Diffraction. Today Singleslit diffraction Diffraction by a circular aperture Use of phasors in diffraction Doubleslit diffraction


 Marlene Casey
 1 years ago
 Views:
Transcription
1 Diffraction Today Singleslit diffraction Diffraction by a circular aperture Use of phasors in diffraction Doubleslit diffraction
2 Diffraction by a single slit
3 Single slit: Pattern on screen Bright and dark fringes appear behind a single very thin slit. As the slit is made narrower the pattern of fringes becomes wider.
4 Single Slit: finding the minima Divide the single slit into many tiny regions. If the top ray and the middle ray interfere destructively, then every pair of rays will also. So each pair cancels each other and we have total cancellation!
5 Single Slit: the first minimum So we get destructive interference if: ( a / 2) sinθ ( λ / 2) asinθ λ Note this mustn t be confused for the condition for constructive interference in the twoslit case! Also note as slit width gets smaller, angle gets larger, and vice versa.
6 Dark Fringes in Diffraction Second dark fringe? First dark fringe.
7 Dark fringes First is at ( a / 4) asinθ asinθ λ As we move up on the screen the next dark fringe occurs when the first ray interferes destructively with the one from onefourth the way down the slit. sinθ λ / 2 2λ We can continue to onesixth, oneeighth, etc. to get all the dark fringes at a sinθ mλ Again note as slit gets narrower, pattern gets wider.
8 Summary of singleslit diffraction Given light of wavelength λ passing through a slit of width a. There are dark fringes (diffraction minima) at angles θ given by a sin θ mλ where m is an integer. Note this exactly the condition for constructive interference between the rays from the top and bottom of the slit. Also note the pattern gets wider as the slit gets narrower. The bright fringes are roughly halfway between the dark fringes. (Not exactly but close enough.)
9 Example: Problem 372 Light of wavelength 441 nm is incident on a narrow slit. On a screen 2 meters away, the distance between the second diffraction minimum and the central maximum is 1.5 cm. (a) Calculate the angle of diffraction θ of the second minimum. (b) Find the width of the slit.
10 Example: (cont d) (a) Calculate the angle of diffraction θ of the second minimum. θ tanθ y D rad (b) Find the width of the slit. λ m a m µ m θ asinθ θ mλ sinθ λ m a
11 Diffraction by a circular aperture Consider a round hole of diameter d. Same idea as a long slit only the geometry is different. Angle for first minimum: Long slit: a sinθ λ Circular hole: d sin θ λ
12 The Rayleigh Criterion Using a circular instrument (telescope, human eye), when can we just resolve two distant objects? When images are separated by distance to first minimum: θ 1.22λ / R d
13 Sample Problem 364 Camera or eye: Smallest resolvable angle to two distant objects: θ 1.22λ / R d
14 Single slit phasor diagram Divide slit into many tiny slits. Use a tiny phasor for each. Add them together graphically. See we get destructive interference if first and last phasors interfere constructively! So the condition for the m th dark fringe is: a sinθ mλ
15 MultipleSlit Diffraction Now we can finally put together our interference and diffraction results to see what really happens with two or more slits. RESULT: We get the twoslit (or multipleslit) pattern as in chapter 35, but modified by the singleslit intensity as an envelope. Instead of all peaks being of the same height, they get weaker at larger angles.
16 DoubleSlit Diffraction a slit width d slit separation θ angle on screen Bright fringes due to 2slit interference: θ θ λ / a, 2λ / a, m λ / Zero due to diffraction: L d
17 Doubleslit diffraction 2 slits of zero width 1 slit of width a 5λ 2 slits of width a 5λ
18 Diffraction grating: Many Slits Very sharp maximum when all rays are in phase. d sinθ mλ m order 1, 2, 3, Firstorder maximum: sinθ λ / d Secondorder maximum: sinθ 2 λ / d
19 Diffraction grating bright lines d sinθ mλ Secondorder maximum: Firstorder maximum: Spectroscopy: separate lines of different wavelengths.
20 Diffraction grating recap Position of lines is determined by separation of rulings. d sinθ mλ Sharpness of lines is determined by number of rulings. θ λ / Nd Resolving power is determined by number of rulings and order of line. RmN
21 Interference with 3 Slits Path difference between rays from adjacent slits: L d sinθ θ L / d Phase difference between rays from adjacent slits: φ L 2 2 π λ π d θ λ Get intensity from phasor diagram:
22 3 Slits Continued 1. Central maximum: 2. First minimum: φ Next maximum: φ 180 φ θ 0 0 E 3E T 2π φ 3 E T 0 I T I 9 0 T d sinθ T E0 IT 0 φ π d sinθ λ / E I 0 I 0 λ 3 2
23 3 Slits Continued 4. Next minimum: φ sin E T I T d λ θ π φ 5. Next maximum: d I I E E d T T / 9 3 sin λ θ λ θ π φ φ 360
24 Summary 9I 0 I 0 θ L / d L 0 λ 3 λ 2 2λ 3 λ θ max m λ / d
25 Five Slits θ m λ / Note we still have max But more slits makes the peaks sharper. d For many slits, we get a diffraction grating.
26 Diffraction Grating
27 Wavelength Resolution of a Grating
28 Width of sharp lines
29 Resolving Power Positions of maximums: d sinθ m λ Small angles: θ θ m λ / m d λ / d Widths of sharp maximums: Wavelengths just resolved: Resolving power definition: R λ λ So we get: θ λ / m m λ λ / d λ / Nd λ N RmN / Nd
30 Example: Yellow sodium vapor lines Problem The strong yellow lines in the sodium spectrum are at wavelengths nm and nm. How many rulings are needed in a diffraction grating to resolve these lines in second order? We need R λ λ 589 nm 0.6 nm 982 R 982 But RmN so N 491 m 2
31 Diffraction II Today Singleslit diffraction review Multiple slit diffraction review Xray diffraction Diffraction intensities
32 Review: Double Slit Path Differences For point P at angle θ triangle shows Ld sinθ For constructive interference we need L m λ where m0,1,2, is any integer. So the bright fringes are at angles given by d sinθ mλ
33 Doubleslit interference fringes So the bright fringes are at angles given by d sinθ m λ And the dark fringes are at angles given by d 1 sinθ ( m+ ) 2 λ
34 Single slit: Pattern on screen Bright and dark fringes appear behind a single very thin slit. As the slit is made narrower the pattern of fringes becomes wider.
35 Dark Fringes in Diffraction
36 Single Slit dark fringes Destructive interference: ( a / 2m) sinθ ( λ / 2) a sinθ mλ Don t confuse this with the condition for constructive interference for two slits! In fact, note that there is a dark fringe when the rays from the top and bottom interfere constructively!
37 Summary of singleslit diffraction Given light of wavelength λ passing through a slit of width a. There are dark fringes (diffraction minima) at angles θ given by a sin θ mλ where m is an integer. Note this exactly the condition for constructive interference between the rays from the top and bottom of the slit. Also note the pattern gets wider as the slit gets narrower. The bright fringes are roughly halfway between the dark fringes. (Not exactly but close enough.)
38 Example: Problem 366 The distance between the first and fifth minima of a singleslit diffraction pattern is 0.35 mm with the screen 40 cm away from the slit, with light of wavelength 550 nm. Find the slit width. asinθ mλ sinθ mλ / a 5λ 1λ 4λ sinθ5 sinθ1 a a a 4λD y5 y1 Dsinθ5 Dsinθ1 a sin θ tanθ y / D a 4λD y y m 2.5 mm
39 Q.361 A slit of width 50 µm is used with monochromatic light to form a diffraction pattern. The distance between dark fringes on a distant screen is 4 mm. If the slit width is increased to 100 µm, what will be the new distance between dark fringes? Give your answer in mm. (In the range 09.)
40 Q.361 A slit of width 50 µm is used with monochromatic light to form a diffraction pattern. The distance between dark fringes on a distant screen is 4 mm. If the slit width is increased to 100 µm, what will be the new distance between dark fringes? Pattern size is inversely proportional to slit size: 2 times slit width means (1/2) times the distance between fringes. Answer: 2 mm.
41 MultipleSlit Diffraction Now we can finally put together our interference and diffraction results to see what really happens with two or more slits. RESULT: We get the twoslit (or multipleslit) pattern as in chapter 35, but modified by the singleslit intensity as an envelope. Instead of all peaks being of the same height, they get weaker at larger angles.
42 DoubleSlit Diffraction a slit width d slit separation θ angle on screen Bright fringes due to 2slit interference: θ θ λ / a, 2λ / a, m λ / Zero due to diffraction: L d
43 Doubleslit diffraction 2 slits of zero width 1 slit of width a 5λ 2 slits of width a 5λ
44 Twoslit and oneslit patterns Actual photograph: (a) two slits (b)one list covered (Figure from text page 1003.)
45 Scaling of diffraction patterns Notice a common feature of interference and diffraction patterns: The largescale features of the pattern are determined by the smallscale regularities of the object, and viceversa. Holograms and Xray diffraction patterns are examples.
46 Example:Sample Problem 365 Two slits: d19.44 nm, a4.05 µm, λ405 nm. (a)how many bright fringes within the central peak? (b)how many in the first side peak?
47 Example:Sample Problem 365 Two slits: d19.44 nm, a4.05 µm, λ405 nm. Solution: Oneslit: θ mλ / a.10,.20,.30,.04, L Twoslit: θ mλ / d.02083m.0208,.0416,.0625,.0833,.1042,.1250, L
48 Q.362 When red laser light is diffracted by two slits of equal width, there are many closely spaced bands of light inside wider bands. What features of the slits determine the separation x between the closelyspaced bands? x (1) Width of the individual slits. (2) Distance between the two slits. (3) Ratio of distance to width. (4) None of the above: it s more complicated.
49 Q.362 When red laser light is diffracted by two slits of equal width, there are many closely spaced bands of light inside wider bands. What features of the slits determine the separation x between the closelyspaced bands? x (1) Width of the individual slits. (2) Distance between the two slits. (3) Ratio of distance to width. (4) None of the above: it s more complicated.
50 XRays Xrays are just light waves with shorter wavelengths and higher photon energies. Since Xray wavelengths are comparable to atomic sizes, they are perfect for studying atoms and the arrangement of atoms in crystals.
51 XRays and Crystals A crystal surface acts like a diffraction grating for X rays. Bragg condition for a bright spot: 2d sinθ mλ
52 Xray crystallogrphy In this way, using xrays of known wavelength we can measure the distances between atoms in a crystal and determine the crystal structure.
53 Singleslit Intensity We know where to find the dark fringes in the singleslit pattern. But can we calculate the actual intensity at a general point? Yes, using the phasor method. Book gives result on page 998: I θ I m sinα α 2 Here I θ is the intensity at angle θ on the screen. I m is the intensity at the central maximum. The angle α φ /2, and φ is the phase difference between the rays from top and bottom of slit.
54 Phasors for Single Slit Break up the slit into many tiny zones, giving many rays of light, which come together on the screen. φ Phase difference between adjacent rays φ Phase difference between top and bottom rays E Amplitude at center Sum of all phasors m E Amplitude at angle θ, get from diagram θ
55 First Maximum and Minimum Remember of course the relation between phase difference and path difference φ 2π λ ( a sin θ ) φ 0 E θ E m E θ 0 φ m(2 π ) a sin θ m λ
56 Intensity for Single Slit E E Rsin( / 2) m Rφ θ 2 φ E φ θ 2sin( / 2) φ E m I θ I m 4sin I m 2 φ ( φ / 2 2) Which gives the textbook result: 2 I sinα θ α
MULTIPLE 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 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 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 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 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 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 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 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 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 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 informationPHY208FALL2008. Week2HW. Introduction to TwoSource Interference. Due at 11:59pm on Friday, September 12, View Grading Details [ Print ]
Assignment Display Mode: View Printable Answers PHY208FALL2008 Week2HW Due at 11:59pm on Friday September 12 2008 View Grading Details [ Print ] The following three problems concern interference from two
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 information the. or may. scales on. Butterfly wing. magnified about 75 times.
Lecture Notes (Applications of Diffraction) Intro:  the iridescent colors seen in many beetles is due to diffraction of light rays hitting the small groovess of its exoskeleton  these ridges are only
More informationLight, Light Bulbs and the Electromagnetic Spectrum
Light, Light Bulbs and the Electromagnetic Spectrum Spectrum The different wavelengths of electromagnetic waves present in visible light correspond to what we see as different colours. Electromagnetic
More informationChapter 23. The Refraction of Light: Lenses and Optical Instruments
Chapter 23 The Refraction of Light: Lenses and Optical Instruments Lenses Converging and diverging lenses. Lenses refract light in such a way that an image of the light source is formed. With a converging
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 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 informationCHAPTER 35. (a) 300 nm (b) δ = 135 o
CHAPTER 35 1* When destructive interference occurs, what happens to the energy in the light waves? The energy is distributed nonuniformly in space; in some regions the energy is below average (destructive
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 informationStudy Guide for Exam on Light
Name: Class: Date: Study Guide for Exam on Light Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which portion of the electromagnetic spectrum is used
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 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 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 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 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 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 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 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 informationInvestigating electromagnetic radiation
Investigating electromagnetic radiation Announcements: First midterm is 7:30pm on 2/17/09 Problem solving sessions M35 and T34,56. Homework due at 12:50pm on Wednesday. We are covering Chapter 4 this
More informationWhat s so special about the laser?
What s so special about the laser? A guide for taking LaserFest into the classroom. Developed by 2010 SPS SOCK interns Patrick Haddox & Jasdeep Maggo. www.spsnational.org Activity 1: Exploring laser light
More informationIt s shape. Sound Beams foundation for a basic understanding. Anatomy of the beam. Focus. Near Zone. Focal Length. Chapter 10
It s shape Sound Beams foundation for a basic understanding It begins the size or diameter of the transducer gradually converges to a narrower point then begins to diverge Chapter 10 Anatomy of the beam
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 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 informationNote it they ancients had known Newton s first law, the retrograde motion of the planets would have told them that the Earth was moving.
6/24 Discussion of the first law. The first law appears to be contained within the second and it is. Why state it? Newton s laws are not always valid they are not valid in, say, an accelerating automobile.
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 informationExperiment #12: The Bohr Atom. Equipment: Spectroscope Hydrogen and Helium Gas Discharge Tubes, Holder, and Variac Flashlight
Experiment #12: The Bohr Atom Purpose: To observe the visible spectrum of hydrogen and helium and verify the Bohr model of the hydrogen atom. Equipment: Spectroscope Hydrogen and Helium Gas Discharge Tubes,
More informationInterference of Light Waves
Chapter 37 Interference of Light Waves CHAPTER OUTLINE 37.1 Conditions for Interference 37.2 Young s DoubleSlit Experiment 37.3 Intensity Distribution of the DoubleSlit Interference Pattern 37.4 Phasor
More informationOptical Interferometers
Optical Interferometers Experiment objectives: Assemble and align Michelson and FabryPerot interferometers, calibrate them using a laser of known wavelength, and then use them characterize the bright
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 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 informationXRay Diffraction. wavelength Electric field of light
Light is composed of electromagnetic radiation with an electric component that modulates versus time perpendicular to the direction it is travelling (the magnetic component is also perpendicular to the
More informationSTOP for science. Light is a wave. Like waves in water, it can be characterized by a wavelength.
INTRODUCTION Most students have encountered rainbows, either spotting them directly on those special days when the raindrops fall while the Sun still finds cloudless regions to peek through, or at least
More informationWaves and Light Extra Study Questions
Waves and Light Extra Study Questions Short Answer 1. Determine the frequency for each of the following. (a) A bouncing spring completes 10 vibrations in 7.6 s. (b) An atom vibrates 2.5 10 10 times in
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 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 informationStanding Waves and the Velocity of Sound
Chapter 8 Standing Waves and the Velocity of Sound 8.1 Purpose In this experiment we will be using resonance points of a sound wave traveling through an open tube to measure the speed of sound in air.
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 informationTeaching Time: Two 50minute periods
Lesson Summary In this lesson, students will build an open spectrograph to calculate the angle the light is transmitted through a holographic diffraction grating. After finding the desired angles, the
More informationCrystal Optics of Visible Light
Crystal Optics of Visible Light This can be a very helpful aspect of minerals in understanding the petrographic history of a rock. The manner by which light is transferred through a mineral is a means
More informationHow is LASER light different from white light? Teacher Notes
How is LASER light different from white light? Teacher Notes Concepts: (1) Light is a type of energy that travels as waves. [6.2.3.1.1] (2) Laser light is different from traditional light sources and must
More informationHolography 1 HOLOGRAPHY
Holography 1 HOLOGRAPHY Introduction and Background The aesthetic appeal and commercial usefulness of holography are both related to the ability of a hologram to store a threedimensional image. Unlike
More informationWhen selecting a sensor for an application the following parameters should be considered:
Memo Title: CCD Sensor Selection Guide Memo Number: 0007 Revision No. / Date: 1.0 Date: 8Sep2009 The CCDsp Scientific camera is available for a variety of different sensors that cover a broad spectrum
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 informationMeasuring the Earth s Diameter from a Sunset Photo
Measuring the Earth s Diameter from a Sunset Photo Robert J. Vanderbei Operations Research and Financial Engineering, Princeton University rvdb@princeton.edu ABSTRACT The Earth is not flat. We all know
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 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 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 informationProcesses affecting propagation of electromagnetic radiation (light)
Chapter 4 Light and Color, and Atmospheric Optics Useful links: http://www.atoptics.co.uk/ http://www.gi.alaska.edu/atmossci/links.mainpage/arcti c_optical.html Processes affecting propagation of electromagnetic
More informationExperimental Study of LaserCompton Scattering in the Nonlinear Regime
Experimental Study of LaserCompton Scattering in the Nonlinear Regime Y. Kamiya, T. Kumita Department of Physics, Tokyo Metropolitan University S. Kashiwagi, T. Hirose, M. Washio Advanced Research Institute
More informationInterference and Diffraction
CHAPTER 9 Interference and Diffraction Copyright Glencoe/McGraHill, a division of The McGraHill Companies, Inc. Practice Problems 9. Interference pages 55 523 page 59. Violet light falls on to slits
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 informationReview for Final  Geometry B
Review for Final  Geometry B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A model is made of a car. The car is 4 meters long and the model is 7 centimeters
More informationUses of Derivative Spectroscopy
Uses of Derivative Spectroscopy Application Note UVVisible Spectroscopy Anthony J. Owen Derivative spectroscopy uses first or higher derivatives of absorbance with respect to wavelength for qualitative
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 informationPassive Optical Resonators
Passive Optical Resonators Optical Cavities and Feedback Back mirror I 0 I 1 Laser medium with gain, G Output mirror I 3 R = 100% R < 100% I 2 Cavities are essential components of the lasers. They provide
More informationWHITE LIGHT AND COLORED LIGHT
grades K 5 Objective This activity offers two simple ways to demonstrate that white light is made of different colors of light mixed together. The first uses special glasses to reveal the colors that make
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 informationILLUSTRATIVE EXAMPLE: Given: A = 3 and B = 4 if we now want the value of C=? C = 3 + 4 = 9 + 16 = 25 or 2
Forensic Spectral Anaylysis: Warm up! The study of triangles has been done since ancient times. Many of the early discoveries about triangles are still used today. We will only be concerned with the "right
More informationTable 1 r (m) I (W/m 2 ) 0.10 477.46 0.20 119.37 0.50 19.10 1.00 4.77 2.00 1.19 5.00 0.19 10.00 0.05 Table 2: Intensities at 1m Distances Power (W)
Light Intensity The term intensity is used to describe the rate at which light spreads over a surface of a given area some distance from a source. The intensity varies with the distance from the source
More informationLecture 12: Cameras and Geometry. CAP 5415 Fall 2010
Lecture 12: Cameras and Geometry CAP 5415 Fall 2010 The midterm What does the response of a derivative filter tell me about whether there is an edge or not? Things aren't working Did you look at the filters?
More informationMAG*I*CAL Reference Standard for TEM
N Norrox Scientific Ltd. MAG*I*CAL Reference Standard for TEM FRAGILE! The MAG*I*CAL calibration reference standard that you are receiving now looks like Figure A, below. If not handled carefully, it will
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 informationXray Crystallography Lectures
Xray Crystallography Lectures 1. Biological imaging by Xray diffraction. An overview. 2. Crystals. Growth, physical properties and diffraction. 3. Working in reciprocal space. Xray intensity data collection
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 informationThe Nature of Electromagnetic Radiation
II The Nature of Electromagnetic Radiation The Sun s energy has traveled across space as electromagnetic radiation, and that is the form in which it arrives on Earth. It is this radiation that determines
More informationBCM 6200  Protein crystallography  I. Crystal symmetry Xray diffraction Protein crystallization Xray sources SAXS
BCM 6200  Protein crystallography  I Crystal symmetry Xray diffraction Protein crystallization Xray sources SAXS Elastic Xray Scattering From classical electrodynamics, the electric field of the electromagnetic
More informationUsing the Spectrophotometer
Using the Spectrophotometer Introduction In this exercise, you will learn the basic principals of spectrophotometry and and serial dilution and their practical application. You will need these skills to
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 informationAcoustooptic modulator
1 of 3 Acoustooptic modulator F An acoustooptic modulator (AOM), also called a Bragg cell, uses the acoustooptic effect to diffract and shift the frequency of light using sound waves (usually at radiofrequency).
More informationAlgebra 2/Trigonometry Practice Test
Algebra 2/Trigonometry Practice Test Part I Answer all 27 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the separate
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 informationCHAPTER 3 THE STRUCTURE OF CRYSTALLINE SOLIDS PROBLEM SOLUTIONS
CHAPTER THE STRUCTURE OF CRYSTALLINE SOLIDS PROBLEM SOLUTIONS Fundamental Concepts.6 Show that the atomic packing factor for HCP is 0.74. The APF is just the total sphere volumeunit cell volume ratio.
More informationPhysics 1230: Light and Color
Physics 1230: Light and Color Exam 1 is tomorrow, Wed. June 9, in class. Covers material from Chapter 1, pgs 125, Lectures and Homework 13. HW4 will be up soon. Due Thursday, 5PM Lecture 5: Shadows,
More informationPhysFest March Holography
PhysFest March 2013 Holography Holography (from the Greek, holos whole + graphe writing) is the science of producing holograms, an advanced form of photography that allows an image to be recorded in three
More informationPhysics 10. Lecture 29A. "There are two ways of spreading light: to be the candle or the mirror that reflects it." Edith Wharton
Physics 10 Lecture 29A "There are two ways of spreading light: to be the candle or the mirror that reflects it." Edith Wharton Converging Lenses What if we wanted to use refraction to converge parallel
More informationChapter 6 Telescopes: Portals of Discovery. How does your eye form an image? Refraction. Example: Refraction at Sunset.
Chapter 6 Telescopes: Portals of Discovery 6.1 Eyes and Cameras: Everyday Light Sensors Our goals for learning:! How does your eye form an image?! How do we record images? How does your eye form an image?
More informationAlignement of a ring cavity laser
Alignement of a ring cavity laser 1 Introduction This manual describes a procedure to align the cavity of our Ti:Sapphire ring laser and its injection with an ArgonIon pump laser beam. The setup is shown
More informationMeasuring the Diameter of the Sun
Chapter 24 Studying the Sun Investigation 24 Measuring the Diameter of the Sun Introduction The sun is approximately 150,000,000 km from Earth. To understand how far away this is, consider the fact that
More information3.14 understand that light waves are transverse waves which can be reflected, refracted and diffracted
Light and Sound 3.14 understand that light waves are transverse waves which can be reflected, refracted and diffracted 3.15 use the law of reflection (the angle of incidence equals the angle of reflection)
More information4.1 Radian and Degree Measure
Date: 4.1 Radian and Degree Measure Syllabus Objective: 3.1 The student will solve problems using the unit circle. Trigonometry means the measure of triangles. Terminal side Initial side Standard Position
More informationChapter 17: Light and Image Formation
Chapter 17: Light and Image Formation 1. When light enters a medium with a higher index of refraction it is A. absorbed. B. bent away from the normal. C. bent towards from the normal. D. continues in the
More information2) A convex lens is known as a diverging lens and a concave lens is known as a converging lens. Answer: FALSE Diff: 1 Var: 1 Page Ref: Sec.
Physics for Scientists and Engineers, 4e (Giancoli) Chapter 33 Lenses and Optical Instruments 33.1 Conceptual Questions 1) State how to draw the three rays for finding the image position due to a thin
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 informationFrom lowest energy to highest energy, which of the following correctly orders the different categories of electromagnetic radiation?
From lowest energy to highest energy, which of the following correctly orders the different categories of electromagnetic radiation? From lowest energy to highest energy, which of the following correctly
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 informationChapter 11. Waves & Sound
Chapter 11 Waves & Sound 11.2 Periodic Waves In the drawing, one cycle is shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position.
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 informationPhysical Science Study Guide Unit 7 Wave properties and behaviors, electromagnetic spectrum, Doppler Effect
Objectives: PS7.1 Physical Science Study Guide Unit 7 Wave properties and behaviors, electromagnetic spectrum, Doppler Effect Illustrate ways that the energy of waves is transferred by interaction with
More informationIntroduction to microstructure
Introduction to microstructure 1.1 What is microstructure? When describing the structure of a material, we make a clear distinction between its crystal structure and its microstructure. The term crystal
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 information