PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE Form Six AL Physics Optical instruments
|
|
|
- Noel Leslie Howard
- 5 years ago
- Views:
Transcription
1 AL Pysics/pticl instruments/p.1 PLK VICW K.T. CHNG SIXTH FRM CLLEGE Form Six AL Pysics pticl Instruments pticl instruments Mgniying glss Microscope Rercting telescope Grting spectrometer Qulittive understnding o ow opticl instruments work (using simple ry digrms only). Mgniying powers o mgniying glss, microscope nd rercting telescope considered s rtio o visul ngles sutended y te imge nd te oject (s otined rom simple ry digrms). Two-lens type only. Formtion o imge t lest distnce o distinct vision. Two-lens type only. Formtion o imge t ininity. Qulittive explntion o te unctions o te collimtor nd te telescope using ry digrms. Use in simple spectrl nlysis. For te purpose o te prcticl exmintion milirity wit use o concve nd convex mirrors, converging nd diverging lenses, nd prisms is expected ut ull instruction on procedure will e given nd knowledge o prticulr metods in not required. A. Bsic Concept 1. Te norml eye cn ocus on oject t ininity (te r point o te norml eye). In tis cse te eye is relxed or sid to e unccommodted. 2. Te eye cn see n oject in gretest detil wen it is plced t certin distnce rom te eye, known s te lest distnce o distinct vision, wic is out 25 cm, or norml eye. Te point t distnce rom te eye is known s its ner point. 3. Visul ngle:- consider n oject plced some distnce rom te eye, nd suppose θ is te ngle in rdin sutended y it t te eye. Te lengt o te imge ormed y te eye is proportionl to te ngle sutended t te eye y te oject (i.e. te visul ngle). R oject L θ θ imge ** (i) A & B, sme size visul ngle o A - visul ngle o B - As >, B ppers lrger tn A. (ii) P & Q, ctul size o P > ctul size o Q owever, visul ngle sutended y P & Q re te sme ence, P & Q ppers to e te sme size. A B (i) A B P Q P&Q θ (ii)
2 AL Pysics/pticl instruments/p.2 4. Angulr Mgniiction:- - Some instruments (e.g. telescope nd microscope) re designed to increse te visul ngle, so tt te oject viewed cn e mde to pper muc lrger wit teir elp. - Beore tese instruments re used, te visul ngle te oject sutended =. - Ater te instruments re used, te visul ngle te inl imge sutended =. - Te ngulr mgniiction, M, o te instrument is deined s M = / (mgniying power o te instrument) B. Simple Microscope or Mgniying glss 1. A microscope is n instrument used or viewing ner ojects. Wen it is in norml use, te imge ormed y te microscope is t te ner point o te eye. 2. Wit te unided eye, te oject is seen clerest A wen it is plced t te ner point. 3. A converging lens L is used s mgniying glss to view te oject. Te oject is moved until its imge is t te ner point o te eye nd te imge sutends n visul ngle t te eye. L 4. Hence, te ngulr mgniiction o te ' mgniying glss ' I F M ' = = = 5. Te rtio / is equl to te rtio o imge distnce v to te oject distnce u, i.e. v/u By lens ormul, + = 1 u v v u = v 1 ence, ' = v u = 1 = ( + 1) ence, numericlly M = From te ormul, it ollows tt lens o sort ocl lengt is required or ig ngulr mgniiction. ** Wt we ve just consider is te norml use Top point o te mgniying glss, were te imge o imge ormed is t te ner point o te eye nd te eye is ccommodted. In ct te imge my e ormed t oter point nd still tere is te mgniying eect. ne specil cse is tt te F L C
3 AL Pysics/pticl instruments/p.3 imge is ormed t ininity, owever, wic is not norml use o mgniying glss, te eye is undergoing te lest strin nd is unccommodted. In tis cse te oject must e plced t te ocus, F, o te lens. Suppose tt te ocl lengt o te lens is. Te visul ngle o te imge sutended t te eye is ten /. Hence, te ngulr mgniiction, M, is given y M = = = Notice tt te ngulr mgniiction vries etween / nd / + 1 wen te imge is ormed etween ininity nd te ner point. Exmple:- Q.1 Wic o te ollowing two ojects would give rise to te lrger imge on te retin o te umn eye? () A mn o eigt 2.0 m t rnge o 0.20 km, or () te Moon, wic sutends n ngle o 9 mrd t te Ert s surce? Q.2 An oject 10 mm ig is to e viewed troug simple mgniying glss o ocl lengt 50 mm. (1) Imge t ininity () Were sould te oject e plced? () Wt ngle does te inl imge sutend t n eye plced very close to te lens? (c) Wt ngle would te oject sutend t te ner point, 250 mm rom te eye? (d) Wt ngulr mgniiction is otined? (2) Imge t ner point Repet Q.() - (d) o (1). Is tere ny dvntge to e otined in orming te inl imge (i) t ininity, (ii) t te ner point, (iii) closer tn te ner point? iscuss. C. Compound Microscope u ojective eyepiece I 2 L 1 1 v F e I L 2 2
4 AL Pysics/pticl instruments/p.4 1. Te mgniying power o single lens, M, is greter te smller te ocl lengt o te lens. However te ocl lengt o mgniying glss cnnot e too smll, ecuse grinding lens o sort ocl lengt is very diicult. 2. Compound microscope:- - Compound microscope is composed o two seprted lenses. - Te lens nerer to te oject is clled te ojective; te lens troug wic te inl imge is viewed is clled te eyepiece. - Te ojective nd te eyepiece re ot converging nd ot ve smll ocl lengts. 3. Working Principle:- - Wen te microscope is used, te oject is plced t sligtly greter distnce rom te ojective tn its ocl lengt. - A lrge inverted rel imge is ten ormed t I 1. - Te eyepiece is djusted so tt I 1 is nerer to te eyepiece tn te ocus F e nd tus lrge virtul imge is ormed t I 2. - I te inl imge I 2 is ormed t te lest distnce o distinct vision,, rom te eye, te microscope is sid to e in norml use. 4. ngulr mgniiction, M = / were is te visul ngle sutended y te oject t te unided eye. ence M 2 2 = =. Astronomicl Telescope ojective C 1 1 I T F e 2 eyepiece E C top point o inl imge 1. An stronomicl telescope mde rom lenses consists o n ojective o long ocl lengt nd n eyepiece o sort ocl lengt. 2. Te telescope is in norml djustment wen te inl imge is ormed t ininity Te ojective lens collects prllel rys rom te distnt oject so it orms n imge I t its ocus. -As F e nd re t te sme plce. - Te inl imge is ormed t ininity. 4. Te ngulr mgniiction o te telescope M = /
5 AL Pysics/pticl instruments/p.5 Since te telescope lengt is very smll compred wit te distnce o te oject rom eiter lens, we cn tke te ngle sutended t te unided eye y te oject s tt sutended t te ojective lens, s sown. ence M 2 = = For ig mgniiction, te ojective sould ve long ocl lengt, 1, nd te eyepiece sort ocl lengt, ** Eye-Ring o Telescope A E F e B 1 2 eyering = imge o AB in E - Wen oject is viewed y n opticl instrument, only tose rys rom te oject wic re ounded y te edge o te ojective lens enter te instrument. - Wit given ojective, te est position o te eye is one were it collect s muc ligt s possile rom tt pssing troug te ojective. - Tis position is were te imge o te ojective AB in te eyepiece ormed. - Te smll circulr imge is clled te eye-ring. - It is te est position were te eye cn collect te mximum mount o ligt entering te ojective rom outside so tt it s wide ield o view. E. Spectrometer * ligt source collimtor telescope crosswire pltorm 1. Te spectrometer is designed to produce nd mke mesurements on te spectr o ligt sources nd is used wit dirction grting (or prism). 2. Te instrument consists o
6 AL Pysics/pticl instruments/p.6 (i) ixed collimtor wit movle slit o djustle widt (to produce prllel em o ligt rom te source illuminting te slit), (ii) turntle (ving circulr scle) on wic te grting or prism is plced nd (iii) telescope (wit vernier scle) rottle out te sme verticl xis s te turntle.
7 AL Pysics/pticl instruments/p.7 3. Preliminry djustments: (i) Eyepiece - move in te tue contining te cross-wires until te cross-wires re clerly seen. - An imge ormed on te wires will ten e distinct. (ii) Telescope - A distnt oject is viewed troug te telescope nd te distnce o te ojective rom te cross-wire eyepiece djusted y tum-screw until tere is no prllx etween te imge o te distnt oject nd te cross-wires. - Prllel rys entering te telescope re now rougt to ocus t te cross-wires. (iii) Collimtor - Te telescope is turned into line wit te collimtor, nd te slit, illuminted wit sodium ligt, is moved in or out o te collimtor tue until tere is no prllx etween te imge o te slit nd te cross-wires. - Te slit is t te principl ocus o te collimtor lens wic is producing prllel em. (iv)levelling te tle. 4. Appliction: - mesurement o te wvelengt (wit dirction grting) - Simple spectr nlysis (wit dirction grting) - mesurement o te rerctive index o glss prism
I N V E S T I C E D O R O Z V O J E V Z D Ě L Á V Á N Í
GEOMETRICAL OPTICS 1. Mirrors I N V E S T I C E D O R O Z V O J E V Z D Ě L Á V Á N Í their unction is bsed on the lw o relection types : plne curved relecting surces: ordinry metl lyer covered by glss
OPTICAL INSTRUMENTS CHAPTER 19
CHAPTER 9 OPTICAL INSTRUMENTS 9. THE EYE Opticl instruments re used primrily to ssist the eye in viewing n object. Let us first discuss in brief the construction of humn eye nd the mechnism by which we
Chapter 2 Differentiation
Cpter Differentition. Introduction In its initil stges differentition is lrgely mtter of finding limiting vlues, wen te vribles ( δ ) pproces zero, nd to begin tis cpter few emples will be tken. Emple..:
A P P E N D I X POWERS OF TEN AND SCIENTIFIC NOTATION A P P E N D I X SIGNIFICANT FIGURES
A POWERS OF TEN AND SCIENTIFIC NOTATION In science, very lrge nd very smll deciml numbers re conveniently expressed in terms of powers of ten, some of wic re listed below: 0 3 0 0 0 000 0 3 0 0 0 0.00
Trigonometric Functions
Exercise. Degrees nd Rdins Chpter Trigonometric Functions EXERCISE. Degrees nd Rdins 4. Since 45 corresponds to rdin mesure of π/4 rd, we hve: 90 = 45 corresponds to π/4 or π/ rd. 5 = 7 45 corresponds
Kiel Probes. General Information
Kiel s Generl Informtion Aerodynmic Properties Kiel probes re used to mesure totl pressure in fluid strem were te direction of flow is unknown or vries wit operting conditions. Teir correction fctor is
Data Provided: A formula sheet and table of physical constants is attached to this paper.
PHY15-B PHY47 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 009-010 ASTRONOMY DEPARTMENT
Section 4.7 Inverse Trigonometric Functions
Section 7 Inverse Trigonometric Functions 89 9 Domin: 0, q Rnge: -q, q Zeros t n, n nonnegtive integer 9 Domin: -q, 0 0, q Rnge: -q, q Zeros t, n non-zero integer Note: te gr lso suggests n te end-bevior
Optical Imaging. Optical Imaging
Opticl Imgig Mirror Lee Imgig Itrumet eye cmer microcope telecope... imgig Wve Optic Opticl Imgig relectio or rerctio c crete imge o oject ielly, ec oject poit mp to imge poit exmple: urce o till lke relectio:
Topic 6b Finite Difference Approximations
/8/8 Course Instructor Dr. Rymond C. Rump Oice: A 7 Pone: (95) 747 6958 E Mil: rcrump@utep.edu Topic 6b Finite Dierence Approximtions EE 486/5 Computtionl Metods in EE Outline Wt re inite dierence pproximtions?
8Similarity ONLINE PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8.4 re nd volume scle fctors 8. Review Plese refer to the Resources t in the Prelims section of your eookplus for comprehensive step-y-step
Lecture 10. Lecture 10
Lecture 0 Telescope [Reading assignment: Hect 5.7.4, 5.7.7] A telescope enlarges te apparent size o a distant object so tat te image subtends a larger angle (rom te eye) tan does te object. Te telescope
8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8. re nd volume scle fctors 8. Review U N O R R E TE D P G E PR O O FS 8.1 Kick off with S Plese refer to the Resources t in the Prelims
Use of Trigonometric Functions
Unit 03 Use of Trigonometric Functions 1. Introduction Lerning Ojectives of tis UNIT 1. Lern ow te trigonometric functions re relted to te rtios of sides of rigt ngle tringle. 2. Be le to determine te
PKK Energy chains. PKK 320 / 200 x 2340 / 200; 5Pz, 1PT55
Energy cins Te order for plstic energy cin sould contin te following dt: Type / dius x Lengt / Widt "Arrngement"; Seprtor rrngement 1 3 Type selection is in ccordnce wit dimeter nd quntity of te lines
interatomic distance
Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule
Chapter 2. Numerical Integration also called quadrature. 2.2 Trapezoidal Rule. 2.1 A basic principle Extending the Trapezoidal Rule DRAWINGS
S Cpter Numericl Integrtion lso clled qudrture Te gol of numericl integrtion is to pproximte numericlly. f(x)dx Tis is useful for difficult integrls like sin(x) ; sin(x ); x + x 4 Or worse still for multiple-dimensionl
CLASS XII PHYSICS. (a) 30 cm, 60 cm (b) 20 cm, 30 cm (c) 15 cm, 20 cm (d) 12 cm, 15 cm. where
PHYSICS combintion o two thin lenses with ocl lengths n respectively orms n imge o istnt object t istnce cm when lenses re in contct. The position o this imge shits by cm towrs the combintion when two
DIFFRACTION OF LIGHT
DIFFRACTION OF LIGHT The phenomenon of bending of light round the edges of obstcles or nrrow slits nd hence its encrochment into the region of geometricl shdow is known s diffrction. P Frunhofer versus
HYPERBOLA. AIEEE Syllabus. Total No. of questions in Ellipse are: Solved examples Level # Level # Level # 3..
HYPERBOLA AIEEE Sllus. Stndrd eqution nd definitions. Conjugte Hperol. Prmetric eqution of te Hperol. Position of point P(, ) wit respect to Hperol 5. Line nd Hperol 6. Eqution of te Tngent Totl No. of
Math 20C Multivariable Calculus Lecture 5 1. Lines and planes. Equations of lines (Vector, parametric, and symmetric eqs.). Equations of lines
Mt 2C Multivrible Clculus Lecture 5 1 Lines nd plnes Slide 1 Equtions of lines (Vector, prmetric, nd symmetric eqs.). Equtions of plnes. Distnce from point to plne. Equtions of lines Slide 2 Definition
Conductance from Transmission Probability
Conductance rom Transmission Probability Kelly Ceung Department o Pysics & Astronomy University o Britis Columbia Vancouver, BC. Canada, V6T1Z1 (Dated: November 5, 005). ntroduction For large conductors,
The Properties of Stars
10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product
Part I: Basic Concepts of Thermodynamics
Prt I: Bsic Concepts o Thermodynmics Lecture 4: Kinetic Theory o Gses Kinetic Theory or rel gses 4-1 Kinetic Theory or rel gses Recll tht or rel gses: (i The volume occupied by the molecules under ordinry
Measuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
Logarithms and Exponential Functions. Gerda de Vries & John S. Macnab. match as necessary, or to work these results into other lessons.
Logritms nd Eponentil Functions Gerd de Vries & Jon S. Mcn It is epected tt students re lred fmilir wit tis mteril. We include it ere for completeness. Te tree lessons given ere re ver sort. Te tecer is
0, i.e. forces act in the same direction. , i.e. forces act in opposite direction. The resultant of two forces is closer to the larger force.
Sttics. Introduction. Sttics is tt brnc of mecnics wic dels wit te study of te system of forces in equilibrium. Mtter : Mtter is nyting wic cn be perceived by our senses of wic cn exert, or be cted on,
1 Review: Volumes of Solids (Stewart )
Lecture : Some Bic Appliction of Te Integrl (Stewrt 6.,6.,.,.) ul Krin eview: Volume of Solid (Stewrt 6.-6.) ecll: we d provided two metod for determining te volume of olid of revolution. Te rt w by dic
KEY CONCEPTS. satisfies the differential equation da. = 0. Note : If F (x) is any integral of f (x) then, x a
KEY CONCEPTS THINGS TO REMEMBER :. The re ounded y the curve y = f(), the -is nd the ordintes t = & = is given y, A = f () d = y d.. If the re is elow the is then A is negtive. The convention is to consider
Quantum transport (Read Kittel, 8th ed., pp )
Quntum trnsport (Red Kittel, 8t ed., pp. 533-554) Wen we ve structure in wic mny collisions tke plce s crriers trnsport cross it, te quntum mecnicl pse of te electron wvefunctions is essentilly rndomized,
Consider a function f we ll specify which assumptions we need to make about it in a minute. Let us reformulate the integral. 1 f(x) dx.
Capter 2 Integrals as sums and derivatives as differences We now switc to te simplest metods for integrating or differentiating a function from its function samples. A careful study of Taylor expansions
Lecture Note 4: Numerical differentiation and integration. Xiaoqun Zhang Shanghai Jiao Tong University
Lecture Note 4: Numericl differentition nd integrtion Xioqun Zng Sngi Jio Tong University Lst updted: November, 0 Numericl Anlysis. Numericl differentition.. Introduction Find n pproximtion of f (x 0 ),
Pythagorean Theorem and Trigonometry
Ptgoren Teorem nd Trigonometr Te Ptgoren Teorem is nient, well-known, nd importnt. It s lrge numer of different proofs, inluding one disovered merin President Jmes. Grfield. Te we site ttp://www.ut-te-knot.org/ptgors/inde.stml
Average Rate of Change (AROC) The average rate of change of y over an interval is equal to change in
Averge Rte o Cnge AROC Te verge rte o cnge o y over n intervl is equl to b b y y cngein y cnge in. Emple: Find te verge rte o cnge o te unction wit rule 5 s cnges rom to 5. 4 4 6 5 4 0 0 5 5 5 5 & 4 5
SSC MAINS (MATHS) MOCK TEST-1 (SOLUTION)
007, OUTRM LINES, ST FLOOR, OPPOSITE MUKHERJEE NGR POLICE STTION, DELHI-09 SSC MINS (MTHS) MOCK TEST- (SOLUTION). (B) Order of surds re,,. LCM of, nd is. So, convert ec surd into surd of order 0 0 0 6
UNIT #6 EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS
Answer Key Name: Date: UNIT # EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS Part I Questions. Te epression 0 can be simpliied to () () 0 0. Wic o te ollowing is equivalent to () () 8 8? 8.
On the diagram below the displacement is represented by the directed line segment OA.
Vectors Sclrs nd Vectors A vector is quntity tht hs mgnitude nd direction. One exmple of vector is velocity. The velocity of n oject is determined y the mgnitude(speed) nd direction of trvel. Other exmples
fractions Let s Learn to
5 simple lgebric frctions corne lens pupil retin Norml vision light focused on the retin concve lens Shortsightedness (myopi) light focused in front of the retin Corrected myopi light focused on the retin
Phys-272 Lecture 25. Geometric Optics Lenses
Phy-7 Lecture 5 Geometric Optic Lee h h Rerctio o Sphericl Surce θ β φ φ α θ + + ; θ θ θ θ i i ( )φ β α + δ φ δ β δ α + R h h h t ; t ; t R h h h φ β α ; ; R + Rerctio o Sphericl Surce R + Mgiictio θ θ
Continuous Random Variable X:
Continuous Rndom Vrile : The continuous rndom vrile hs its vlues in n intervl, nd it hs proility distriution unction or proility density unction p.d. stisies:, 0 & d Which does men tht the totl re under
MAT 1275: Introduction to Mathematical Analysis
1 MT 1275: Intrdutin t Mtemtil nlysis Dr Rzenlyum Slving Olique Tringles Lw f Sines Olique tringles tringles tt re nt neessry rigt tringles We re ging t slve tem It mens t find its si elements sides nd
CONIC SECTIONS. Chapter 11
CONIC SECTIONS Chpter. Overview.. Sections of cone Let l e fied verticl line nd m e nother line intersecting it t fied point V nd inclined to it t n ngle α (Fig..). Fig.. Suppose we rotte the line m round
A Discussion on Formulas of Seismic Hydrodynamic Pressure
Interntionl Forum on Energy Environment Science nd Mterils (IFEESM 2017) A Discussion on Formuls of Seismic Hydrodynmic Pressure Liu Himing1 To Xixin2 1 Cin Mercnts Congqing Communiction Reserc & Design
The Trapezoidal Rule
_.qd // : PM Pge 9 SECTION. Numericl Integrtion 9 f Section. The re of the region cn e pproimted using four trpezoids. Figure. = f( ) f( ) n The re of the first trpezoid is f f n. Figure. = Numericl Integrtion
GEOMETRY Properties of lines
www.sscexmtuto.com GEOMETRY Popeties of lines Intesecting Lines nd ngles If two lines intesect t point, ten opposite ngles e clled veticl ngles nd tey ve te sme mesue. Pependicul Lines n ngle tt mesues
Thomas Whitham Sixth Form
Thoms Whithm Sith Form Pure Mthemtics Unit C Alger Trigonometry Geometry Clculus Vectors Trigonometry Compound ngle formule sin sin cos cos Pge A B sin Acos B cos Asin B A B sin Acos B cos Asin B A B cos
This chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2
1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion
Simulation of Eclipsing Binary Star Systems. Abstract
Simultion of Eclipsing Binry Str Systems Boris Yim 1, Kenny Chn 1, Rphel Hui 1 Wh Yn College Kowloon Diocesn Boys School Abstrct This report briefly introduces the informtion on eclipsing binry str systems.
Review of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
*GMT41* *24GMT4101* Mathematics. Unit T4 (With calculator) Higher Tier [GMT41] WEDNESDAY 6 JUNE 9.15 am am. 2 hours.
![*GMT41* *24GMT4101* Mathematics. Unit T4 (With calculator) Higher Tier [GMT41] WEDNESDAY 6 JUNE 9.15 am am. 2 hours.](/thumbs/85/91904760.jpg "*GMT41* *24GMT4101* Mathematics. Unit T4 (With calculator) Higher Tier [GMT41] WEDNESDAY 6 JUNE 9.15 am am. 2 hours.")
entre Numer ndidte Numer Mtemtics Generl ertificte Secondry Eduction 0 Unit T4 (Wit clcultor) Higer Tier [GMT4] WEDNESDAY 6 JUNE 9.5 m.5 m *GMT4* *GMT4* TIME ours. INSTRUTIONS TO ANDIDATES Write your entre
Continuity and Differentiability
Continuity and Dierentiability Tis capter requires a good understanding o its. Te concepts o continuity and dierentiability are more or less obvious etensions o te concept o its. Section - INTRODUCTION
A = h w (1) Error Analysis Physics 141
Introduction In all brances of pysical science and engineering one deals constantly wit numbers wic results more or less directly from experimental observations. Experimental observations always ave inaccuracies.
Date Lesson Text TOPIC Homework. Solving for Obtuse Angles QUIZ ( ) More Trig Word Problems QUIZ ( )
UNIT 5 TRIGONOMETRI RTIOS Dte Lesson Text TOPI Homework pr. 4 5.1 (48) Trigonometry Review WS 5.1 # 3 5, 9 11, (1, 13)doso pr. 6 5. (49) Relted ngles omplete lesson shell & WS 5. pr. 30 5.3 (50) 5.3 5.4
Applications of Bernoulli s theorem. Lecture - 7
Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.
Homework Assignment 6 Solution Set
Homework Assignment 6 Solution Set PHYCS 440 Mrch, 004 Prolem (Griffiths 4.6 One wy to find the energy is to find the E nd D fields everywhere nd then integrte the energy density for those fields. We know
Derivatives, Finding Roots, Interpolating and Integration
Derivtives, Finding Roots, Interpolting nd Integrtion Doing Numericl Derivtives Altoug tking derivtives is very esy opertion for ll of you, tere re situtions were it must e done numericlly. For exmple,
Numerical Integration Problems
Integrtion COS 33 Nuericl Integrtion Proles Bsic D nuericl integrtion Given ility to evlute or ny, ind Gol: est ccurcy wit ewest sples Clssic prole even nlytic unctions not necessrily integrle in closed
Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis
Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source
Time in Seconds Speed in ft/sec (a) Sketch a possible graph for this function.
4. Are under Curve A cr is trveling so tht its speed is never decresing during 1-second intervl. The speed t vrious moments in time is listed in the tle elow. Time in Seconds 3 6 9 1 Speed in t/sec 3 37
β 1 = 2 π and the path length difference is δ 1 = λ. The small angle approximation gives us y 1 L = tanθ 1 θ 1 sin θ 1 = δ 1 y 1
rgsdle (zdr8) HW13 ditmire (58335) 1 This print-out should hve 1 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. 001 (prt 1 of ) 10.0 points
12 Basic Integration in R
14.102, Mt for Economists Fll 2004 Lecture Notes, 10/14/2004 Tese notes re primrily bsed on tose written by Andrei Bremzen for 14.102 in 2002/3, nd by Mrek Pyci for te MIT Mt Cmp in 2003/4. I ve mde only
THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES
THREE-DIMENSIONAL KINEMATICS OF RIGID BODIES 1. TRANSLATION Figure shows rigid body trnslting in three-dimensionl spce. Any two points in the body, such s A nd B, will move long prllel stright lines if
Fundamental Theorem of Calculus
Funmentl Teorem of Clculus Liming Png 1 Sttement of te Teorem Te funmentl Teorem of Clculus is one of te most importnt teorems in te istory of mtemtics, wic ws first iscovere by Newton n Leibniz inepenently.
IMPULSE-BASED SIMULATION OF INEXTENSIBLE CLOTH
IMPULSE-BASED SIMULATION OF INEXTENSIBLE CLOTH Jn Bender nd Dniel Byer Institut für Betries- und Dilogssysteme Universität Krlsrue Am Fsnengrten 5 76128 Krlsrue Germny ABSTRACT In tis pper n impulse-sed
Flexible Beam. Objectives
Flexile Bem Ojectives The ojective of this l is to lern out the chllenges posed y resonnces in feedck systems. An intuitive understnding will e gined through the mnul control of flexile em resemling lrge
Alg. Sheet (1) Department : Math Form : 3 rd prep. Sheet
Ciro Governorte Nozh Directorte of Eduction Nozh Lnguge Schools Ismili Rod Deprtment : Mth Form : rd prep. Sheet Alg. Sheet () [] Find the vlues of nd in ech of the following if : ) (, ) ( -5, 9 ) ) (,
Laser Safety. Safe clinical application of laser radiation. Frits F.M. de Mul ffmdemul(at)gmail.
Lser Sfety Sfe clinicl ppliction of lser rdition Frits F.M. de Mul 2016 www.demul.net/frits emil: ffmdemul(t)gmil.com Lser Sfety Sfe clinicl ppliction of lser rdition Contents: 1. Physicl / mthemticl explntion
Section 2.1 Special Right Triangles
Se..1 Speil Rigt Tringles 49 Te --90 Tringle Setion.1 Speil Rigt Tringles Te --90 tringle (or just 0-60-90) is so nme euse of its ngle mesures. Te lengts of te sies, toug, ve very speifi pttern to tem
PKK Energy chains. PKK 320 / 200 x 2340 / 200; 5Pz, 1PT55. The order for a plastic energy chain PKK should contain the following data:
Energ cins Te order for plstic energ cin sould contin te following dt: 1 Tpe / dius Lengt / Widt "Arrngement"; Seprtor rrngement 2 3 Emple: Tpe selection is in ccordnce wit dimeter nd quntit of te lines
2. VECTORS AND MATRICES IN 3 DIMENSIONS
2 VECTORS AND MATRICES IN 3 DIMENSIONS 21 Extending the Theory of 2-dimensionl Vectors x A point in 3-dimensionl spce cn e represented y column vector of the form y z z-xis y-xis z x y x-xis Most of the
Motion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons
n eperiment of the Electron topic Motion of Electrons in Electric nd Mgnetic Fields & Mesurement of the Chrge to Mss Rtio of Electrons Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1.
nr 2 nr 4 Correct Answer 1 Explanation If mirror is rotated by anglethan beeping incident ray fixed, reflected ray rotates by 2 Option 4
Q. No. A small plane mirror is placed at the centero a spherical screen o radius R. A beam o light is alling on the mirror. I the mirror makes n revolution per second, the speed o light on the screen ater
KINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011
Physics 9 Fll 0 Homework - s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you
Chapter Runge-Kutta 2nd Order Method for Ordinary Differential Equations
Cter. Runge-Kutt nd Order Metod or Ordnr Derentl Eutons Ater redng ts cter ou sould be ble to:. understnd te Runge-Kutt nd order metod or ordnr derentl eutons nd ow to use t to solve roblems. Wt s te Runge-Kutt
Chapter 23. Geometric Optics
Cpter 23 Geometric Optic Ligt Wt i ligt? Wve or prticle? ot Geometric optic: ligt trvel i trigt-lie pt clled ry Ti i true if typicl ditce re muc lrger t te wvelegt Geometric Optic 2 Wt it i out eome ddreed
Precalculus Notes: Unit 6 Law of Sines & Cosines, Vectors, & Complex Numbers. A can be rewritten as
Dte: 6.1 Lw of Sines Syllus Ojetie: 3.5 Te student will sole pplition prolems inoling tringles (Lw of Sines). Deriing te Lw of Sines: Consider te two tringles. C C In te ute tringle, sin In te otuse tringle,
a * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2
18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions
BRIEF NOTES ADDITIONAL MATHEMATICS FORM
BRIEF NOTES ADDITIONAL MATHEMATICS FORM CHAPTER : FUNCTION. : + is the object, + is the imge : + cn be written s () = +. To ind the imge or mens () = + = Imge or is. Find the object or 8 mens () = 8 wht
Chapter 2 Limits and Continuity. Section 2.1 Rates of Change and Limits (pp ) Section Quick Review 2.1
Section. 6. (a) N(t) t (b) days: 6 guppies week: 7 guppies (c) Nt () t t t ln ln t ln ln ln t 8. 968 Tere will be guppies ater ln 8.968 days, or ater nearly 9 days. (d) Because it suggests te number o
Purpose of the experiment
Newton s Lws II PES 6 Advnced Physics Lb I Purpose of the experiment Exmine two cses using Newton s Lws. Sttic ( = 0) Dynmic ( 0) fyi fyi Did you know tht the longest recorded flight of chicken is thirteen
NOT TO SCALE. We can make use of the small angle approximations: if θ á 1 (and is expressed in RADIANS), then
3. Stellr Prllx y terrestril stndrds, the strs re extremely distnt: the nerest, Proxim Centuri, is 4.24 light yers (~ 10 13 km) wy. This mens tht their prllx is extremely smll. Prllx is the pprent shifting
10. AREAS BETWEEN CURVES
. AREAS BETWEEN CURVES.. Ares etween curves So res ove the x-xis re positive nd res elow re negtive, right? Wrong! We lied! Well, when you first lern out integrtion it s convenient fiction tht s true in
Columns and Stability
ARCH 331 Note Set 1. Su01n Columns nd Stilit Nottion: A = nme or re A36 = designtion o steel grde = nme or width C = smol or compression C c = column slenderness clssiiction constnt or steel column design
1 ELEMENTARY ALGEBRA and GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE
ELEMENTARY ALGEBRA nd GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the exmples, work the prolems, then check your nswers t the end of ech topic. If you don t get the nswer given, check
Lesson-5 ELLIPSE 2 1 = 0
Lesson-5 ELLIPSE. An ellipse is the locus of point which moves in plne such tht its distnce from fied point (known s the focus) is e (< ), times its distnce from fied stright line (known s the directri).
1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?
Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt
Analytically, vectors will be represented by lowercase bold-face Latin letters, e.g. a, r, q.
1.1 Vector Alger 1.1.1 Sclrs A physicl quntity which is completely descried y single rel numer is clled sclr. Physiclly, it is something which hs mgnitude, nd is completely descried y this mgnitude. Exmples
2016 PRELIM 2 PAPER 2 MARK SCHEME
06 River Valley Hig Scool Prelim Paper Mark Sceme 06 PRELIM PAPER MARK SCHEME (a) V 5.00 X 85. 9V 3 I.7 0 X V I X V I X 0.03 0. 85.9 5.00.7 X 48.3 00 X X 900 00 [A0] Anomalous data can be identified. Systematic
Farey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University
U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions
Krazy Katt, the mechanical cat
Krazy Katt, te mecanical cat Te cat rigting relex is a cat's innate ability to orient itsel as it alls in order to land on its eet. Te rigting relex begins to appear at 3 4 weeks o age, and is perected
Chapter 36. a λ 2 2. (minima-dark fringes) Diffraction and the Wave Theory of Light. Diffraction by a Single Slit: Locating the Minima, Cont'd
Chpter 36 Diffrction In Chpter 35, we sw how light bes pssing through ifferent slits cn interfere with ech other n how be fter pssing through single slit flres-iffrcts- in Young's experient. Diffrction
at its center, then the measure of this angle in radians (abbreviated rad) is the length of the arc that subtends the angle.
Notes 6 ngle Mesure Definition of Rdin If circle of rdius is drwn with the vertex of n ngle Mesure: t its center, then the mesure of this ngle in rdins (revited rd) is the length of the rc tht sutends
Taylor Series and the Mean Value Theorem of Derivatives
1 - Taylor Series and te Mean Value Teorem o Derivatives Te numerical solution o engineering and scientiic problems described by matematical models oten requires solving dierential equations. Dierential
COSC 3361 Numerical Analysis I Numerical Integration and Differentiation (III) - Gauss Quadrature and Adaptive Quadrature
COSC 336 Numericl Anlysis I Numericl Integrtion nd Dierentition III - Guss Qudrture nd Adptive Qudrture Edgr Griel Fll 5 COSC 336 Numericl Anlysis I Edgr Griel Summry o the lst lecture I For pproximting
MAT 1800 FINAL EXAM HOMEWORK
MAT 800 FINAL EXAM HOMEWORK Read te directions to eac problem careully ALL WORK MUST BE SHOWN DO NOT USE A CALCULATOR Problems come rom old inal eams (SS4, W4, F, SS, W) Solving Equations: Let 5 Find all
Exponentials and Logarithms Review Part 2: Exponentials
Eponentials and Logaritms Review Part : Eponentials Notice te difference etween te functions: g( ) and f ( ) In te function g( ), te variale is te ase and te eponent is a constant. Tis is called a power
Wave Phenomena Physics 15c
Wve Phenomen Physics 15c Lecture Diffrction (H&L Chpter 11) Wht We Did Lst Time! Studied interference! or more wves overlp " Amplitudes dd up " Intensity = (mplitude) does not dd up! Thin-film interference!
Chapter 10 Light- Reflectiion & Refraction
Capter 0 Ligt- Relectiion & Reraction Intext Questions On Page 68 Question : Deine te principal ocus o a concae irror. Principal ocus o te concae irror: A point on principal axis on wic parallel ligt rays
INTRODUCTION AND MATHEMATICAL CONCEPTS
Capter 1 INTRODUCTION ND MTHEMTICL CONCEPTS PREVIEW Tis capter introduces you to te basic matematical tools for doing pysics. You will study units and converting between units, te trigonometric relationsips