# Physics 3340 Spring Fourier Optics

Size: px
Start display at page:

Download "Physics 3340 Spring Fourier Optics"

## Transcription

1 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. We will construct a Fourier Optical Analyzer that can display both the real and Fourier image of any object. Introduction The optical system we will use is shown in Figure 4.1. In this experiment we will use commercial compound lenses instead of the simple lenses we have used so far. We will use a microscope objective to expand the laser beam and camera lenses when we need a large aperture converging optic. The beam is first focused at point P by the microscope objective. Microscope objectives are labeled by their magnification, m, which is related to their focal length, f, by f=(160 mm)/m. The second lens, L, is used to refocus the beam at the point P'. Since P' is conjugate to the initial focal point, P, P' is on a diffraction plane. A white screen placed at P' will show the diffraction pattern associated with the object slide, O. The object slide can be placed anywhere between L and P'. Microscope objective 40x Zeiss (+)10mm lens Object Diffraction plane Zeiss (+)10mm lens Diverging zoom lens (-)50 mm f.l. He-Ne laser f f P OA Laser L1 P L O D L3 L4 I I s3 s3 s s s4 s4 Figure 4.1. Converging beam Fourier optical analyzer. The diffraction pattern on the screen is given by the expression: I0 I u, v dxdyf x, yexp i ux vy (4.1) In this expression, I 0 is the intensity incident on the object, is the distance measured from the object to the diffraction plane, and u and v are x and y angular coordinates in the Fourier Optics 4.1 Spring 011

2 diffraction plane, measured from the point where the object intersects the optical axis. The final two lenses, L3 and L4, are used to create a magnified image, I, of the object. The combination of a converging lens, which creates an image I', and a diverging lens placed to the left of I', is called a zoom lens. This arrangement can provide a very large magnification. By alternately inserting and removing a screen at the diffraction plane, D, the direct and diffracted images can easily be compared. You can also block a portion of the diffraction pattern at D and see what the reconstructed image at I looks like with certain spatial Fourier components missing. This process is called spatial filtering. Fourier Optics 4. Spring 011

3 Introduction to Fourier Optics The Fourier Optics experiment that you are about to do builds upon knowledge that you might have gained about basic diffraction, perhaps via the Fraunhofer Diffraction Experiment. For completeness and to begin discussion of the Fourier Optics process, we repeat here the discussion of diffraction for the simpler Fraunhofer case: Fraunhofer diffraction discussion "Diffraction" refers to the spreading of waves and appearance of fringes that occur when a wave front is constricted by an aperture in a screen that is otherwise opaque. The light pattern changes as you move away from the aperture, being characterized by three regions. Plane waves Intensity profiles X Z OA Intensity Aperture Shadow Fresnel Diffraction Z ~ a / Fraunhofer Diffraction Figure 3.1 Diffraction of plane waves at an aperture. 1. In the shadow region, close to the aperture, the boundary of the transmitted light is sharp and resembles the aperture in shape.. As you move away into the Fresnel region, the beam width remains comparable to that in the aperture, but narrow fringes appear at the edges. 3. Far away, in the Fraunhofer region, the beam spreads to a width much greater than that of the aperture and is flanked by many weaker fringes. The Fraunhofer region is chosen for simple experiments because the broader fringes are easier to measure with an optical detector of finite aperture, and the calculations are more straightforward than in region. Fourier Optics 4.3 Spring 011

4 y x P(x,y) R r x y Z axis Incident waves Aperture da Figure 3.. Geometry for the Kirchoff-Fresnel diffraction integral. z Observation plane The Huygens-Fresnel principle governs diffraction phenomena: "Every unobstructed element of a wavefront acts as a source of spherical waves with the same frequency as the primary wave. The amplitude of the optical field beyond is a superposition of all these wavelets taking account of their amplitudes and phases." The Kirchoff-Fresnel diffraction integral gives quantitative expression to these ideas. Consider plane waves incident on an aperture from the left, as shown in Figure 3.. The incident field is described via: E z, t E e INC 0 i kz t The field in the aperture i.e., where z=0, is then INC 0 the wave front of area, da', and at position, r x, y,0 i t E 0, t E e. A typical element of, then acts as a source of Huygens wavelets. Our light detector sits at a point P in the observation screen, at a vector distance, R, from the origin of the aperture. Note that the distance of the detector, P, from the element da', is given by: r R r The field at P due to the element da' is then equal to: it ikr Ee 0 e de P da r Source strength Huygens spherical wave The field at P due to the entire aperture is then a superposition of the wavelets from all the elemental areas: 0 E P Aperture Area it ikr Ee e da r The detector measures the light intensity at P, rather than the electric field strength. Fourier Optics 4.4 Spring 011

5 Intensity is given by the magnitude of the time averaged Poynting vector, ˆ 0 0 S E B E Z z. Therefore, the detector measures: 0 I P E P Z Where Z is the characteristic impedance (the ratio of the electric field magnitude to the magnetic field magnitude try it out, go ahead, take the ratio of an electric field to a magnetic field and see how the units work out. It s Ohms.) of free space. In the Fraunhofer experiment, we study the diffraction through a single-slit aperture. The aperture is a slit of width, a, while the detector is a photodiode at position, P. Evaluation of the Kirchoff-Fresnel integral for the slit gives the following prediction for the diffracted intensity: xa sin a z I P x, z I INC z xa z This prediction is subject to the condition that the observation point is far enough away so that z a. From a practical perspective, z 10a is sufficiently far away for the theory to be quite accurate. Notice that the formula applies to a situation in which plane waves of uniform intensity are incident normal to a long narrow slit of uniform width. Further, the rays from different parts of the slit to a given observing point are effectively parallel (the Fraunhofer condition). To observe Fraunhofer diffraction, the design of the experiment must mimic these conditions as closely as is possible. The condition on parallelism of rays is adequately satisfied at a distance of z 10a or more, since the error depends on the square of this quantity. The case of Fourier Optics. Now that you ve been reminded of how Fraunhofer diffraction works, let s see how Fourier Optics works. The Fraunhofer case assumes that observations are made far enough away so that the light rays that cause the diffraction pattern are well treated as being effectively parallel. In Fourier optics, we use a converging lens to cause these parallel rays that leave a diffracting object to produce the diffraction pattern at a more convenient location (the focal plane of the lens), rather than requiring that we put detectors very far away from the object, where the parallel rays would eventually interfere to produce the Fraunhofer pattern. To understand how the lens functions to create the diffraction pattern, just think about what a converging lens does to parallel light rays. In the simplest case of a lens illuminated by Fourier Optics 4.5 Spring 011

6 rays that travel parallel to the optical axis, the lens focuses the rays to a point on the optical axis. This position is the so-called focal point of the lens. In this case, the lens takes a set of parallel light rays traveling at a particular angle to the optical axis, and converges them to a point. What does the lens do to a beam of light composed of parallel rays, but where the rays travel at some angle to the optical axis? For that case, consider the diagram in Figure 4.. Focal point, f Figure 4.. Parallel rays incident on the lens from the left are focused to a point, but not a point on the optical axis. The position of the point for the case of thin lenses is one focal length past the lens, and f tan above the optical axis. As the figure shows, for two of the parallel rays, the rules of geometrical optics tell us what to do: For the ray passing through the focal point, we know that it leaves the lens parallel to the optical axis. For the ray passing through the center of the lens, in the thin lens limit, there is no deflection of the ray. These two rays cross at a common point. In fact, ALL the rays converge at this point. Therefore, a lens will take a parallel beam at some incident angle to the optical axis, and converge it to a point, but the point is located off the axis. Now you are in a position to see how Fourier Optics works: A lens maps the angle incident parallel beams onto distinct spatial points. For every plane wave incident at some angle, the lens creates a delta-function intensity at some position on the focal plane. The statement, The Fourier Transform of a plane wave is a delta-function, should be triggered at this point. If you have several different incident plane waves, you will have several different bright spots at the focal plane. You are building the Fourier Transform as in Equation 4.1. If you diffract a plane wave through an object, like you did for the single slit in the Fraunhofer experiment, you will get a set of diffracted plane waves travelling in different directions. You can then either let Fourier Optics 4.6 Spring 011

7 them travel to infinity, where they interfere to produce the Fraunhofer pattern, or you can use a lens to produce the same pattern of bright spots at the focal plane of the lens. The Converging Beam Fourier System The discussion above emphasizes the way a lens maps the plane waves leaving a diffracting object onto bright spots at the focal plane of the lens. However, in this experiment, you are constructing a converging beam system. How does it work? One way to understand it is to think of the Zeiss camera lens as effectively acting like two lenses. One of the messages of geometrical optics is that any pair of lenses can be replaced by a single lens with a focal length whose inverse is the sum of the inverse focal lengths of the partner lenses (or if you like, the diopters add!). Another message is that the order of optical components does not matter if they are closely spaced. OK, so split the Zeiss into two lenses and swap the second lens and the diffracting object, so the object is between the two lenses. Set the focal length of the first so that the point source, P (see Figure 4.1), is located at the focal point of that lens. The point source then results in plane wave parallel rays exiting that first lens and illuminating the object of interest. The object then diffracts beams in various directions. The second lens then converts the diffracted beams back into bright points at its focal plane. If you work through the geometrical optics, the diffracted points will be found to be at point, P, as in Figure 4.1. That s it! Fourier Optics 4.7 Spring 011

8 Outline of the Experiment 1. Using your results from the prelab as a guide set up the Fourier Optical Analyzer. Make whatever adjustments or changes that are needed to get good direct and Fourier images.. Examine the formation of diffraction patterns. Try to understand in as much detail as you can the relationship between the direct and the Fourier image. Can you verify the idea that parallel rays from different directions lead to spots at different spatial positions off the optical axis? Can you understand diffraction from simple shapes like round and square holes of different sizes? If so, then look at regular arrays of the same objects. Your goal is to connect the spatial shape to the Fourier Transform, and then observe whether the intensity at the point P bears any resemblance to that transform. 3. Ronchi grating. The diffraction pattern of the Ronchi grating is closely related to the Fourier transform of a square wave. Which Fourier components are visible? Recall (or derive) that a square wave has only the odd harmonic components. How is this visible in the diffraction image? 4. Spatial filtering. First look at the Ronchi. How does the reconstructed image look if you a) remove the central (zeroth order) diffraction spot, b) let only the third order spots go through, c) let only the zeroth order spot pass? Next, use crossed Ronchi Gratings to create a checkerboard object. Can you find a way to filter the light at the diffraction plane so that all of the horizontal lines are removed from the reconstructed image? 5. Explore Look at some of the other objects available in the lab. What features can be removed or emphasized by spatial filtering? Fourier Optics 4.8 Spring 011

9 Problems These problems will give you a starting design for the Fourier Optical Analyzer. Do not be afraid to make changes once you get to the lab. 1. Refer to Figure 4.1. We will carry out our design using thin lens formulas. A 40x microscope objective has a 4 mm focal length. So the point P is 4 mm to the right of L1. Suppose we want the distance from P to P' to be 10 cm. A) Where should we put the 10 mm focal length camera lens L? You will find that this problem has two solutions. Choose the one with L closest to L1. b) Assuming that the laser beam begins with a 1 mm diameter, what will the beam diameter be at L?. Suppose now that the object, O, is placed 5 cm to the right of L, and L3 is placed 8 cm to the right of P'. a) Where is the image point I'? b) Now suppose that we want the final image, I, to be 100 cm to the right of L3. Where should we put the diverging lens, L4? 3. Make a sketch of the system showing the positions of all lenses and images. Remember: Converging f>0 Diverging f<0 Object to left s>0 Object to right s<0 Fourier Optics 4.9 Spring 011

### 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. 3 Fall 2005 Diffraction

More information

### 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

More information

### 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

More information

### 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

More information

### 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

More information

### Imaging Systems Laboratory II. Laboratory 8: The Michelson Interferometer / Diffraction April 30 & May 02, 2002

1051-232 Imaging Systems Laboratory II Laboratory 8: The Michelson Interferometer / Diffraction April 30 & May 02, 2002 Abstract. In the last lab, you saw that coherent light from two different locations

More information

### Lecture 21. Physics 1202: Lecture 21 Today s Agenda

Physics 1202: Lecture 21 Today s Agenda Announcements: Team problems today Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon Homework

More information

### Be aware that there is no universal notation for the various quantities.

Fourier Optics v2.4 Ray tracing is limited in its ability to describe optics because it ignores the wave properties of light. Diffraction is needed to explain image spatial resolution and contrast and

More information

### Diffraction. modern investigations date from Augustin Fresnel

Diffraction Diffraction controls the detail you can see in optical instruments, makes holograms, diffraction gratings and much else possible, explains some natural phenomena Diffraction was discovered

More information

### GIST OF THE UNIT BASED ON DIFFERENT CONCEPTS IN THE UNIT (BRIEFLY AS POINT WISE). RAY OPTICS

209 GIST OF THE UNIT BASED ON DIFFERENT CONCEPTS IN THE UNIT (BRIEFLY AS POINT WISE). RAY OPTICS Reflection of light: - The bouncing of light back into the same medium from a surface is called reflection

More information

### PHYS 160 Astronomy. When analyzing light s behavior in a mirror or lens, it is helpful to use a technique called ray tracing.

Optics Introduction In this lab, we will be exploring several properties of light including diffraction, reflection, geometric optics, and interference. There are two sections to this lab and they may

More information

### Chapter 25. Optical Instruments

Chapter 25 Optical Instruments Optical Instruments Analysis generally involves the laws of reflection and refraction Analysis uses the procedures of geometric optics To explain certain phenomena, the wave

More information

### FRAUNHOFER AND FRESNEL DIFFRACTION IN ONE DIMENSION

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

More information

### 12:40-2:40 3:00-4:00 PM

Physics 294H l Professor: Joey Huston l email:huston@msu.edu l office: BPS3230 l Homework will be with Mastering Physics (and an average of 1 hand-written problem per week) Help-room hours: 12:40-2:40

More information

### Chapter 18 Optical Elements

Chapter 18 Optical Elements GOALS When you have mastered the content of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms and use it in an operational

More information

### Physics. Light Waves & Physical Optics

Physics Light Waves & Physical Optics Physical Optics Physical optics or wave optics, involves the effects of light waves that are not related to the geometric ray optics covered previously. We will use

More information

### Mirrors and Lenses. Images can be formed by reflection from mirrors. Images can be formed by refraction through lenses.

Mirrors and Lenses Images can be formed by reflection from mirrors. Images can be formed by refraction through lenses. Notation for Mirrors and Lenses The object distance is the distance from the object

More information

### Chapter Wave Optics. MockTime.com. Ans: (d)

Chapter Wave Optics Q1. Which one of the following phenomena is not explained by Huygen s construction of wave front? [1988] (a) Refraction Reflection Diffraction Origin of spectra Q2. Which of the following

More information

### Laboratory 7: Properties of Lenses and Mirrors

Laboratory 7: Properties of Lenses and Mirrors Converging and Diverging Lens Focal Lengths: A converging lens is thicker at the center than at the periphery and light from an object at infinity passes

More information

### 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

More information

### GEOMETRICAL OPTICS Practical 1. Part I. BASIC ELEMENTS AND METHODS FOR CHARACTERIZATION OF OPTICAL SYSTEMS

GEOMETRICAL OPTICS Practical 1. Part I. BASIC ELEMENTS AND METHODS FOR CHARACTERIZATION OF OPTICAL SYSTEMS Equipment and accessories: an optical bench with a scale, an incandescent lamp, matte, a set of

More information

### Physics 431 Final Exam Examples (3:00-5:00 pm 12/16/2009) TIME ALLOTTED: 120 MINUTES Name: Signature:

Physics 431 Final Exam Examples (3:00-5:00 pm 12/16/2009) TIME ALLOTTED: 120 MINUTES Name: PID: Signature: CLOSED BOOK. TWO 8 1/2 X 11 SHEET OF NOTES (double sided is allowed), AND SCIENTIFIC POCKET CALCULATOR

More information

### 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

More information

### ABC Math Student Copy. N. May ABC Math Student Copy. Physics Week 13(Sem. 2) Name. Light Chapter Summary Cont d 2

Page 1 of 12 Physics Week 13(Sem. 2) Name Light Chapter Summary Cont d 2 Lens Abberation Lenses can have two types of abberation, spherical and chromic. Abberation occurs when the rays forming an image

More information

### Applications of Optics

Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 26 Applications of Optics Marilyn Akins, PhD Broome Community College Applications of Optics Many devices are based on the principles of optics

More information

### Physics 23 Laboratory Spring 1987

Physics 23 Laboratory Spring 1987 DIFFRACTION AND FOURIER OPTICS Introduction This laboratory is a study of diffraction and an introduction to the concepts of Fourier optics and spatial filtering. The

More information

### Physics 3340 Spring 2005

Physics 3340 Spring 2005 Holography Purpose The goal of this experiment is to learn the basics of holography by making a two-beam transmission hologram. Introduction A conventional photograph registers

More information

### Name: Lab Partner: Section:

Chapter 10 Thin Lenses Name: Lab Partner: Section: 10.1 Purpose In this experiment, the formation of images by concave and convex lenses will be explored. The application of the thin lens equation and

More information

### 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

More information

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY. 2.71/2.710 Optics Spring 14 Practice Problems Posted May 11, 2014

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71/2.710 Optics Spring 14 Practice Problems Posted May 11, 2014 1. (Pedrotti 13-21) A glass plate is sprayed with uniform opaque particles. When a distant point

More information

### 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

More information

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY Mechanical Engineering Department. 2.71/2.710 Final Exam. May 21, Duration: 3 hours (9 am-12 noon)

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Mechanical Engineering Department 2.71/2.710 Final Exam May 21, 2013 Duration: 3 hours (9 am-12 noon) CLOSED BOOK Total pages: 5 Name: PLEASE RETURN THIS BOOKLET WITH

More information

### EE119 Introduction to Optical Engineering Spring 2003 Final Exam. Name:

EE119 Introduction to Optical Engineering Spring 2003 Final Exam Name: SID: CLOSED BOOK. THREE 8 1/2 X 11 SHEETS OF NOTES, AND SCIENTIFIC POCKET CALCULATOR PERMITTED. TIME ALLOTTED: 180 MINUTES Fundamental

More information

### NANO 703-Notes. Chapter 9-The Instrument

1 Chapter 9-The Instrument Illumination (condenser) system Before (above) the sample, the purpose of electron lenses is to form the beam/probe that will illuminate the sample. Our electron source is macroscopic

More information

### Transmission electron Microscopy

Transmission electron Microscopy Image formation of a concave lens in geometrical optics Some basic features of the transmission electron microscope (TEM) can be understood from by analogy with the operation

More information

### ECEN 4606, UNDERGRADUATE OPTICS LAB

ECEN 4606, UNDERGRADUATE OPTICS LAB Lab 2: Imaging 1 the Telescope Original Version: Prof. McLeod SUMMARY: In this lab you will become familiar with the use of one or more lenses to create images of distant

More information

### Readings: Hecht, Chapter 24

5. GEOMETRIC OPTICS Readings: Hecht, Chapter 24 Introduction In this lab you will measure the index of refraction of glass using Snell s Law, study the application of the laws of geometric optics to systems

More information

### 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

More information

### Single Slit Diffraction

PC1142 Physics II Single Slit Diffraction 1 Objectives Investigate the single-slit diffraction pattern produced by monochromatic laser light. Determine the wavelength of the laser light from measurements

More information

### 25 cm. 60 cm. 50 cm. 40 cm.

Geometrical Optics 7. The image formed by a plane mirror is: (a) Real. (b) Virtual. (c) Erect and of equal size. (d) Laterally inverted. (e) B, c, and d. (f) A, b and c. 8. A real image is that: (a) Which

More information

### 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

More information

### Class XII - Physics Wave Optics Chapter-wise Problems

Class XII - hysics Wave Optics Chapter-wise roblems Multiple Choice Question :- 10.1 Consider a light beam incident from air to a glass slab at Brewster s angle as shown in Fig. 10.1. A polaroid is placed

More information

### Reading: Lenses and Mirrors; Applications Key concepts: Focal points and lengths; real images; virtual images; magnification; angular magnification.

Reading: Lenses and Mirrors; Applications Key concepts: Focal points and lengths; real images; virtual images; magnification; angular magnification. 1.! Questions about objects and images. Can a virtual

More information

### 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

More information

### 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

More information

### A simple and effective first optical image processing experiment

A simple and effective first optical image processing experiment Dale W. Olson Physics Department, University of Northern Iowa, Cedar Falls, IA 50614-0150 Abstract: Optical image processing experiments

More information

### Week IV: FIRST EXPERIMENTS WITH THE ADVANCED OPTICS SET

Week IV: FIRST EXPERIMENTS WITH THE ADVANCED OPTICS SET The Advanced Optics set consists of (A) Incandescent Lamp (B) Laser (C) Optical Bench (with magnetic surface and metric scale) (D) Component Carriers

More information

### LOS 1 LASER OPTICS SET

LOS 1 LASER OPTICS SET Contents 1 Introduction 3 2 Light interference 5 2.1 Light interference on a thin glass plate 6 2.2 Michelson s interferometer 7 3 Light diffraction 13 3.1 Light diffraction on a

More information

### Average: Standard Deviation: Max: 99 Min: 40

1 st Midterm Exam Average: 83.1 Standard Deviation: 12.0 Max: 99 Min: 40 Please contact me to fix an appointment, if you took less than 65. Chapter 33 Lenses and Op/cal Instruments Units of Chapter 33

More information

### HOLIDAY HOME WORK PHYSICS CLASS-12B AUTUMN BREAK 2018

HOLIDAY HOME WK PHYSICS CLASS-12B AUTUMN BREAK 2018 NOTE: 1. THESE QUESTIONS ARE FROM PREVIOUS YEAR BOARD PAPERS FROM 2009-2018 CHAPTERS EMI,AC,OPTICS(BUT TRY TO SOLVE ONLY NON-REPEATED QUESTION) QUESTION

More information

### Image Formation by Lenses

Image Formation by Lenses Bởi: OpenStaxCollege Lenses are found in a huge array of optical instruments, ranging from a simple magnifying glass to the eye to a camera s zoom lens. In this section, we will

More information

### Physics 2310 Lab #5: Thin Lenses and Concave Mirrors Dr. Michael Pierce (Univ. of Wyoming)

Physics 2310 Lab #5: Thin Lenses and Concave Mirrors Dr. Michael Pierce (Univ. of Wyoming) Purpose: The purpose of this lab is to introduce students to some of the properties of thin lenses and mirrors.

More information

### Criteria for Optical Systems: Optical Path Difference How do we determine the quality of a lens system? Several criteria used in optical design

Criteria for Optical Systems: Optical Path Difference How do we determine the quality of a lens system? Several criteria used in optical design Computer Aided Design Several CAD tools use Ray Tracing (see

More information

### Converging and Diverging Surfaces. Lenses. Converging Surface

Lenses Sandy Skoglund 2 Converging and Diverging s AIR Converging If the surface is convex, it is a converging surface in the sense that the parallel rays bend toward each other after passing through the

More information

### Phys 102 Lecture 21 Optical instruments

Phys 102 Lecture 21 Optical instruments 1 Today we will... Learn how combinations of lenses form images Thin lens equation & magnification Learn about the compound microscope Eyepiece & objective Total

More information

### Chapter 4: Fourier Optics

Chapter 4: Fourier Optics P4-1. Calculate the Fourier transform of the function rect(2x)rect(/3) The rectangular function rect(x) is given b 1 x 1/2 rect( x) when 0 x 1/2 P4-2. Assume that ( gx (, )) G

More information

### Lecture 17. Image formation Ray tracing Calculation. Lenses Convex Concave. Mirrors Convex Concave. Optical instruments

Lecture 17. Image formation Ray tracing Calculation Lenses Convex Concave Mirrors Convex Concave Optical instruments Image formation Laws of refraction and reflection can be used to explain how lenses

More information

### Optics and Images. Lenses and Mirrors. Matthew W. Milligan

Optics and Images Lenses and Mirrors Light: Interference and Optics I. Light as a Wave - wave basics review - electromagnetic radiation II. Diffraction and Interference - diffraction, Huygen s principle

More information

### Geometric Optics. This is a double-convex glass lens mounted in a wooden frame. We will use this as the eyepiece for our microscope.

I. Before you come to lab Read through this handout in its entirety. II. Learning Objectives As a result of performing this lab, you will be able to: 1. Use the thin lens equation to determine the focal

More information

### Video. Part I. Equipment

1 of 7 11/8/2013 11:32 AM There are two parts to this lab that can be done in either order. In Part I you will study the Laws of Reflection and Refraction, measure the index of refraction of glass and

More information

### 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

More information

### 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

More information

### Department of Physics & Astronomy Undergraduate Labs. Thin Lenses

Thin Lenses Reflection and Refraction When light passes from one medium to another, part of the light is reflected and the rest is transmitted. Light rays that are transmitted undergo refraction (bending)

More information

### Section A Conceptual and application type questions. 1 Which is more observable diffraction of light or sound? Justify. (1)

INDIAN SCHOOL MUSCAT Department of Physics Class : XII Physics Worksheet - 6 (2017-2018) Chapter 9 and 10 : Ray Optics and wave Optics Section A Conceptual and application type questions 1 Which is more

More information

### Assignment X Light. Reflection and refraction of light. (a) Angle of incidence (b) Angle of reflection (c) principle axis

Assignment X Light Reflection of Light: Reflection and refraction of light. 1. What is light and define the duality of light? 2. Write five characteristics of light. 3. Explain the following terms (a)

More information

### 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

More information

### 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:

More information

### Phys 531 Lecture 9 30 September 2004 Ray Optics II. + 1 s i. = 1 f

Phys 531 Lecture 9 30 September 2004 Ray Optics II Last time, developed idea of ray optics approximation to wave theory Introduced paraxial approximation: rays with θ 1 Will continue to use Started disussing

More information

### Phy Ph s y 102 Lecture Lectur 21 Optical instruments 1

Phys 102 Lecture 21 Optical instruments 1 Today we will... Learn how combinations of lenses form images Thin lens equation & magnification Learn about the compound microscope Eyepiece & objective Total

More information

### APPLICATIONS FOR TELECENTRIC LIGHTING

APPLICATIONS FOR TELECENTRIC LIGHTING Telecentric lenses used in combination with telecentric lighting provide the most accurate results for measurement of object shapes and geometries. They make attributes

More information

### 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

More information

### Lecture Outline Chapter 27. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 27 Physics, 4 th Edition James S. Walker Chapter 27 Optical Instruments Units of Chapter 27 The Human Eye and the Camera Lenses in Combination and Corrective Optics The Magnifying

More information

### Design of a digital holographic interferometer for the. ZaP Flow Z-Pinch

Design of a digital holographic interferometer for the M. P. Ross, U. Shumlak, R. P. Golingo, B. A. Nelson, S. D. Knecht, M. C. Hughes, R. J. Oberto University of Washington, Seattle, USA Abstract The

More information

### 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

More information

### LEOK-3 Optics Experiment kit

LEOK-3 Optics Experiment kit Physical optics, geometrical optics and fourier optics Covering 26 experiments Comprehensive documents Include experiment setups, principles and procedures Cost effective solution

More information

### Physics 1C. Lecture 25B

Physics 1C Lecture 25B "More than 50 years ago, Austrian researcher Ivo Kohler gave people goggles thats severely distorted their vision: The lenses turned the world upside down. After several weeks, subjects

More information

### Fiber Optic Communications

Fiber Optic Communications ( Chapter 2: Optics Review ) presented by Prof. Kwang-Chun Ho 1 Section 2.4: Numerical Aperture Consider an optical receiver: where the diameter of photodetector surface area

More information

### PHYS 1020 LAB 7: LENSES AND OPTICS. Pre-Lab

PHYS 1020 LAB 7: LENSES AND OPTICS Note: Print and complete the separate pre-lab assignment BEFORE the lab. Hand it in at the start of the lab. Pre-Lab Start by reading the entire prelab and lab write-up.

More information

### EE119 Introduction to Optical Engineering Spring 2002 Final Exam. Name:

EE119 Introduction to Optical Engineering Spring 2002 Final Exam Name: SID: CLOSED BOOK. FOUR 8 1/2 X 11 SHEETS OF NOTES, AND SCIENTIFIC POCKET CALCULATOR PERMITTED. TIME ALLOTTED: 180 MINUTES Fundamental

More information

### Chapter 34. Images. Copyright 2014 John Wiley & Sons, Inc. All rights reserved.

Chapter 34 Images Copyright 34-1 Images and Plane Mirrors Learning Objectives 34.01 Distinguish virtual images from real images. 34.02 Explain the common roadway mirage. 34.03 Sketch a ray diagram for

More information

### Astronomy 80 B: Light. Lecture 9: curved mirrors, lenses, aberrations 29 April 2003 Jerry Nelson

Astronomy 80 B: Light Lecture 9: curved mirrors, lenses, aberrations 29 April 2003 Jerry Nelson Sensitive Countries LLNL field trip 2003 April 29 80B-Light 2 Topics for Today Optical illusion Reflections

More information

### Phys214 Fall 2004 Midterm Form A

1. A clear sheet of polaroid is placed on top of a similar sheet so that their polarizing axes make an angle of 30 with each other. The ratio of the intensity of emerging light to incident unpolarized

More information

### 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

More information

### 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

More information

### a) (6) How much time in milliseconds does the signal require to travel from the satellite to the dish antenna?

General Physics II Exam 3 - Chs. 22 25 - EM Waves & Optics April, 203 Name Rec. Instr. Rec. Time For full credit, make your work clear. Show formulas used, essential steps, and results with correct units

More information

### Big League Cryogenics and Vacuum The LHC at CERN

Big League Cryogenics and Vacuum The LHC at CERN A typical astronomical instrument must maintain about one cubic meter at a pressure of

More information

### Test Review # 8. Physics R: Form TR8.17A. Primary colors of light

Physics R: Form TR8.17A TEST 8 REVIEW Name Date Period Test Review # 8 Light and Color. Color comes from light, an electromagnetic wave that travels in straight lines in all directions from a light source

More information

### 1 Laboratory 7: Fourier Optics

1051-455-20073 Physical Optics 1 Laboratory 7: Fourier Optics 1.1 Theory: References: Introduction to Optics Pedrottis Chapters 11 and 21 Optics E. Hecht Chapters 10 and 11 The Fourier transform is an

More information

### Properties of optical instruments. Visual optical systems part 2: focal visual instruments (microscope type)

Properties of optical instruments Visual optical systems part 2: focal visual instruments (microscope type) Examples of focal visual instruments magnifying glass Eyepieces Measuring microscopes from the

More information

### Wave Optics. Why is the sky blue? What causes the beautiful colors in a soap bubble or an oil

HAPTER26 C. Return to Table of Contents Wave Optics Colors produced by a thin layer of oil on the surface of water result from constructive and destructive interference of light. Why is the sky blue? What

More information

### Lecture 2: Geometrical Optics. Geometrical Approximation. Lenses. Mirrors. Optical Systems. Images and Pupils. Aberrations.

Lecture 2: Geometrical Optics Outline 1 Geometrical Approximation 2 Lenses 3 Mirrors 4 Optical Systems 5 Images and Pupils 6 Aberrations Christoph U. Keller, Leiden Observatory, keller@strw.leidenuniv.nl

More information

### 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

More information

### Thin Lenses. Lecture 25. Chapter 23. Ray Optics. Physics II. Course website:

Lecture 25 Chapter 23 Physics II Ray Optics Thin Lenses Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html

More information

### R.B.V.R.R. WOMEN S COLLEGE (AUTONOMOUS) Narayanaguda, Hyderabad.

R.B.V.R.R. WOMEN S COLLEGE (AUTONOMOUS) Narayanaguda, Hyderabad. DEPARTMENT OF PHYSICS QUESTION BANK FOR SEMESTER III PAPER III OPTICS UNIT I: 1. MATRIX METHODS IN PARAXIAL OPTICS 2. ABERATIONS UNIT II

More information

### Chapter 34 Geometric Optics

Chapter 34 Geometric Optics Lecture by Dr. Hebin Li Goals of Chapter 34 To see how plane and curved mirrors form images To learn how lenses form images To understand how a simple image system works Reflection

More information

### Optics Laboratory Spring Semester 2017 University of Portland

Optics Laboratory Spring Semester 2017 University of Portland Laser Safety Warning: The HeNe laser can cause permanent damage to your vision. Never look directly into the laser tube or at a reflection

More information

### Chapter 3 Op,cal Instrumenta,on

Imaging by an Op,cal System Change in curvature of wavefronts by a thin lens Chapter 3 Op,cal Instrumenta,on 3-1 Stops, Pupils, and Windows 3-4 The Camera 3-5 Simple Magnifiers and Eyepieces 1. Magnifiers

More information

### 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

More information

### 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

More information

### 19. Ray Optics. S. G. Rajeev. April 2, 2009

9. Ray Optics S. G. Rajeev April 2, 2009 When the wave length is small light travels along straightlines called rays. Ray optics (also called geometrical optics) is the study of this light in this situation.

More information