Radial Polarization Converter With LC Driver USER MANUAL

ARCoptix Radial Polarization Converter With LC Driver USER MANUAL Arcoptix S.A Ch. Trois-portes 18 2000 Neuchâtel Switzerland Mail: info@arcoptix.com Tel: ++41 32 731 04 66 Principle of the radial polarization

### CONFOCAL MICROSCOPE CM-1

CONFOCAL MICROSCOPE CM-1 USER INSTRUCTIONS Scientific Instruments Dr. J.R. Sandercock Im Grindel 6 Phone: +41 44 776 33 66 Fax: +41 44 776 33 65 E-Mail: info@jrs-si.ch Internet: www.jrs-si.ch 1. Properties

### AY 105 Lab Experiment #1: Radiometry/Photometry

AY 105 Lab Experiment #1: Radiometry/Photometry Purpose This lab will introduce you to working on an optical table. Many of the principles of optical alignment (in three dimensions), stray light control,

### MICROWAVE OPTICS. Instruction Manual and Experiment Guide for the PASCO scientific Model WA-9314B G

Includes Teacher's Notes and Typical Experiment Results Instruction Manual and Experiment Guide for the PASCO scientific Model WA-9314B 012-04630G MICROWAVE OPTICS 10101 Foothills Blvd. Roseville, CA 95678-9011

### SUBJECT: PHYSICS. Use and Succeed.

SUBJECT: PHYSICS I hope this collection of questions will help to test your preparation level and useful to recall the concepts in different areas of all the chapters. Use and Succeed. Navaneethakrishnan.V

### Bruker Dimension Icon AFM Quick User s Guide

Bruker Dimension Icon AFM Quick User s Guide March 3, 2015 GLA Contacts Jingjing Jiang (jjiang2@caltech.edu 626-616-6357) Xinghao Zhou (xzzhou@caltech.edu 626-375-0855) Bruker Tech Support (AFMSupport@bruker-nano.com

### USING THE 2 TELETUBE XLS TM & TELECAT XLS TM ADJUSTABLE SIGHT TUBE

USING THE 2 TELETUBE XLS TM & TELECAT XLS TM ADJUSTABLE SIGHT TUBE Revised 09/20/08 With the rapid proliferation of larger-aperture, low f-ratio Newtonian telescopes with 2" focusers and larger diagonal

### Physical Optics. Diffraction.

Physical Optics. Diffraction. Interference Young s interference experiment Thin films Coherence and incoherence Michelson interferometer Wave-like characteristics of light Huygens-Fresnel principle Interference.

### Introduction to Optics Work in Y1Lab

Introduction to Optics Work in Y1Lab Short Tutorial on Optics Safety & Good working practices A. Lens Imaging (Ray Optics) B. Single-slit diffraction (Wave Optics) Year 1 Laboratory, Physics, Imperial

### MSE 595T Transmission Electron Microscopy. Laboratory III TEM Imaging - I

MSE 595T Basic Transmission Electron Microscopy TEM Imaging - I Purpose The purpose of this lab is to: 1. Make fine adjustments to the microscope alignment 2. Obtain a diffraction pattern 3. Obtain an

### PhysicsAndMathsTutor.com 1

PhysicsAndMathsTutor.com 1 Q1. Just over two hundred years ago Thomas Young demonstrated the interference of light by illuminating two closely spaced narrow slits with light from a single light source.

### Lenses. Optional Reading Stargazer: the life and times of the TELESCOPE, Fred Watson (Da Capo 2004).

Lenses Equipment optical bench, incandescent light source, laser, No 13 Wratten filter, 3 lens holders, cross arrow, diffuser, white screen, case of lenses etc., vernier calipers, 30 cm ruler, meter stick

### Chapter 34 The Wave Nature of Light; Interference. Copyright 2009 Pearson Education, Inc.

Chapter 34 The Wave Nature of Light; Interference 34-7 Luminous Intensity The intensity of light as perceived depends not only on the actual intensity but also on the sensitivity of the eye at different

### EXPRIMENT 3 COUPLING FIBERS TO SEMICONDUCTOR SOURCES

EXPRIMENT 3 COUPLING FIBERS TO SEMICONDUCTOR SOURCES OBJECTIVES In this lab, firstly you will learn to couple semiconductor sources, i.e., lightemitting diodes (LED's), to optical fibers. The coupling

### Spatial Light Modulator (SLM) Workshop, BFY 2012 Conference Douglas Martin and Shannon O Leary Lawrence University and Lewis & Clark College

Spatial Light Modulator (SLM) Workshop, BFY 2012 Conference Douglas Martin and Shannon O Leary Lawrence University and Lewis & Clark College Briefly, a spatial light modulator (SLM) is a liquid crystal

### Collimation Tester Instructions

Description Use shear-plate collimation testers to examine and adjust the collimation of laser light, or to measure the wavefront curvature and divergence/convergence magnitude of large-radius optical

### 1.6 Beam Wander vs. Image Jitter

8 Chapter 1 1.6 Beam Wander vs. Image Jitter It is common at this point to look at beam wander and image jitter and ask what differentiates them. Consider a cooperative optical communication system that

### Measurement of the Modulation Transfer Function (MTF) of a camera lens. Laboratoire d Enseignement Expérimental (LEnsE)

Measurement of the Modulation Transfer Function (MTF) of a camera lens Aline Vernier, Baptiste Perrin, Thierry Avignon, Jean Augereau, Lionel Jacubowiez Institut d Optique Graduate School Laboratoire d

### Test procedures Page: 1 of 5

Test procedures Page: 1 of 5 1 Scope This part of document establishes uniform requirements for measuring the numerical aperture of optical fibre, thereby assisting in the inspection of fibres and cables

### I = I 0 cos 2 θ (1.1)

Chapter 1 Faraday Rotation Experiment objectives: Observe the Faraday Effect, the rotation of a light wave s polarization vector in a material with a magnetic field directed along the wave s direction.

### PHYS General Physics II Lab Diffraction Grating

1 PHYS 1040 - General Physics II Lab Diffraction Grating In this lab you will perform an experiment to understand the interference of light waves when they pass through a diffraction grating and to determine

### O5: Lenses and the refractor telescope

O5. 1 O5: Lenses and the refractor telescope Introduction In this experiment, you will study converging lenses and the lens equation. You will make several measurements of the focal length of lenses and

### Astronomical Cameras

Astronomical Cameras I. The Pinhole Camera Pinhole Camera (or Camera Obscura) Whenever light passes through a small hole or aperture it creates an image opposite the hole This is an effect wherever apertures

### Holography as a tool for advanced learning of optics and photonics

Holography as a tool for advanced learning of optics and photonics Victor V. Dyomin, Igor G. Polovtsev, Alexey S. Olshukov Tomsk State University 36 Lenin Avenue, Tomsk, 634050, Russia Tel/fax: 7 3822

### DESIGNING AND IMPLEMENTING AN ADAPTIVE OPTICS SYSTEM FOR THE UH HOKU KE`A OBSERVATORY ABSTRACT

DESIGNING AND IMPLEMENTING AN ADAPTIVE OPTICS SYSTEM FOR THE UH HOKU KE`A OBSERVATORY University of Hawai`i at Hilo Alex Hedglen ABSTRACT The presented project is to implement a small adaptive optics system

### Optical design of a high resolution vision lens

Optical design of a high resolution vision lens Paul Claassen, optical designer, paul.claassen@sioux.eu Marnix Tas, optical specialist, marnix.tas@sioux.eu Prof L.Beckmann, l.beckmann@hccnet.nl Summary:

### EOP3056 Optical Metrology and Testing Experiment OM2: The Mach-Zehnder Interferometer

EOP3056 Optical Metrology and Testing Experiment OM2: The Mach-Zehnder Interferometer 1.0 Objectives To construct a Mach-Zehnder interferometer from discrete optical components. To explain how Mach-Zehnder

### 10.2 Images Formed by Lenses SUMMARY. Refraction in Lenses. Section 10.1 Questions

10.2 SUMMARY Refraction in Lenses Converging lenses bring parallel rays together after they are refracted. Diverging lenses cause parallel rays to move apart after they are refracted. Rays are refracted

### 880 Quantum Electronics Optional Lab Construct A Pulsed Dye Laser

880 Quantum Electronics Optional Lab Construct A Pulsed Dye Laser The goal of this lab is to give you experience aligning a laser and getting it to lase more-or-less from scratch. There is no write-up

### Mach Zehnder Interferometer Apparatus:

Mach Zehnder Interferometer Apparatus: Parts for Interferometer: 1.) Breadboard 12 x24 \$282 Quantity:1 http://www.thorlabs.com/thorproduct.cfm?partnumber=mb1224 2.) 2 Kinematic Optics Mount \$75 Quantity:

### Make Your Own Digital Spectrometer With Diffraction Grating

Make Your Own Digital Spectrometer With Diffraction Grating T. Z. July 6, 2012 1 Introduction and Theory Spectrums are very useful for classify atoms and materials. Although digital spectrometers such

### arxiv:physics/ v1 [physics.optics] 12 May 2006

Quantitative and Qualitative Study of Gaussian Beam Visualization Techniques J. Magnes, D. Odera, J. Hartke, M. Fountain, L. Florence, and V. Davis Department of Physics, U.S. Military Academy, West Point,

### How-to guide. Working with a pre-assembled THz system

How-to guide 15/06/2016 1 Table of contents 0. Preparation / Basics...3 1. Input beam adjustment...4 2. Working with free space antennas...5 3. Working with fiber-coupled antennas...6 4. Contact details...8

### UCI ZEEMAN EFFECT. Observe the fine structure lines of mercury and the Zeeman splitting of one or more of these lines as a function of magnetic field.

UCI ZEEMAN EFFECT OBJECTIVES Observe the fine structure lines of mercury and the Zeeman splitting of one or more of these lines as a function of magnetic field. Compare the observed splitting with theoretical

### IMAGE FORMATION. Light source properties. Sensor characteristics Surface. Surface reflectance properties. Optics

IMAGE FORMATION Light source properties Sensor characteristics Surface Exposure shape Optics Surface reflectance properties ANALOG IMAGES An image can be understood as a 2D light intensity function f(x,y)

### OPTICS AND LASER PHYSICS LABORATORY #10 INSIDE A LASER CAVITY -- EXPLORING STABILITY, POLARIZATION, AND MODES with Mark Chawla and Chris Baird

-- EXPLORING STABILITY, POLARIZATION, AND MODES with Mark Chawla and Chris Baird What is a laser cavity and how is it deemed to be stable? Most laser cavities are made up of a surprisingly small number

### Microwave Optics. Department of Physics & Astronomy Texas Christian University, Fort Worth, TX. January 16, 2014

Microwave Optics Department of Physics & Astronomy Texas Christian University, Fort Worth, TX January 16, 2014 1 Introduction Optical phenomena may be studied at microwave frequencies. Visible light has

### INSTRUCTION MANUAL FOR THE MODEL C OPTICAL TESTER

INSTRUCTION MANUAL FOR THE MODEL C OPTICAL TESTER INSTRUCTION MANUAL FOR THE MODEL C OPTICAL TESTER Data Optics, Inc. (734) 483-8228 115 Holmes Road or (800) 321-9026 Ypsilanti, Michigan 48198-3020 Fax:

### AP Physics Problems -- Waves and Light

AP Physics Problems -- Waves and Light 1. 1974-3 (Geometric Optics) An object 1.0 cm high is placed 4 cm away from a converging lens having a focal length of 3 cm. a. Sketch a principal ray diagram for

### Chapter 17: Wave Optics. What is Light? The Models of Light 1/11/13

Chapter 17: Wave Optics Key Terms Wave model Ray model Diffraction Refraction Fringe spacing Diffraction grating Thin-film interference What is Light? Light is the chameleon of the physical world. Under

### Department of Mechanical and Aerospace Engineering, Princeton University Department of Astrophysical Sciences, Princeton University ABSTRACT

Phase and Amplitude Control Ability using Spatial Light Modulators and Zero Path Length Difference Michelson Interferometer Michael G. Littman, Michael Carr, Jim Leighton, Ezekiel Burke, David Spergel

### Chapter 8. The Telescope. 8.1 Purpose. 8.2 Introduction A Brief History of the Early Telescope

Chapter 8 The Telescope 8.1 Purpose In this lab, you will measure the focal lengths of two lenses and use them to construct a simple telescope which inverts the image like the one developed by Johannes

### The 34th International Physics Olympiad

The 34th International Physics Olympiad Taipei, Taiwan Experimental Competition Wednesday, August 6, 2003 Time Available : 5 hours Please Read This First: 1. Use only the pen provided. 2. Use only the

### Computer Generated Holograms for Optical Testing

Computer Generated Holograms for Optical Testing Dr. Jim Burge Associate Professor Optical Sciences and Astronomy University of Arizona jburge@optics.arizona.edu 520-621-8182 Computer Generated Holograms

### Microscope anatomy, image formation and resolution

Microscope anatomy, image formation and resolution Ian Dobbie Buy this book for your lab: D.B. Murphy, "Fundamentals of light microscopy and electronic imaging", ISBN 0-471-25391-X Visit these websites:

### 28 The diagram shows an experiment which has been set up to demonstrate two-source interference, using microwaves of wavelength λ.

PhysicsndMathsTutor.com 28 The diagram shows an experiment which has been set up to demonstrate two-source interference, using microwaves of wavelength λ. 9702/1/M/J/02 X microwave transmitter S 1 S 2

### CHAPTER 9 POSITION SENSITIVE PHOTOMULTIPLIER TUBES

CHAPTER 9 POSITION SENSITIVE PHOTOMULTIPLIER TUBES The current multiplication mechanism offered by dynodes makes photomultiplier tubes ideal for low-light-level measurement. As explained earlier, there

### Katarina Logg, Kristofer Bodvard, Mikael Käll. Dept. of Applied Physics. 12 September Optical Microscopy. Supervisor s signature:...

Katarina Logg, Kristofer Bodvard, Mikael Käll Dept. of Applied Physics 12 September 2007 O1 Optical Microscopy Name:.. Date:... Supervisor s signature:... Introduction Over the past decades, the number

### Education in Microscopy and Digital Imaging

Contact Us Carl Zeiss Education in Microscopy and Digital Imaging ZEISS Home Products Solutions Support Online Shop ZEISS International ZEISS Campus Home Interactive Tutorials Basic Microscopy Spectral

### Exploring TeachSpin s Two-Slit Interference, One Photon at a Time Workshop Manual

Introduction Exploring TeachSpin s Nobel Laureate Richard Feynman, one of the most joyous practitioners of physics, described single photon interference as a phenomenon which is impossible, absolutely

### Practice Problems for Chapter 25-26

Practice Problems for Chapter 25-26 1. What are coherent waves? 2. Describe diffraction grating 3. What are interference fringes? 4. What does monochromatic light mean? 5. What does the Rayleigh Criterion

### PHYS 1112L - Introductory Physics Laboratory II

PHYS 1112L - Introductory Physics Laboratory II Laboratory Advanced Sheet Snell's Law 1. Objectives. The objectives of this laboratory are a. to determine the index of refraction of a liquid using Snell's

### Date Morning/Afternoon Time allowed: 1 hour 30 minutes

AS Level Physics B (Advancing Physics) H157/02 Physics in depth Practice Question Paper Date Morning/Afternoon Time allowed: 1 hour 30 minutes You must have: the Data, Formulae and Relationships Booklet

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science

Student Name Date MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.161 Modern Optics Project Laboratory Laboratory Exercise No. 6 Fall 2016 Electro-optic

C. BALLAERA: UTILIZING A 4-F FOURIER OPTICAL SYSTEM UTILIZING A 4-F FOURIER OPTICAL SYSTEM TO LEARN MORE ABOUT IMAGE FILTERING Author: Corrado Ballaera Research Conducted By: Jaylond Cotten-Martin and

### Projects in Optics. Applications Workbook

Projects in Optics Applications Workbook Created by the technical staff of Newport Corporation with the assistance of Dr. Donald C. O Shea of the School of Physics at the Georgia Institute of Technology.

### VISUAL PHYSICS ONLINE DEPTH STUDY: ELECTRON MICROSCOPES

VISUAL PHYSICS ONLINE DEPTH STUDY: ELECTRON MICROSCOPES Shortly after the experimental confirmation of the wave properties of the electron, it was suggested that the electron could be used to examine objects

### The Lightwave Model 142 CW Visible Ring Laser, Beam Splitter, Model ATM- 80A1 Acousto-Optic Modulator, and Fiber Optic Cable Coupler Optics Project

The Lightwave Model 142 CW Visible Ring Laser, Beam Splitter, Model ATM- 80A1 Acousto-Optic Modulator, and Fiber Optic Cable Coupler Optics Project Stephen W. Jordan Seth Merritt Optics Project PH 464

### Lab 12. Optical Instruments

Lab 12. Optical Instruments Goals To construct a simple telescope with two positive lenses having known focal lengths, and to determine the angular magnification (analogous to the magnifying power of a

### Hartmann Sensor Manual

Hartmann Sensor Manual 2021 Girard Blvd. Suite 150 Albuquerque, NM 87106 (505) 245-9970 x184 www.aos-llc.com 1 Table of Contents 1 Introduction... 3 1.1 Device Operation... 3 1.2 Limitations of Hartmann

### 6 Experiment II: Law of Reflection

Lab 6: Microwaves 3 Suggested Reading Refer to the relevant chapters, 1 Introduction Refer to Appendix D for photos of the apparatus This lab allows you to test the laws of reflection, refraction and diffraction

### Chapter 24. The Wave Nature of Light

Ch-24-1 Chapter 24 The Wave Nature of Light Questions 1. Does Huygens principle apply to sound waves? To water waves? Explain how Huygens principle makes sense for water waves, where each point vibrates

### INTRODUCTION THIN LENSES. Introduction. given by the paraxial refraction equation derived last lecture: Thin lenses (19.1) = 1. Double-lens systems

Chapter 9 OPTICAL INSTRUMENTS Introduction Thin lenses Double-lens systems Aberrations Camera Human eye Compound microscope Summary INTRODUCTION Knowledge of geometrical optics, diffraction and interference,