DOCSLIB.ORG

Electromagnetic Wave Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Electromagnetic Wave Theory Electromagnetic Wave Theory Wei-Chih Wang ME557 Department of Mechanical Engineering w wang University of Washington 1 Refraction and reflection (wave equation) The incident beam is characterized by its wavelength λi, its frequency νi and its velocity c and n ε µ λ , f , C 0 n ε µ λ , f , C ,, r r, r r refracted beam is o,, ο o i ι o characterized by its wavelength λr, its frequency νr and its velocity c , the simple dispersion relation for vacuum. Co = fi λi C = fr λr w wang 2 The speed of light in a medium is related to the electric and magnetic properties of the medium, and the speed of light in vacuum can be expressed as o The speed of light in a material to the material "constants" εr and the corresponding magnetic permeability µ0 of vacuum and µr of the material is 1 c = µr µoεrεo w wang 3 The index of refraction n of a non-magnetic material µr = 1 is linked to the dielectric constant εr via a simple relation, which is a rather direct result of the Maxwell equations. c o 1 / µ o ε o = = ε r = n c 1 / µ r µ o ε r ε o Plug back into dispersion relation, c λ f o = i i = n c λr fr Since f = f i r, λ n = i w wang λr 4 Maxwell Equations Integral form in the absence of magnetic or polarized media: I. Faraday's law of induction dl II. Ampere's law III. Gauss' law for magnetism IV. Gauss' law for electricity E = Electric Field (V/m) ρ = charge density (c/m3) i = electric current (A) 2 2 B = Magnetic flux density(Web/m , T) ε0 = permittivity J = current density(A/m ) D = Electric flux density (c/m2) µ = permeability c = speed of light or electric displacement field 0 H = Magnetic Field (A/m) ΦB = Magnetic flux (Web) P = Polarization -19 -6 -12 q = chargew wang 1.6x10 coulombs, µo = 1.26x10 H/m, εo = 8.85x10 F/m 5 Electric flux For instance, Gauss's law states that the flux of the electric field out of a closed surface is proportional to the electric charge enclosed in the surface (regardless of how that charge is distributed). The constant of proportionality is the reciprocal of the permittivity of free space. Its integral form is: The electric flux in an unclosed surface: φ = E ⋅dA E ∫ Sometimes electric flux appears in φ = D ⋅dA = εE ⋅dA terms of flux density D as: E ∫ ∫ w wang 6 The electric elasticity equation (Displacement field) D= ε E Where E = electric field ε = permittivity (dielectric constant) -12 in air εo = 8.85x10 F/m w wang 7 Magnetic flux We know from Gauss's law for magnetism that in a close surface, Normally, the magnetic flux in an φB = B ⋅dA unclosed surface ∫ Where B = magnetic flux density w wang 8 But when the generated fields pass through magnetic materials which themselves contribute internal magnetic fields, ambiguities can arise about what part of the field comes from the external currents and what comes from the material itself. It has been common practice to define another magnetic field quantity, usually called the "magnetic field strength" designated by H. It can be defined by the relationship Β = µ H + M M = magnetization. Normally, the M = 0 for nonmagnetic material -6 If in air, µo = 1.26x10 H/m w wang 9 Faraday’s Law of Induction dl This line integral is equal to the generated voltage or emf in the loop, so Faraday's law is the basis for electric generators. It also forms the basis for inductors and transformers. w wang 10 Ampere's Law In the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop. This is useful for the calculation of magnetic field for simple geometries. w wang 11 Gauss’s Law for Magnetism The net magnetic flux out of any closed surface is zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole. The net flux will always be zero for dipole sources. If there were a magnetic monopole source, this would give a non-zero area integral. The divergence of a vector field is proportional to the point source density, so the form of Gauss' law for magnetic fields is then a statement that there are no magnetic monopoles. w wang 12 Gauss’s Law for Electricity The electric flux out of any closed surface is proportional to the total charge enclosed within the surface. The integral form of Gauss' Law finds application in calculating electric fields around charged objects. In applying Gauss' law to the electric field of a point charge, one can show that it is consistent with Coulomb's law. While the area integral of the electric field gives a measure of the net charge enclosed, the divergence of the electric field gives a measure of the density of sources. It also has implications for the conservation of charge. w wang 13 Maxwell Equations − ∂B Faraday’s Law ∇× E = ∂t ∂D Ampere’s Law ∇× H = J + ∂t Gauss’s Law for ∇ • B = 0 Magnetism Gauss’s Law for Electricity ∇ • D = ρ E = Electric Field (V/m) ρ = charge density (c/m3) i = electric current (A) 2 2 B = Magnetic flux density(Web/m , T) ε0 = permittivity J = current density(A/m ) 2 D = Electric flux density (c/m ) µ0 = permeability c = speed of light H = Magneticw wang Field (A/m) ΦB = Magnetic flux (Web) P = Polarization 14 Wave equation Maxwell's Equations contain the wave equation for electromagnetic waves. One approach to obtaining the wave equation: 1. Take the curl of Faraday's law: 2. Substitute Ampere's law for a charge and current-free region: This is the three-dimensional wave equation in vector form. It looks more familiar when reduced a plane wave with field in the x-direction only: w wang 15 Curl The curl of a vector function is the vector product of the del operator with a vector function: where i,j,k are unit vectors in the x, y, z directions. It can also be expressed in determinant form: w wang 16 Curl in Cylindrical Polar Coordinates The curl in cylindrical polar coordinates, expressed in determinant form is: w wang 17 Curl in Spherical Polar Coordinates The curl in spherical polar coordinates, expressed in determinant form is: w wang 18 Use ∇×(∇× E) = ∇(∇ • E) − ∇2E Wave equation 2 2 becomes ∇ E +ω µoεo E = 0 We consider the simple solution where E field is parallel to the x axis and its function of z coordinate only, the wave equation then becomes, ∂2E x +ω 2µ ε E = 0 ∂z 2 o o x A solution to the above differential equation is − jkz E = xˆEoe Substitute above equation into wave equation yields, 2 2 2 2 (dispersion relation) w wang(−k +ωµεµε)E = 0 k =ω 19 Let’s transform the solution for the wave equation into real space and time, (assume time harmonic field) E E(z,t) = Re{Ee jωt } = xˆE cos(ωt − kz) o x k H k = 2π/λ, where k = wave number z Image we riding along with the wave, we asked what Velocity shall we move in order to keep up with the wave, The answer is phase of the wave to be constant ωt - kz = a constant The velocity of propagation is therefore given by, dz ω 1 = v = = (phase velocity) dt k w wang µoεo 20 Poynting’s Theorem For a time –harmonic electromagnetic wave, the power density Per unit area associate with the wave is defined in complex Representation by vector S, S S= E x H* (W/m2) hyperphysics Time average pontying vector <s> is defined as average of the Time domain Poynting vector S over a period T=2π/ω. 1 2π < S >= d(ωt)E(x, y, z,t)× H (x, y, z,t) 2π ∫0 (or) 1 w wang < S >= Re{E × H} 21 2 Boundary Conditions y nˆ ε1 H 1 H w H3 4 H2 x ε2 l At an interface between two media, the file quantities must satisfy Certain conditions. Consider an interface between two dielectric media With dielectric constants ε1 and ε2, in the z component Ampere’s Law, we have, ∂H ∂H y − x = J + jwD ∂x ∂y z z or H 4 − H3 H1 − H 2 − = J z + jwDz w wang l w 22 Now let area shrink to a point where w goes to zero before l does. So Jz =Js ~ Jvw, then H 2 − H1 = J z Or in general, nˆ ×(H 2 − H1) = J s Applying the same above argument to Faraday’s Law and we get, nˆ ×(E1 − E2 ) = 0 The tangential electric field E is continuous across the boundary surface.The discontinuity in the tangential component of H is equal to the surface current density Js. w wang 23 Apply the divergence theory ∇ • B = 0 and ∇ • D = ρ for The pillbox volume shown y nˆ ε 1 w x ε2 l As w -> 0, we get (B1 − B2 ) • nˆ = 0 (D1 − D2 ) • nˆ = ρ The normal component of B is continuous across the boundary surface.The discontinuity in the normal component of D is equal to the surface charge density ρ w wang 24 Boundary Condition for Perfect Conductor On the surface of a perfect conductor, E2 = 0 and H2= 0 y nˆ ε 1 w x ε2 l w wang 25 Reflection and Transmission (TE, S wave) µ1, ε1, n1 µ2, ε2, n2 r Rl Eo − jkrxx+ jkrzz H = (xˆkrz + zˆkrx ) e x ωµ1 t − jktxx− jktzz E = yˆTl Eoe r − jkrxx+ jkrzz E = yˆRl Eoe θr θt z θi i − jkxx− jky y E = yˆEoe t Tl Eo − jktxx− jktzz H = (−xˆktz + zˆktx ) e ωµ2 E R =reflection coefficient H i = (−xˆk + zˆk ) o e− jkxx− jkzz l z x T =transmission coefficient ωµ1 l TE = transverse electric, perpendicularly polarized (E perpendicular to plan of incident) w wang 26 If neither two are perfect conductors, Js=0, then boundary conditions requires both the tangential electric-filed and magnetic-field components be continuous at z =0 thus, − jkxx − jkrxx − jktxx e + Rle = Tle (E component) − kz − jkxx krz − jkrxx − ktz − jktxx e + Rle = Tle (B component) ωµ1 ωµ1 ωµ2 For the above equations to hold at all x, all components must be the same, thus we get the phase matching condition: kx = k sinθi = krx = kr sinθr = ktx = kt sinθt From this we obtain law of reflection: Since k =k because k2 = k2
Load more

Recommended publications
  • Glossary Physics (I-Introduction)
    1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay.
    [Show full text]
  • Wavefront Decomposition and Propagation Through Complex Models with Analytical Ray Theory and Signal Processing Paul Cristini, Eric De Bazelaire
    Wavefront decomposition and propagation through complex models with analytical ray theory and signal processing Paul Cristini, Eric de Bazelaire To cite this version: Paul Cristini, Eric de Bazelaire. Wavefront decomposition and propagation through complex models with analytical ray theory and signal processing. 2006. hal-00110279 HAL Id: hal-00110279 https://hal.archives-ouvertes.fr/hal-00110279 Preprint submitted on 27 Oct 2006 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. March 31, 2006 14:7 WSPC/130-JCA jca_sbrt Journal of Computational Acoustics c IMACS Wavefront decomposition and propagation through complex models with analytical ray theory and signal processing P. CRISTINI CNRS-UMR5212 Laboratoire de Mod´elisation et d'Imagerie en G´eosciences de Pau Universit´e de Pau et des Pays de l'Adour BP 1155, 64013 Pau Cedex, France [email protected] E. De BAZELAIRE 11, Route du bourg 64230 Beyrie-en-B´earn, France [email protected] Received (Day Month Year) Revised (Day Month Year) We present a novel method which can perform the fast computation of the times of arrival of seismic waves which propagate between a source and an array of receivers in a stratified medium.
    [Show full text]
  • EMT UNIT 1 (Laws of Reflection and Refraction, Total Internal Reflection).Pdf
    Electromagnetic Theory II (EMT II); Online Unit 1. REFLECTION AND TRANSMISSION AT OBLIQUE INCIDENCE (Laws of Reflection and Refraction and Total Internal Reflection) (Introduction to Electrodynamics Chap 9) Instructor: Shah Haidar Khan University of Peshawar. Suppose an incident wave makes an angle θI with the normal to the xy-plane at z=0 (in medium 1) as shown in Figure 1. Suppose the wave splits into parts partially reflecting back in medium 1 and partially transmitting into medium 2 making angles θR and θT, respectively, with the normal. Figure 1. To understand the phenomenon at the boundary at z=0, we should apply the appropriate boundary conditions as discussed in the earlier lectures. Let us first write the equations of the waves in terms of electric and magnetic fields depending upon the wave vector κ and the frequency ω. MEDIUM 1: Where EI and BI is the instantaneous magnitudes of the electric and magnetic vector, respectively, of the incident wave. Other symbols have their usual meanings. For the reflected wave, Similarly, MEDIUM 2: Where ET and BT are the electric and magnetic instantaneous vectors of the transmitted part in medium 2. BOUNDARY CONDITIONS (at z=0) As the free charge on the surface is zero, the perpendicular component of the displacement vector is continuous across the surface. (DIꓕ + DRꓕ ) (In Medium 1) = DTꓕ (In Medium 2) Where Ds represent the perpendicular components of the displacement vector in both the media. Converting D to E, we get, ε1 EIꓕ + ε1 ERꓕ = ε2 ETꓕ ε1 ꓕ +ε1 ꓕ= ε2 ꓕ Since the equation is valid for all x and y at z=0, and the coefficients of the exponentials are constants, only the exponentials will determine any change that is occurring.
    [Show full text]
  • Chapter 22 Reflection and Refraction of Light
    Chapter 22 Reflection and Refraction of Light Problem Solutions 22.1 The total distance the light travels is d2 Dcenter to R Earth R Moon center 2 3.84 108 6.38 10 6 1.76 10 6 m 7.52 10 8 m d 7.52 108 m Therefore, v 3.00 108 m s t 2.51 s 22.2 (a) The energy of a photon is sinc nair n prism 1.00 n prism , where Planck’ s constant is 1.00 8 sinc sin 45 and the speed of light in vacuum is c 3.00 10 m s . If nprism 1.00 1010 m , 6.63 1034 J s 3.00 10 8 m s E 1.99 1015 J 1.00 10-10 m 1 eV (b) E 1.99 1015 J 1.24 10 4 eV 1.602 10-19 J (c) and (d) For the X-rays to be more penetrating, the photons should be more energetic. Since the energy of a photon is directly proportional to the frequency and inversely proportional to the wavelength, the wavelength should decrease , which is the same as saying the frequency should increase . 1 eV 22.3 (a) E hf 6.63 1034 J s 5.00 10 17 Hz 2.07 10 3 eV 1.60 1019 J 355 356 CHAPTER 22 34 8 hc 6.63 10 J s 3.00 10 m s 1 nm (b) E hf 6.63 1019 J 3.00 1029 nm 10 m 1 eV E 6.63 1019 J 4.14 eV 1.60 1019 J c 3.00 108 m s 22.4 (a) 5.50 107 m 0 f 5.45 1014 Hz (b) From Table 22.1 the index of refraction for benzene is n 1.501.
    [Show full text]
  • Model-Based Wavefront Reconstruction Approaches For
    Submitted by Dipl.-Ing. Victoria Hutterer, BSc. Submitted at Industrial Mathematics Institute Supervisor and First Examiner Univ.-Prof. Dr. Model-based wavefront Ronny Ramlau reconstruction approaches Second Examiner Eric Todd Quinto, Ph.D., Robinson Profes- for pyramid wavefront sensors sor of Mathematics in Adaptive Optics October 2018 Doctoral Thesis to obtain the academic degree of Doktorin der Technischen Wissenschaften in the Doctoral Program Technische Wissenschaften JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69 4040 Linz, Osterreich¨ www.jku.at DVR 0093696 Abstract Atmospheric turbulence and diffraction of light result in the blurring of images of celestial objects when they are observed by ground based telescopes. To correct for the distortions caused by wind flow or small varying temperature regions in the at- mosphere, the new generation of Extremely Large Telescopes (ELTs) uses Adaptive Optics (AO) techniques. An AO system consists of wavefront sensors, control algo- rithms and deformable mirrors. A wavefront sensor measures incoming distorted wave- fronts, the control algorithm links the wavefront sensor measurements to the mirror actuator commands, and deformable mirrors mechanically correct for the atmospheric aberrations in real-time. Reconstruction of the unknown wavefront from given sensor measurements is an Inverse Problem. Many instruments currently under development for ELT-sized telescopes have pyramid wavefront sensors included as the primary option. For this sensor type, the relation between the intensity of the incoming light and sensor data is non-linear. The high number of correcting elements to be controlled in real-time or the segmented primary mirrors of the ELTs lead to unprecedented challenges when designing the control al- gorithms.
    [Show full text]
  • Megakernels Considered Harmful: Wavefront Path Tracing on Gpus
    Megakernels Considered Harmful: Wavefront Path Tracing on GPUs Samuli Laine Tero Karras Timo Aila NVIDIA∗ Abstract order to handle irregular control flow, some threads are masked out when executing a branch they should not participate in. This in- When programming for GPUs, simply porting a large CPU program curs a performance loss, as masked-out threads are not performing into an equally large GPU kernel is generally not a good approach. useful work. Due to SIMT execution model on GPUs, divergence in control flow carries substantial performance penalties, as does high register us- The second factor is the high-bandwidth, high-latency memory sys- age that lessens the latency-hiding capability that is essential for the tem. The impressive memory bandwidth in modern GPUs comes at high-latency, high-bandwidth memory system of a GPU. In this pa- the expense of a relatively long delay between making a memory per, we implement a path tracer on a GPU using a wavefront formu- request and getting the result. To hide this latency, GPUs are de- lation, avoiding these pitfalls that can be especially prominent when signed to accommodate many more threads than can be executed in using materials that are expensive to evaluate. We compare our per- any given clock cycle, so that whenever a group of threads is wait- formance against the traditional megakernel approach, and demon- ing for a memory request to be served, other threads may be exe- strate that the wavefront formulation is much better suited for real- cuted. The effectiveness of this mechanism, i.e., the latency-hiding world use cases where multiple complex materials are present in capability, is determined by the threads’ resource usage, the most the scene.
    [Show full text]
  • 9.2 Refraction and Total Internal Reflection
    9.2 refraction and total internal reflection When a light wave strikes a transparent material such as glass or water, some of the light is reflected from the surface (as described in Section 9.1). The rest of the light passes through (transmits) the material. Figure 1 shows a ray that has entered a glass block that has two parallel sides. The part of the original ray that travels into the glass is called the refracted ray, and the part of the original ray that is reflected is called the reflected ray. normal incident ray reflected ray ␪ ␪i r ␪r ϭ ␪i air glass ␪2 refracted ray Figure 1 A light ray that strikes a glass surface is both reflected and refracted. Refracted and reflected rays of light account for many things that we encounter in our everyday lives. For example, the water in a pool can look shallower than it really is. A stick can look as if it bends at the point where it enters the water. On a hot day, the road ahead can appear to have a puddle of water, which turns out to be a mirage. These effects are all caused by the refraction and reflection of light. refraction The direction of the refracted ray is different from the direction of the incident refraction the bending of light as it ray, an effect called refraction. As with reflection, you can measure the direction of travels at an angle from one medium the refracted ray using the angle that it makes with the normal. In Figure 1, this to another angle is labelled θ2.
    [Show full text]
  • Descartes' Optics
    Descartes’ Optics Jeffrey K. McDonough Descartes’ work on optics spanned his entire career and represents a fascinating area of inquiry. His interest in the study of light is already on display in an intriguing study of refraction from his early notebook, known as the Cogitationes privatae, dating from 1619 to 1621 (AT X 242-3). Optics figures centrally in Descartes’ The World, or Treatise on Light, written between 1629 and 1633, as well as, of course, in his Dioptrics published in 1637. It also, however, plays important roles in the three essays published together with the Dioptrics, namely, the Discourse on Method, the Geometry, and the Meteorology, and many of Descartes’ conclusions concerning light from these earlier works persist with little substantive modification into the Principles of Philosophy published in 1644. In what follows, we will look in a brief and general way at Descartes’ understanding of light, his derivations of the two central laws of geometrical optics, and a sampling of the optical phenomena he sought to explain. We will conclude by noting a few of the many ways in which Descartes’ efforts in optics prompted – both through agreement and dissent – further developments in the history of optics. Descartes was a famously systematic philosopher and his thinking about optics is deeply enmeshed with his more general mechanistic physics and cosmology. In the sixth chapter of The Treatise on Light, he asks his readers to imagine a new world “very easy to know, but nevertheless similar to ours” consisting of an indefinite space filled everywhere with “real, perfectly solid” matter, divisible “into as many parts and shapes as we can imagine” (AT XI ix; G 21, fn 40) (AT XI 33-34; G 22-23).
    [Show full text]
  • Reflection, Refraction, and Total Internal Reflection
    From The Physics Classroom's Physics Interactives http://www.physicsclassroom.com Reflection, Refraction, and Total Internal Reflection Purpose: To investigate the effect of the angle of incidence upon the brightness of a reflected ray and refracted ray at a boundary and to identify the two requirements for total internal reflection. Getting Ready: Navigate to the Refraction Interactive at The Physics Classroom website: http://www.physicsclassroom.com/Physics-Interactives/Refraction-and-Lenses/Refraction Navigational Path: www.physicsclassroom.com ==> Physics Interactives ==> Refraction and Lenses ==> Refraction Getting Acquainted: Once you've launched the Interactive and resized it, experiment with the interface to become familiar with it. Observe how the laser can be dragged about the workspace, how it can be turned On (Go button) and Cleared, how the substance on the top and the bottom of the boundary can be changed, and how the protractor can be toggled on and off and repositioned. Also observe that there is an incident ray, a reflected ray and a refracted ray; the angle for each of these rays can be measured. Part 1: Reflection and Refraction Set the top substance to Air and the bottom substance to Water. Drag the laser under the water so that you can shoot it upward through the water at the boundary with air (don't do this at home ... nor in the physics lab). Toggle the protractor to On. Then collect data for light rays approaching the boundary with the following angles of incidence (Θincidence). If there is no refracted ray, then put "--" in the table cell for the angle of refraction (Θrefraction).
    [Show full text]
  • Physics 30 Lesson 8 Refraction of Light
    Physics 30 Lesson 8 Refraction of Light Refer to Pearson pages 666 to 674. I. Reflection and refraction of light At any interface between two different mediums, some light will be reflected and some will be refracted, except in certain cases which we will soon discover. When problem solving for refraction, we usually ignore the reflected ray. Glass prism II. Index of refraction The fastest that light can travel is in a vacuum (c = 3.00 x 108 m/s). In other substances, the speed of light is always slower. The index of refraction is a ratio of the speed of light in vacuum with the speed of light in the medium: speed in vacuum (c) index of refraction (n) speed in medium (v) c n= v Some common indices of refraction are: Substance Index of refraction (n) vacuum 1.0000 Notice that the index of refraction (n) air 1.0003 is always greater than or equal to 1 water 1.33 ethyl alcohol 1.36 and that it has no units. quartz (fused) 1.46 glycerine 1.47 Lucite or Plexiglas 1.51 glass (crown) 1.52 sodium chloride 1.53 glass (crystal) 1.54 ruby 1.54 glass (flint) 1.65 zircon 1.92 diamond 2.42 Dr. Ron Licht 8 – 1 www.structuredindependentlearning.com Example 1 The index of refraction for crown glass was measured to be 1.52. What is the speed of light in crown glass? c n v c v n 3.00 108 m v s 1.52 8 m v 1.97 ×10 s III.
    [Show full text]
  • Wavefront Coding Fluorescence Microscopy Using High Aperture Lenses
    Wavefront Coding Fluorescence Microscopy Using High Aperture Lenses Matthew R. Arnison*, Carol J. Cogswelly, Colin J. R. Sheppard*, Peter Törökz * University of Sydney, Australia University of Colorado, U. S. A. y Imperial College, U. K. z 1 Extended Depth of Field Microscopy In recent years live cell fluorescence microscopy has become increasingly important in biological and medical studies. This is largely due to new genetic engineering techniques which allow cell features to grow their own fluorescent markers. A pop- ular example is green fluorescent protein. This avoids the need to stain, and thereby kill, a cell specimen before taking fluorescence images, and thus provides a major new method for observing live cell dynamics. With this new opportunity come new challenges. Because in earlier days the process of staining killed the cells, microscopists could do little additional harm by squashing the preparation to make it flat, thereby making it easier to image with a high resolution, shallow depth of field lens. In modern live cell fluorescence imag- ing, the specimen may be quite thick (in optical terms). Yet a single 2D image per time–step may still be sufficient for many studies, as long as there is a large depth of field as well as high resolution. Light is a scarce resource for live cell fluorescence microscopy. To image rapidly changing specimens the microscopist needs to capture images quickly. One of the chief constraints on imaging speed is the light intensity. Increasing the illumination will result in faster acquisition, but can affect specimen behaviour through heating, or reduce fluorescent intensity through photobleaching.
    [Show full text]
  • Topic 3: Operation of Simple Lens
    V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Topic 3: Operation of Simple Lens Aim: Covers imaging of simple lens using Fresnel Diffraction, resolu- tion limits and basics of aberrations theory. Contents: 1. Phase and Pupil Functions of a lens 2. Image of Axial Point 3. Example of Round Lens 4. Diffraction limit of lens 5. Defocus 6. The Strehl Limit 7. Other Aberrations PTIC D O S G IE R L O P U P P A D E S C P I A S Properties of a Lens -1- Autumn Term R Y TM H ENT of P V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Ray Model Simple Ray Optics gives f Image Object u v Imaging properties of 1 1 1 + = u v f The focal length is given by 1 1 1 = (n − 1) + f R1 R2 For Infinite object Phase Shift Ray Optics gives Delta Fn f Lens introduces a path length difference, or PHASE SHIFT. PTIC D O S G IE R L O P U P P A D E S C P I A S Properties of a Lens -2- Autumn Term R Y TM H ENT of P V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Phase Function of a Lens δ1 δ2 h R2 R1 n P0 P ∆ 1 With NO lens, Phase Shift between , P0 ! P1 is 2p F = kD where k = l with lens in place, at distance h from optical, F = k0d1 + d2 +n(D − d1 − d2)1 Air Glass @ A which can be arranged to|giv{ze } | {z } F = knD − k(n − 1)(d1 + d2) where d1 and d2 depend on h, the ray height.
    [Show full text]