Phys 2310 Fri. Oct. 23, 2017 Today s Topics. Begin Chapter 6: More on Geometric Optics Reading for Next Time

Similar documents
Minimizing spherical aberrations Exploiting the existence of conjugate points in spherical lenses

Professor Wei Zhu. 1. Sampling from the Normal Population

SYSTEMS OF NON-LINEAR EQUATIONS. Introduction Graphical Methods Close Methods Open Methods Polynomial Roots System of Multivariable Equations

Multiple Choice Test. Chapter Adequacy of Models for Regression

Lecture 10: Condensed matter systems

( m is the length of columns of A ) spanned by the columns of A : . Select those columns of B that contain a pivot; say those are Bi

Chapter Linear Regression

= y and Normed Linear Spaces

Triangles Technique for Time and Location Finding of the Lightning Discharge in Spherical Model of the Earth

Tutorial on Strehl ratio, wavefront power series expansion, Zernike polynomials expansion in small aberrated optical systems By Sheng Yuan

Question 1. Typical Cellular System. Some geometry TELE4353. About cellular system. About cellular system (2)

Lecture 7 Diffusion. Our fluid equations that we developed before are: v t v mn t

Sensorless A.C. Drive with Vector Controlled Synchronous Motor

Skin Effect and Formation Damage

Negative Exponent a n = 1 a n, where a 0. Power of a Power Property ( a m ) n = a mn. Rational Exponents =

Chapter 2: Descriptive Statistics

University of Pavia, Pavia, Italy. North Andover MA 01845, USA

Chapter 1 Functions and Graphs

Harmonic Curvatures in Lorentzian Space

Centroids & Moments of Inertia of Beam Sections

ˆ SSE SSE q SST R SST R q R R q R R q

Theory study about quarter-wave-stack dielectric mirrors

Lesson 5. Chapter 7. Wiener Filters. Bengt Mandersson. r k s r x LTH. September Prediction Error Filter PEF (second order) from chapter 4

COORDINATE SYSTEMS, COORDINATE TRANSFORMS, AND APPLICATIONS

Lecturer: Ivan Kassamakov, Docent Assistant: Kalle Hanhijärvi. Course webpage:

General Method for Calculating Chemical Equilibrium Composition

ROOT-LOCUS ANALYSIS. Lecture 11: Root Locus Plot. Consider a general feedback control system with a variable gain K. Y ( s ) ( ) K

APPLICATIONS OF FD APPROXIMATIONS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

1 Solution to Problem 6.40

Fairing of Parametric Quintic Splines

VIII Dynamics of Systems of Particles

Idea is to sample from a different distribution that picks points in important regions of the sample space. Want ( ) ( ) ( ) E f X = f x g x dx

Layered structures: transfer matrix formalism

Multiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades

Phys 2310 Wed. Sept. 7, 2017 Today s Topics

Investigation of Partially Conditional RP Model with Response Error. Ed Stanek

Detection and Estimation Theory

( ) ( ) Last Time. 3-D particle in box: summary. Modified Bohr model. 3-dimensional Hydrogen atom. Orbital magnetic dipole moment

cos kd kd 2 cosθ = π 2 ± nπ d λ cosθ = 1 2 ± n N db

DERIVATION OF THE BASIC LAWS OF GEOMETRIC OPTICS

Chapter 6 Area and Volume

Multivariate Transformation of Variables and Maximum Likelihood Estimation

Non-axial symmetric loading on axial symmetric. Final Report of AFEM

Maximum likelihood estimate of phylogeny. BIOL 495S/ CS 490B/ MATH 490B/ STAT 490B Introduction to Bioinformatics April 24, 2002

Lecture 07: Poles and Zeros

ENGI 4421 Propagation of Error Page 8-01

ENGI 4421 Joint Probability Distributions Page Joint Probability Distributions [Navidi sections 2.5 and 2.6; Devore sections

Chapter 3. Differentiation 3.2 Differentiation Rules for Polynomials, Exponentials, Products and Quotients

Chapter 3. Many-Electron Atoms

Consumer theory. A. The preference ordering B. The feasible set C. The consumption decision. A. The preference ordering. Consumption bundle

d dt d d dt dt Also recall that by Taylor series, / 2 (enables use of sin instead of cos-see p.27 of A&F) dsin

This may involve sweep, revolution, deformation, expansion and forming joints with other curves.

Infinitesimal Automorphisms in the Tangent Bundle of a Riemannian Manifold with Horizontal Lift of Affine Connection

T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, )

REVIEW OF SIMPLE LINEAR REGRESSION SIMPLE LINEAR REGRESSION

Chapter 19 Webassign Help Problems

BENDING OF BEAM. Compressed layer. Elongated. layer. Un-strained. layer. NA= Neutral Axis. Compression. Unchanged. Elongation. Two Dimensional View

Chapter 4 Multiple Random Variables

VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles.

Born-Oppenheimer Approximation. Kaito Takahashi

The Geometric Proof of the Hecke Conjecture

RECAPITULATION & CONDITIONAL PROBABILITY. Number of favourable events n E Total number of elementary events n S

CHAPTER 5 : SERIES. 5.2 The Sum of a Series Sum of Power of n Positive Integers Sum of Series of Partial Fraction Difference Method

Objectives. Learning Outcome. 7.1 Centre of Gravity (C.G.) 7. Statics. Determine the C.G of a lamina (Experimental method)

ESS Line Fitting

Lecture 11: Introduction to nonlinear optics I.

Consider two masses m 1 at x = x 1 and m 2 at x 2.

8.6 Order-Recursive LS s[n]

Midterm Exam 1, section 1 (Solution) Thursday, February hour, 15 minutes

L. Yaroslavsky. Selected Topics in Image Processing Part 1. Imaging transforms in digital computers

Auchmuty High School Mathematics Department Sequences & Series Notes Teacher Version

Reaction Time VS. Drug Percentage Subject Amount of Drug Times % Reaction Time in Seconds 1 Mary John Carl Sara William 5 4

Java Applets / Flash Java Applet vs. Flash

are positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures.

Exam 1. Sept. 22, 8:00-9:30 PM EE 129. Material: Chapters 1-8 Labs 1-3

ETIKA V PROFESII PSYCHOLÓGA

Physics Courseware Electromagnetism

FORMULAE. 8. a 2 + b 2 + c 2 ab bc ca = 1 2 [(a b)2 + (b c) 2 + (c a) 2 ] 10. (a b) 3 = a 3 b 3 3ab (a b) = a 3 3a 2 b + 3ab 2 b 3

Fall 2004/05 Solutions to Assignment 5: The Stationary Phase Method Provided by Mustafa Sabri Kilic. I(x) = e ixt e it5 /5 dt (1) Z J(λ) =

Centers of Gravity - Centroids

THIS PAGE DECLASSIFIED IAW E

Exponential Generating Functions - J. T. Butler

Optical Remote Sensing with DIfferential Absorption Lidar (DIAL)

MEI Structured Mathematics. Module Summary Sheets. Numerical Methods (Version B reference to new book)

Determining the Best Linear Unbiased Predictor of PSU Means with the Data. included with the Random Variables. Ed Stanek

FI 2201 Electromagnetism

A stopping criterion for Richardson s extrapolation scheme. under finite digit arithmetic.

BINOMIAL THEOREM An expression consisting of two terms, connected by + or sign is called a

Kinematics. Redundancy. Task Redundancy. Operational Coordinates. Generalized Coordinates. m task. Manipulator. Operational point

Module Title: Business Mathematics and Statistics 2

BINOMIAL THEOREM NCERT An expression consisting of two terms, connected by + or sign is called a

Rotational Kinetic Energy

Inference for A One Way Factorial Experiment. By Ed Stanek and Elaine Puleo

Photographing a time interval

THE ROYAL STATISTICAL SOCIETY 2016 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 5

Physics 111 Lecture 5 (Walker: 3.3-6) Vectors & Vector Math Motion Vectors Sept. 11, 2009

Suppose we have observed values t 1, t 2, t n of a random variable T.

CH E 374 Computational Methods in Engineering Fall 2007

Chapter 3. Differentiation 3.3 Differentiation Rules

Ideal multigrades with trigonometric coefficients

Transcription:

Py F. Oct., 7 Today Topc Beg Capte 6: Moe o Geometc Optc eadg fo Next Tme

Homewok t Week HW # Homewok t week due Mo., Oct. : Capte 4: #47, 57, 59, 6, 6, 6, 6, 67, 7

Supplemetal: Tck ee ad e Sytem Pcple Plae of a Tck e Defto & Geomety Fo tck le code magay plae fom wc ay dvege/covege to/fom fty Te Nodal pot N, N ae te pot wee tee plae co optcal ax Fot ad Back focal legt ae te dtace fom te vetce V, V of te le. Offax ay pag toug Nodal pot coepod to te Cef ay of a t le Fg. 6. V H ad V H

Supplemetal: Tck ee ad e Sytem Note tat te Nodal pot ca le outde te le f t togly bet. e Make Equato fo a Tck e f Devato mla to tat fo compoud t le but we ad text wll kp: é ù l dl ú û l ê ë Te locato of te pcple plae, : f l d f l d l l l ad 4

Supplemetal: Multple Tck ee Code te two tck lee ow at gt. Fo two tck lee ee text: f f f d f f H H fd f ad: ad H H fd f Note tee a eo te text fo te above equato. 5

6 Supplemetal: Optcal Abeato ee uffe fom abeato due to ue of pecal uface o ax lgt, boke ymmety offax lgt ad dpeo of gla deped o l. ecall ftode teoy we we aume q ~ q Td ode teoy eult we we aume q ~ q q /! Devato extemely tedou wt exteve algeba o we ad text wll kp t: Specal Abeato If we deve te fomula fo efacto at a gle pecal uface wt tdode teoy we get: ú ú û ù ê ê ë é o o o Wee te tem multpled by epeet a coecto to ou ftode appoxmato. Te lage te lage te coecto. Tu we ca top dow te le to educe S.A.

Supplemetal: Optcal Abeato Afte lot of algeba oe ca deve a equato fo te devato of a wavefot emegg fom a pecal uface elatve to a pefect pee ceteed o te mage, te Gaua efeece pee ee Bo & Wolf, Pcple of Optc I pola cood. te devato fom te Gaua efeecepee f : 4 f B Cy co q Dy 4 Te coepodg ay Abeato ae : Dx B q Fy q coq Dy q! ad, Dy B coq Fy co q C D y coq Ey! So fo ay adu, tcke, object dtace, ad ay egt you ca compute te coeffcet. Ey coq Fy coq!

Supplemetal: Optcal Abeato Sedel woked out ow te coeffcet ca be calculated fo eac uface: Sum. te Sedel Tee coeffcetca te be computed ad ae kow a ad uface: So fo eac addtoal teobject ad etace pupl. te ft ufacefom beg te dtace of ad wt ad uface ad tem allowg fo apecal a Wee : Coma, : Dtoto, Feld : Cuvatue of, Atgmatm :, Abeato : Specal 4 d t t d t t b b H F t t b H E t t b H D b H C b B þ ý ü î í ì þ ý ü î í ì þ ý ü î í ì þ ý ü î í ì þ ý ü î í ì å å å å å

Supplemetal: Optcal Abeato Cotollg Specal Abeato SA va ape of te le SA ca be cotolled omewat by bedg a le Focal legt ema almot te ame SA ca be caged Code te ape facto: q Note tat by cagg a le ape q we ca educe but ot elmate SA. Negatve lee ave egatve SA o combato of potve ad egatve lee ae ued to educe SA. 9

Supplemetal: Optcal Abeato Coma eult we mage ae fomed fom offax ay ay efacted toug dffeet aul mag of te le Ca be tougt of a a cage magfcato wt ay dtace fom te le cete. Tdode devato complex but effect foud to deped o, offax agle, ad te le ape q. Alo deped o te object dtace lke SA.

Supplemetal: Optcal Abeato Bot Specal Abeato ad Coma deped o te object dtace a well. T expeed tem of te poto facto. p o o Mmzg Specal Abeato ad Coma va le ape. We ca mmze SA ad Coma of a le fo a gve object dtace. Fo fty ee fgue at gt. Te geeal oluto ca be foud ome text but complex.

eadg t Week By Wededay: F C.4 Y&F Itumet