Light. Light is a Particle. Light can travel through the vacuum of space, but waves can t travel in a vacuum. So light must be a particle!
|
|
- Randolph Hubbard
- 6 years ago
- Views:
Transcription
1 Light Light is Wve Light is refrted in lenses. Light diffrting round two fingers (look lose) uses s of drkness: destrutive interferene. Light must e wve! Light is Prtile Light n trvel through the vuum of spe, ut wves n t trvel in vuum. So light must e prtile! Light is Both This ontrdition perplexed sientists for mny, mny yers, ut the evidene must e elieved: light is oth wve nd prtile. Pkets of light we ll photons. Speed of Light: 3 x 10 8 m/se Origins of Light nd Color Sound is fst: 340 m/se, ut light is fster: 3 x 10 8 m/se! Tht s 3 with 8 zeroes or 300,000,000 m/se. Light n irle the erth 27 times in one seond! Sientists now elieve tht nothing n go fster thn light. The speed of light is the ultimte speed limit. Photons (light) ome from eletrons flling from high eletron orits to low orits. These orits re lso lled energy levels. 8p 10 Energy n rise n eletron to higher energy level. energy in 8p 10 When the eletron flls k, photon is given off: light! photon out (lue) Beuse eh element hs different numer of protons, eh element hs slightly different eletron energy levels nd gives off different olors. From their olors we n tell the hemil mkeup of strs. The sky is lue euse oxygen toms give off lue photons. Visile Light White light in Prism Wht we ll visile light is mde up of mny different olors. Eh olor hs different wvelength nd different frequeny. Rinow out Red Ornge Yellow Green Blue Indigo Violet A prism uses refrtion to seprte the different wvelengths (olors) of visile light. The first letters spell: ROY G BIV Colors hve Different Energies You know tht different olor flmes give off different mounts of het. Red flmes re the oolest nd lue flmes re the hottest. As you move from Red to Blue, light GAINS energy. White light is mde up of ll olors. Tht is why white flme is the hottest! EM Spetrum Visile Light is very smll prt of the entire Eletromgneti (EM) Spetrum. Rdio wves Mirowves Infrred Visile Ultr- X-rys Gmm Light violet Rys Low Energy Low Frequeny Long Wvelength wht we n see Red Ornge Yellow Green Blue Indigo Violet High Energy High Frequeny Short Wvelength Rdio wves used to trnsmit rdio nd television signls. Wvelengths rnge from hundreds of meters to less thn entimeter. This is why rdio towers hve to e so tll. Mirowves used to ook food nd y ell phones. Wvelengths rnge from 30 m to 1 mm. Infrred (invisile het) 1 mm to 700 nnometers (700 illionths of meter). Visile (white) light from 700 to 400 nnometers. stephenmurry.om Ultrviolet light invisile wvelengths from 400 nnometers to 10 nnometers. Prt of sunlight urns your skin nd n use ner. The ozone lyer protets us from most of the sun s ultrviolet light. X-rys Used in mediine nd industry. Wvelengths re from 10 nnometers to.01 nnometers (10 trillionth of meter). Gmm rys the most powerful nd dngerous form of rdition. Wvelengths less thn.01 nnometers. Emitted y nuler retions, they n rek hemil nd nuler onds.
2 1. Photon 2. 3 x 10 8 m/se 3. Prism 4. Light A. The fstest speed in the universe: the speed of light. B. An orit of eletrons. To move from low to high requires energy. C. All light: visile nd invisile. D. Used to seprte white light into its olors. 1. Rdio wves 2. Infrred 3. Ultrviolet 4. X-rys A. Eletromgneti wves we feel s het. B. Dngerous EM wves tht hve very high energy nd ome from nuler retions. C. EM wves tht hve very low energy nd long wvelengths. D. EM wves tht n pss through skin nd hve short wvelengths. 5. EM Spetrum 6. Energy Level E. A single prtile or pket of light. F. A wve tht n trvel through vuum. 5. Gmm rys 6. Mirowves E. EM wves with more energy thn visile light nd n use sunurns. F. Long wvelengths; used in ell phones. Is light wve or prtile. Prove your nswer: Put these three in order from slowest to fstest: Light wves; sound wves; wter wves. Where does light ome from? Put these from shortest to longest wvelengths Rdio wves Ultrviolet X-rys Visile Mirowves Why do we see lightening nd her the thunder few seonds lter? Put these from lest energy to most energy. Rdio wves Ultrviolet X-rys Visile Mirowves Find the period of 10 Hz wve. If wve s fifth hrmoni hs frequeny of 35 Hz, wht is its nturl frequeny nd wht is the frequeny of H 3? A wve hs these hrteristis: 25 Hz nd 8 m. Find speed. Find its period: A sound hnges from 25 db to 5 db. How do we her the hnge? You her thunder 3 seonds fter you see the lightening. How fr wy is the storm? Wht hrmoni is this? Mrk the nodes nd nti-nodes. Mrk one wvelength on the hrmoni. Cn humns her this frequeny? You re in onert hll nd yell up to the eiling. It tkes 1 seond for the eho to ome k to you. How high is the eiling? Find the fundmentl frequeny: 3rd hrmoni frequeny: 40 Hz stephenmurry.om
3 Optis The Study of Light Refrtion Light slows down in glss. Here the left side slows down first using the light to end to the left. GLASS Light speeds up in ir. Here the left side speeds up first using the light to end to the right. Light refrts when pssing etween two sustnes t n. light ry The right side hits first nd slows down: ends to the right. GLASS GLASS If the light does not enter t n, it does not end. Refletion Norml n imginry 90 o (perpendiulr to surfe. Angle of Inidene the etween the inoming ry nd the norml. Angle of Refletion the etween the outgoing ry nd the norml. Light reflets t shiny oundries we ll mirrors. norml (90 o to mirror) of inidene 60 o 60 o of refletion MIRROR of inidene = of refletion Fous Every lens or mirror hs ple where ll of the prllel rys will meet. This is known s the fol point or fous. fol point or fous Stright Lines Mirrors nd lenses n mke things look igger or smller euse our eyes lwys think tht light omes from stright s, even if they hve een refrted or refleted. ir wter imge Ojet vs. Imge The is wht you re looking t: the tul thing. The imge is wht you think you see: the enlrged, redued, or moved. Lenses Lenses work y refrtion, y the light ending when moving etween two sustnes. A onvex lens mgnifies. Lenses nd mirrors work opposite of eh other. If onve lens redues, then onve mirror mgnifies. Conve or Convex onve Conve looks like the sides hve ved in. Mirrors Mirrors work y refletion, y the ounding of light off of shiny surfe. Imges in mirrors lwys look twie s fr wy s the. Ex. An imge looks 20 m wy in mirror. How fr wy is the? Answer: Hlf the distne: 10 meters. A onvex mirror redues. imge onvex lens A onvex lens is onvergent the light rys ome together. imge A onve lens redues. onve lens A onve lens is divergent the light rys spred prt. Convex the middle is igger thn the ends. onvex Optil Systems Mirosopes nd telesopes re optil systems tht use omintions of lenses nd/or mirrors to mgnify light. Comining optil devies llows us to see very distnt or very smll s. imge onvex mirror A onvex mirror is divergent. A onve mirror mgnifies imge onve mirror A onve mirror is onvergent.
4 Misellneous Light Topis Totl Internl Refletion Light usully psses through ler oundries, ut if it strikes t n greter thn the ritil will sty inside the medium (glss, ir, et.). Totl internl refletion is when ll the light is refleted k inside the medium. The ritil for glss is out 41 o. glss tue Totl Internl Refletion: light pst the ritil nnot espe. Fier Optis Fier optis work y totl internl refletion. Fier optis pss light through flexile glss or plsti tues (lled fiers). These tues n e ent llowing light to e direted where it is wnted. Fier opti sopes n see round orners. Fier opti les rry muh of the ommunitions of our world (Internet nd phone) euse it trvels t the speed of light. Inndesent Light Inndesent (norml )light uls mke light y very high het. The filment glows right when enough eletriity flows through it. Inndesent light is very ineffiient euse most of the energy is lost s het. filment Inndesent Lightul Types of Lights Fluoresent Lightul Fluoresent lights re four times more effiient thn inndesent uls. 3/4 of the energy of n inndesent ul is lost to het. Fluoresent Light In fluoresent light uls eletriity exites gs inside, emitting mostly UV light. The white oting on the outside of the ul sors the UV light nd emits white light. Light is trnsverse wve (virting 90 o to the diretion of motion). Norml light is hoti, with trnsverse wves moving in ll diretions. A polrizer llows only light going one diretion to go through (like om). norml light polrizer Polriztion polrized light 2nd polrizer turned 90 o no light gets through 2nd polrizer Only light in one diretion n get through polrizer. Two polrizers turned 90 o n nel out ll light. Polriztion lso llows smll omputers nd lultors sreens to mke letters nd imges. Polriztion is used in some sunglsses to redue glre. Glow-in-the-Drk Lsers LASER Light Amplifition y Stimulted Emission of Rdition Glow-in-the-drk (photoluminesent) s ontin the element phosphorous. When phosphorous eletrons re energized, they ome down few t time, giving off light over time. When ll the eletrons hve fllen the phosphorous goes drk. Visile light rehrges them (rising them up) so tht they give off light gin. How Lsers Work Lsers give off light of one prtiulr wvelength. This omes from foring sustne (usully gs) to give off light. This light ounes k nd forth etween mirrors, using other toms to give off more light. When the light is powerful enough it espes s lser em. prism Compt lser light refrts, ut does not spred out in prism. Why We Use Lsers Phosphorous toms give off light grdully, seeming to glow-in-the-drk. Lser light is ompt: it doesn t spred out like regulr light. Tht s why we use them for pointers nd why they don t end in prisms. Lsers n e powerful. Some lsers re used industry nd mediine for preision utting. Militry lsers re just now le to low up inoming missiles.
5 1. Totl internl refletion 2. Critil 3. Fier optis 4. Inndesent 5. Fluoresent 6. Filment A. Light reted from high het. B. The prt of light ul tht glows when hot nd mkes inndesent light. C. When ll light nnot espe glss or nother medium nd stys inside. D. The pst whih light nnot espe. E. Tehnology sed on ending light in les. F. Effiient light from UV rdition. How n light e redireted y fier optis? Cn fier opti le e ent ny diretion? Why or why not? 1. Polriztion 2. Polrizer 3. Photoluminesene 4. Phosphorous 5. Lser lens A. An tht sreens out ll ut light in one diretion. B. Light mplifition y stimulted emissions of rdition. C. An element tht releses light slowly; used in glow-in-the-drk s. D. The t of only llowing one-diretionl light to pss through filter. E. Ojets tht give off light slowly. Show where the 3 light rys will go. Conve or onvex lens? Wht do we ll the dot? Mgnifying or reduing? Convergent or divergent? You hve n offie uilding nd need to ut ost. Wht kind of lights will you use nd why? Light is pssed through polrizer. How ould you nel out light with seond polrizer? Wht element is photoluminesent nd why? mirror Use RGB to mke these olors. Cyn Yellow White Blk Green Mgent Show where the light will go. Conve or onvex mirror? Mgnifying or reduing? Convergent or divergent? Use CMYK to mke these olors. Blue Red White Blk Green Mgent Why don t lsers spred out into rinow in prism? A onvex lens is onvergent/divergent nd mgnifies/redues. A onve lens is onvergent/divergent nd mgnifies/redues. A onvex mirror is onvergent/divergent nd mgnifies/redues. A onve mirror is onvergent/divergent nd mgnifies/redues. Angle of inidene: Angle of refletion: Norml: Inident ry: Refleted ry: M i rr or d If the of inidene is 25 o, wht is the of refletion? If the etween the inident nd refleted rys is 80 o, wht is the of refletion? If n imge look 20 meters wy in mirror how fr wy is the? An is 4 meters wy from mirror. How fr wy does the imge look? Using CMYK Wht olor does yellow sor? Wht olors does yn reflet? Wht hs more energy: Rdio wves or Visile light? Wht hs shorter wvelength: Ultrviolet or Gmm rys? Wht hs higher frequeny: Visile light or Infrred? A sound wve hs period of 0.5 ses. Find its frequeny. Find the wvelength of the ove wve. If the fourth hrmoni of stnding wve is 48 Hz, find the fundmentl frequeny. You her your eho 6 seonds fter you yell into nyon. How wide is the nyon?
6 1. Optis 2. Imge 3. Ojet 4. Conve 5. Convex 6. Convergent 7. Divergent A. The study of how light ehves. B. A lens or mirror tht is igger in the middle. C. Light rys tht spred prt. D. Where your eyes think something is. E. Light rys tht ome together. F. Wht you re tully looking t. G. A lens or mirror tht is igger t the ends. 1. Norml 2. Mirror 3. Angle of inidene 4. Angle of refletion 5. Lens 6. Fous A. A drwn perpendiulr to the surfe of mirror or lens. B. An optil devie tht works y refrtion to end light. C. From the norml to the inoming ry. D. From the norml to the outgoing ry. E. Where ll prllel rys ome together. F. An optil devie tht works y refletion. The of inidene is: The of refletion is: The norml is: The inident ry is: The refleted ry is: A onvex lens is onvergent/divergent nd mgnifies/redues. A onve lens is onvergent/divergent nd mgnifies/redues. A onvex mirror is onvergent/divergent nd mgnifies/redues. A onve mirror is onvergent/divergent nd mgnifies/redues. Wht quntities re these units for? m mi m s 2 hr s volts Kg Km Meters Joules Se Wtts Ω N Amps Hz If sound is 60 db loud. Answer how mny db these would e: 1) A sound twie s loud: 2) A sound hlf s loud: A sound wve hs wvelength of 20 m. Find its frequeny. Mirror d You stnd 2 feet in front of mirror. How fr wy does your imge seem? d Whih letter shows where the inoming light ry will go? Whih rrow shows the pth tken y the lens? The etween the inident ry nd refleted ry is 60 o. Wht is the of refletion? The of refletion is 40 o. Wht is the of inidene? If wve s fourth hrmoni hs frequeny of 24 Hz, wht is its nturl frequeny nd wht is the frequeny of H 6? Find its period: Wht hrmoni is this? Could humn her this frequeny? Mrk the nodes nd nti-nodes. How mny wvelengths is it? If sound wve s frequeny is 100 Hz. Wht is its period? You yell into nyon nd it tkes 3 seonds for the eho to ome k to you. How fr wy is the other side of the nyon? Find the fundmentl frequeny: 5th hrmoni frequeny: Cn we her this frequeny? 100 Hz
The Nature of Light. Light is a propagating electromagnetic waves
The Nture of Light Light is propgting electromgnetic wves Index of Refrction n: In mterils, light intercts with toms/molecules nd trvels slower thn it cn in vcuum, e.g., vwter The opticl property of trnsprent
More information3.5.1 Single slit diffraction
3.5.1 Single slit diffrction Wves pssing through single slit will lso diffrct nd produce n interference pttern. The reson for this is to do with the finite width of the slit. We will consider this lter.
More informationLecture 8: Graph-theoretic problems (again)
COMP36111: Advned Algorithms I Leture 8: Grph-theoreti prolems (gin) In Prtt-Hrtmnn Room KB2.38: emil: iprtt@s.mn..uk 2017 18 Reding for this leture: Sipser: Chpter 7. A grph is pir G = (V, E), where V
More information3.5.1 Single slit diffraction
3..1 Single slit diffrction ves pssing through single slit will lso diffrct nd produce n interference pttern. The reson for this is to do with the finite width of the slit. e will consider this lter. Tke
More informationOPTICS. (b) 3 3. (d) (c) , A small piece
AQB-07-P-106 641. If the refrctive indices of crown glss for red, yellow nd violet colours re 1.5140, 1.5170 nd 1.518 respectively nd for flint glss re 1.644, 1.6499 nd 1.685 respectively, then the dispersive
More informationCS 241 Week 4 Tutorial Solutions
CS 4 Week 4 Tutoril Solutions Writing n Assemler, Prt & Regulr Lnguges Prt Winter 8 Assemling instrutions utomtilly. slt $d, $s, $t. Solution: $d, $s, nd $t ll fit in -it signed integers sine they re 5-it
More informationPhysics 152. Diffraction. Difrraction Gratings. Announcements. Friday, February 2, 2007
ics Fri Feb.02. Announcements Diffrction Difrrction Grtings Fridy, Februry 2, 2007 Help sessions: W 9-10 pm in NSC 118 Msteringics WU #5 due Mondy WU #6 due Wednesdy http://www.voltnet.com/ldder/ A bem
More informationSolids. Solids. Curriculum Ready.
Curriulum Rey www.mthletis.om This ooklet is ll out ientifying, rwing n mesuring solis n prisms. SOM CUES The Som Cue ws invente y Dnish sientist who went y the nme of Piet Hein. It is simple 3 # 3 #
More informationCalculus Differentiation
//007 Clulus Differentition Jeffrey Seguritn person in rowot miles from the nerest point on strit shoreline wishes to reh house 6 miles frther down the shore. The person n row t rte of mi/hr nd wlk t rte
More informationInternet Routing. IP Packet Format. IP Fragmentation & Reassembly. Principles of Internet Routing. Computer Networks 9/29/2014.
omputer Networks 9/29/2014 IP Pket Formt Internet Routing Ki Shen IP protool version numer heder length (words) for qulity of servie mx numer remining hops (deremented t eh router) upper lyer protool to
More informationAnswer Key Lesson 6: Workshop: Angles and Lines
nswer Key esson 6: tudent Guide ngles nd ines Questions 1 3 (G p. 406) 1. 120 ; 360 2. hey re the sme. 3. 360 Here re four different ptterns tht re used to mke quilts. Work with your group. se your Power
More informationCS 551 Computer Graphics. Hidden Surface Elimination. Z-Buffering. Basic idea: Hidden Surface Removal
CS 55 Computer Grphis Hidden Surfe Removl Hidden Surfe Elimintion Ojet preision lgorithms: determine whih ojets re in front of others Uses the Pinter s lgorithm drw visile surfes from k (frthest) to front
More informationGreedy Algorithm. Algorithm Fall Semester
Greey Algorithm Algorithm 0 Fll Semester Optimiztion prolems An optimiztion prolem is one in whih you wnt to fin, not just solution, ut the est solution A greey lgorithm sometimes works well for optimiztion
More informationSection 10.4 Hyperbolas
66 Section 10.4 Hyperbols Objective : Definition of hyperbol & hyperbols centered t (0, 0). The third type of conic we will study is the hyperbol. It is defined in the sme mnner tht we defined the prbol
More informationError Numbers of the Standard Function Block
A.2.2 Numers of the Stndrd Funtion Blok evlution The result of the logi opertion RLO is set if n error ours while the stndrd funtion lok is eing proessed. This llows you to rnh to your own error evlution
More informationPOLAROID SPECTRA FULL SWITCH USER MANUAL
POLAROID SPECTRA FULL SWITCH USER MANUAL 1200 Front View i Sonr rnge finder b Film door relese c Film door d Film exit e Film shde f Quintic, three-element, 125mm lens g Progrmmed flsh h Photocell i Self-timer
More informationLesson 4.4. Euler Circuits and Paths. Explore This
Lesson 4.4 Euler Ciruits nd Pths Now tht you re fmilir with some of the onepts of grphs nd the wy grphs onvey onnetions nd reltionships, it s time to egin exploring how they n e used to model mny different
More informationSMALL SIZE EDGE-FED SIERPINSKI CARPET MICROSTRIP PATCH ANTENNAS
Progress In Eletromgnetis Reserh C, Vol. 3, 195 22, 28 SMALL SIZE EDGE-FED SIERPINSKI CARPET MICROSTRIP PATCH ANTENNAS W.-L. Chen nd G.-M. Wng Rdr Engineering Deprtment Missile Institute of Air Fore Engineering
More informationLine The set of points extending in two directions without end uniquely determined by two points. The set of points on a line between two points
Lines Line Line segment Perpendiulr Lines Prllel Lines Opposite Angles The set of points extending in two diretions without end uniquely determined by two points. The set of points on line between two
More informationRadiation & Matter 3: Refraction
Rdition & Mtter 3: Refrction Refrction AIM The effects of refrction (the chnge of direction tht tkes plce when light psses fro ir into glss) y hve been et during n erlier study of Physics. The i of this
More informationCOMP 423 lecture 11 Jan. 28, 2008
COMP 423 lecture 11 Jn. 28, 2008 Up to now, we hve looked t how some symols in n lphet occur more frequently thn others nd how we cn sve its y using code such tht the codewords for more frequently occuring
More informationIntroduction to Algebra
INTRODUCTORY ALGEBRA Mini-Leture 1.1 Introdution to Alger Evlute lgeri expressions y sustitution. Trnslte phrses to lgeri expressions. 1. Evlute the expressions when =, =, nd = 6. ) d) 5 10. Trnslte eh
More informationFinal Exam Review F 06 M 236 Be sure to look over all of your tests, as well as over the activities you did in the activity book
inl xm Review 06 M 236 e sure to loo over ll of your tests, s well s over the tivities you did in the tivity oo 1 1. ind the mesures of the numered ngles nd justify your wor. Line j is prllel to line.
More informationIf you are at the university, either physically or via the VPN, you can download the chapters of this book as PDFs.
Lecture 5 Wlks, Trils, Pths nd Connectedness Reding: Some of the mteril in this lecture comes from Section 1.2 of Dieter Jungnickel (2008), Grphs, Networks nd Algorithms, 3rd edition, which is ville online
More informationProblems. .,..,... : Problems of increasing difficulty. CP: Cumulative problems incorporating material from earlier chapters.
1106 CHPTER 33 The Nture nd Propgtion of Light RIDGING PROLEM Reflection nd Refrction Figure 33.38 shows rectngulr glss block tht hs metl reflector on one fce nd wter on n djoining fce. light bem strikes
More informationCameras. Importance of camera models
pture imges mesuring devie Digitl mers mers fill in memor ith olor-smple informtion D hrge-oupled Devie insted of film film lso hs finite resolution grininess depends on speed IS 00 00 6400 sie 35mm IMAX
More informationCan Pythagoras Swim?
Overview Ativity ID: 8939 Mth Conepts Mterils Students will investigte reltionships etween sides of right tringles to understnd the Pythgoren theorem nd then use it to solve prolems. Students will simplify
More informationUnit #9 : Definite Integral Properties, Fundamental Theorem of Calculus
Unit #9 : Definite Integrl Properties, Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl
More informationParadigm 5. Data Structure. Suffix trees. What is a suffix tree? Suffix tree. Simple applications. Simple applications. Algorithms
Prdigm. Dt Struture Known exmples: link tble, hep, Our leture: suffix tree Will involve mortize method tht will be stressed shortly in this ourse Suffix trees Wht is suffix tree? Simple pplitions History
More informationprisms Prisms Specifications Catalogue number BK7 Wedge, Beam Deviation, deg
Cotings Wedge Steer bems in opticl systems Cn be used in pirs for continuous ngulr djustment T Hving selected n pproprite wedge, it is esy to crete precise bem devition without ffecting other bem prmeters.
More informationFig.25: the Role of LEX
The Lnguge for Specifying Lexicl Anlyzer We shll now study how to uild lexicl nlyzer from specifiction of tokens in the form of list of regulr expressions The discussion centers round the design of n existing
More informationElectromagnetic Waves
Eletromagneti Waves Physis 6C Eletromagneti (EM) waves are produed by an alternating urrent in a wire. As the harges in the wire osillate bak and forth, the eletri field around them osillates as well,
More informationWelch Allyn CardioPerfect Workstation Installation Guide
Welch Allyn CrdioPerfect Worksttion Instlltion Guide INSTALLING CARDIOPERFECT WORKSTATION SOFTWARE & ACCESSORIES ON A SINGLE PC For softwre version 1.6.6 or lter For network instlltion, plese refer to
More informationGrade 7/8 Math Circles Geometric Arithmetic October 31, 2012
Fculty of Mthemtics Wterloo, Ontrio N2L 3G1 Grde 7/8 Mth Circles Geometric Arithmetic Octoer 31, 2012 Centre for Eduction in Mthemtics nd Computing Ancient Greece hs given irth to some of the most importnt
More informationCMPUT101 Introduction to Computing - Summer 2002
CMPUT Introdution to Computing - Summer 22 %XLOGLQJ&RPSXWHU&LUFXLWV Chpter 4.4 3XUSRVH We hve looked t so fr how to uild logi gtes from trnsistors. Next we will look t how to uild iruits from logi gtes,
More informationChapter 9. Greedy Technique. Copyright 2007 Pearson Addison-Wesley. All rights reserved.
Chpter 9 Greey Tehnique Copyright 2007 Person Aison-Wesley. All rights reserve. Greey Tehnique Construts solution to n optimiztion prolem piee y piee through sequene of hoies tht re: fesile lolly optiml
More information10.2 Graph Terminology and Special Types of Graphs
10.2 Grph Terminology n Speil Types of Grphs Definition 1. Two verties u n v in n unirete grph G re lle jent (or neighors) in G iff u n v re enpoints of n ege e of G. Suh n ege e is lle inient with the
More informationClinopyroxene. Pyroxene. Clinopyroxene. Compositional Groups
Cpx - or Cli Monolini Composition sed on 3 end memer omponents CSiO 3 - wollstonite MgSiO 3 - linoensttite FeSiO 3 - linoferrosilite Cpx generl formul Augite C,Mg,Fe,Al) 2 (Si, Al) 2 O 6 Common px hedenergite
More information2. What are the types of diffraction and give the differences between them? (June 2005, June 2011)
UNIT-1 b DIFFRACTION Diffrction:A) Distinction between Fresnel nd Frunhofer diffrction, B) diffrction due to single slit, N-slits,C) Diffrction grting experiment. 1 A) Distinction between Fresnel nd Frunhofer
More informationMcAfee Web Gateway
Relese Notes Revision C MAfee We Gtewy 7.6.2.11 Contents Aout this relese Enhnement Resolved issues Instlltion instrutions Known issues Additionl informtion Find produt doumenttion Aout this relese This
More informationPackage Contents. Wireless-G USB Network Adapter with SpeedBooster USB Cable Setup CD-ROM with User Guide (English only) Quick Installation
A Division of Ciso Systems, In. Pkge Contents Wireless-G USB Network Adpter with SpeedBooster USB Cle Setup CD-ROM with User Guide (English only) Quik Instlltion 2,4 GHz 802.11g Wireless Model No. Model
More informationBulletin 854K 60 mm Control Tower Stack Lights
Produt Overview/Seletion s UL Type 4/4X/13, IP66 Stking onfigurtions 1 5 modules high per single stk "No tools" lens ssemly Surfe, vertil, M20 threded tue, quik relese se, 1/2 in. NPT, doule-sided se,
More informationMath 227 Problem Set V Solutions. f ds =
Mth 7 Problem Set V Solutions If is urve with prmetriztion r(t), t b, then we define the line integrl f ds b f ( r(t) ) dr dt (t) dt. Evlute the line integrl f(x,y,z)ds for () f(x,y,z) xosz, the urve with
More informationTo access your mailbox from inside your organization. For assistance, call:
2001 Ative Voie, In. All rights reserved. First edition 2001. Proteted y one or more of the following United Sttes ptents:,070,2;,3,90;,88,0;,33,102;,8,0;,81,0;,2,7;,1,0;,90,88;,01,11. Additionl U.S. nd
More informationThe Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center
Resource Overview Quntile Mesure: Skill or Concept: 80Q Multiply two frctions or frction nd whole numer. (QT N ) Excerpted from: The Mth Lerning Center PO Box 99, Slem, Oregon 9709 099 www.mthlerningcenter.org
More informationUnit 3: Optics Chapter 4
Unit 3: Optics Chapter 4 History of Light https://www.youtube.com/watch?v=j1yiapztlos History of Light Early philosophers (Pythagoras) believed light was made up of tiny particles Later scientist found
More informationLecture 13: Graphs I: Breadth First Search
Leture 13 Grphs I: BFS 6.006 Fll 2011 Leture 13: Grphs I: Bredth First Serh Leture Overview Applitions of Grph Serh Grph Representtions Bredth-First Serh Rell: Grph G = (V, E) V = set of verties (ritrry
More informationGENG2140 Modelling and Computer Analysis for Engineers
GENG4 Moelling n Computer Anlysis or Engineers Letures 9 & : Gussin qurture Crete y Grn Romn Joles, PhD Shool o Mehnil Engineering, UWA GENG4 Content Deinition o Gussin qurture Computtion o weights n points
More informationCS553 Lecture Introduction to Data-flow Analysis 1
! Ide Introdution to Dt-flow nlysis!lst Time! Implementing Mrk nd Sweep GC!Tody! Control flow grphs! Liveness nlysis! Register llotion CS553 Leture Introdution to Dt-flow Anlysis 1 Dt-flow Anlysis! Dt-flow
More informationZZ - Advanced Math Review 2017
ZZ - Advnced Mth Review Mtrix Multipliction Given! nd! find the sum of the elements of the product BA First, rewrite the mtrices in the correct order to multiply The product is BA hs order x since B is
More informationGEOMETRIC OPTICS. LENSES refract light, so we need to know how light bends when entering and exiting a lens and how that interaction forms an image.
I. What is GEOMTERIC OPTICS GEOMETRIC OPTICS In geometric optics, LIGHT is treated as imaginary rays. How these rays interact with at the interface of different media, including lenses and mirrors, is
More informationSection 9.2 Hyperbolas
Section 9. Hperols 597 Section 9. Hperols In the lst section, we lerned tht plnets hve pproimtel ellipticl orits round the sun. When n oject like comet is moving quickl, it is le to escpe the grvittionl
More informationDigital Design. Chapter 1: Introduction. Digital Design. Copyright 2006 Frank Vahid
Chpter : Introduction Copyright 6 Why Study?. Look under the hood of computers Solid understnding --> confidence, insight, even better progrmmer when wre of hrdwre resource issues Electronic devices becoming
More informationRepresentation of Numbers. Number Representation. Representation of Numbers. 32-bit Unsigned Integers 3/24/2014. Fixed point Integer Representation
Representtion of Numbers Number Representtion Computer represent ll numbers, other thn integers nd some frctions with imprecision. Numbers re stored in some pproximtion which cn be represented by fixed
More informationPRISMS. Don t see exactly what you are looking for? CVI Laser Optics specializes in prototype to volume production manufacturing!
PRISMS Mirrors CVI Lser Optics mnufctures lrge selection of high qulity prisms for use in mny pplictions including diverse industril nd scientific uses, lser trcking nd lignment, spectroscopy, nd militry
More information5 ANGLES AND POLYGONS
5 GLES POLYGOS urling rige looks like onventionl rige when it is extene. However, it urls up to form n otgon to llow ots through. This Rolling rige is in Pington sin in Lonon, n urls up every Friy t miy.
More informationFig.1. Let a source of monochromatic light be incident on a slit of finite width a, as shown in Fig. 1.
Answer on Question #5692, Physics, Optics Stte slient fetures of single slit Frunhofer diffrction pttern. The slit is verticl nd illuminted by point source. Also, obtin n expression for intensity distribution
More informationRight Angled Trigonometry. Objective: To know and be able to use trigonometric ratios in rightangled
C2 Right Angled Trigonometry Ojetive: To know nd e le to use trigonometri rtios in rightngled tringles opposite C Definition Trigonometry ws developed s method of mesuring ngles without ngulr units suh
More informationNaming 3D objects. 1 Name the 3D objects labelled in these models. Use the word bank to help you.
Nming 3D ojects 1 Nme the 3D ojects lelled in these models. Use the word nk to help you. Word nk cue prism sphere cone cylinder pyrmid D A C F A B C D cone cylinder cue cylinder E B E prism F cue G G pyrmid
More information6.045J/18.400J: Automata, Computability and Complexity. Quiz 2: Solutions. Please write your name in the upper corner of each page.
6045J/18400J: Automt, Computbility nd Complexity Mrh 30, 2005 Quiz 2: Solutions Prof Nny Lynh Vinod Vikuntnthn Plese write your nme in the upper orner of eh pge Problem Sore 1 2 3 4 5 6 Totl Q2-1 Problem
More informationMidterm Exam CSC October 2001
Midterm Exm CSC 173 23 Otoer 2001 Diretions This exm hs 8 questions, severl of whih hve suprts. Eh question indites its point vlue. The totl is 100 points. Questions 5() nd 6() re optionl; they re not
More informationEXPONENTIAL & POWER GRAPHS
Eponentil & Power Grphs EXPONENTIAL & POWER GRAPHS www.mthletics.com.u Eponentil EXPONENTIAL & Power & Grphs POWER GRAPHS These re grphs which result from equtions tht re not liner or qudrtic. The eponentil
More informationLily Yen and Mogens Hansen
SKOLID / SKOLID No. 8 Lily Yen nd Mogens Hnsen Skolid hs joined Mthemticl Myhem which is eing reformtted s stnd-lone mthemtics journl for high school students. Solutions to prolems tht ppered in the lst
More informationWhat is it? How does it work? How do we use it?
What is it? How does it work? How do we use it? Dual Nature http://www.youtube.com/watch?v=dfpeprq7ogc o Electromagnetic Waves display wave behavior o Created by oscillating electric and magnetic fields
More informationLINX MATRIX SWITCHERS FIRMWARE UPDATE INSTRUCTIONS FIRMWARE VERSION
Overview LINX MATRIX SWITCHERS FIRMWARE UPDATE INSTRUCTIONS FIRMWARE VERSION 4.4.1.0 Due to the omplex nture of this updte, plese fmilirize yourself with these instrutions nd then ontt RGB Spetrum Tehnil
More informationMa/CS 6b Class 1: Graph Recap
M/CS 6 Clss 1: Grph Recp By Adm Sheffer Course Detils Adm Sheffer. Office hour: Tuesdys 4pm. dmsh@cltech.edu TA: Victor Kstkin. Office hour: Tuesdys 7pm. 1:00 Mondy, Wednesdy, nd Fridy. http://www.mth.cltech.edu/~2014-15/2term/m006/
More informationWidth and Bounding Box of Imprecise Points
Width nd Bounding Box of Impreise Points Vhideh Keikh Mrten Löffler Ali Mohdes Zhed Rhmti Astrt In this pper we study the following prolem: we re given set L = {l 1,..., l n } of prllel line segments,
More informationPhys 1020, Day 18: Questions? Cameras, Blmfld Reminders: Next Up: digital cameras finish Optics Note Final Project proposals next week!
Lights. Action. Phys 1020, Day 18: Questions? Cameras, Blmfld 15.1 Reminders: Next Up: digital cameras finish Optics Note Final Project proposals next week! 1 What have we learned in this section: 1) Lasers
More informationCOMP108 Algorithmic Foundations
Grph Theory Prudene Wong http://www.s.liv..uk/~pwong/tehing/omp108/201617 How to Mesure 4L? 3L 5L 3L ontiner & 5L ontiner (without mrk) infinite supply of wter You n pour wter from one ontiner to nother
More informationTries. Yufei Tao KAIST. April 9, Y. Tao, April 9, 2013 Tries
Tries Yufei To KAIST April 9, 2013 Y. To, April 9, 2013 Tries In this lecture, we will discuss the following exct mtching prolem on strings. Prolem Let S e set of strings, ech of which hs unique integer
More informationLecture 12 : Topological Spaces
Leture 12 : Topologil Spes 1 Topologil Spes Topology generlizes notion of distne nd loseness et. Definition 1.1. A topology on set X is olletion T of susets of X hving the following properties. 1. nd X
More informationChapter 2. 3/28/2004 H133 Spring
Chpter 2 Newton believe tht light ws me up of smll prticles. This point ws ebte by scientists for mny yers n it ws not until the 1800 s when series of experiments emonstrte wve nture of light. (But be
More informationDistance vector protocol
istne vetor protool Irene Finohi finohi@i.unirom.it Routing Routing protool Gol: etermine goo pth (sequene of routers) thru network from soure to Grph strtion for routing lgorithms: grph noes re routers
More informationLight and all its colours
Light and all its colours Hold a CD to the light You can see all the colours of the rainbow The CD is a non-luminous body It is reflecting white light from the sun Where do the colours come from? Truth
More informationCS 340, Fall 2016 Sep 29th Exam 1 Note: in all questions, the special symbol ɛ (epsilon) is used to indicate the empty string.
CS 340, Fll 2016 Sep 29th Exm 1 Nme: Note: in ll questions, the speil symol ɛ (epsilon) is used to indite the empty string. Question 1. [10 points] Speify regulr expression tht genertes the lnguge over
More informationReview Packet #3 Notes
SCIE 40, Spring 0 Miller Review Pket # Notes Mpping Nottion We use mpping nottion to note how oordinte hnges. For exmple, if the point ( ) trnsformed under mpping nottion of ( x, y) ( x, y), then it eomes
More informationIn the last lecture, we discussed how valid tokens may be specified by regular expressions.
LECTURE 5 Scnning SYNTAX ANALYSIS We know from our previous lectures tht the process of verifying the syntx of the progrm is performed in two stges: Scnning: Identifying nd verifying tokens in progrm.
More information1.1. Interval Notation and Set Notation Essential Question When is it convenient to use set-builder notation to represent a set of numbers?
1.1 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS Prepring for 2A.6.K, 2A.7.I Intervl Nottion nd Set Nottion Essentil Question When is it convenient to use set-uilder nottion to represent set of numers? A collection
More informationDistributed Systems Principles and Paradigms
Distriuted Systems Priniples nd Prdigms Christoph Dorn Distriuted Systems Group, Vienn University of Tehnology.dorn@infosys.tuwien..t http://www.infosys.tuwien..t/stff/dorn Slides dpted from Mrten vn Steen,
More informationCS311H: Discrete Mathematics. Graph Theory IV. A Non-planar Graph. Regions of a Planar Graph. Euler s Formula. Instructor: Işıl Dillig
CS311H: Discrete Mthemtics Grph Theory IV Instructor: Işıl Dillig Instructor: Işıl Dillig, CS311H: Discrete Mthemtics Grph Theory IV 1/25 A Non-plnr Grph Regions of Plnr Grph The plnr representtion of
More informationUnit 5 Vocabulary. A function is a special relationship where each input has a single output.
MODULE 3 Terms Definition Picture/Exmple/Nottion 1 Function Nottion Function nottion is n efficient nd effective wy to write functions of ll types. This nottion llows you to identify the input vlue with
More information6.3 Volumes. Just as area is always positive, so is volume and our attitudes towards finding it.
6.3 Volumes Just s re is lwys positive, so is volume nd our ttitudes towrds finding it. Let s review how to find the volume of regulr geometric prism, tht is, 3-dimensionl oject with two regulr fces seprted
More informationLight travels in straight lines, this is referred to as... this means that light does not bend...
SNC 2DI - 10.2 Properties of Light and Reflection Light travels in straight lines, this is referred to as... this means that light does not bend... Reflection : Light travels in a straight line as long
More informationTight triangulations: a link between combinatorics and topology
Tight tringultions: link between ombintoris nd topology Jonthn Spreer Melbourne, August 15, 2016 Topologil mnifolds (Geometri) Topology is study of mnifolds (surfes) up to ontinuous deformtion Complited
More informationVSxF-2/-3/-4 SMALL LINEAR VALVES PN16 FOR MODULATING AND ON/OFF-CONTROL SPECIFICATIONS
VSxF2/3/4 SMLL LINER VLVES PN16 FOR MODULTING ND ON/OFFCONTROL VSxF2 VSxF3 VSxF4 GENERL These smll liner vlves re used in omintion with smll eletri liner vlve tutors nd thermoeletri tutors for the ontrol
More informationBefore We Begin. Introduction to Spatial Domain Filtering. Introduction to Digital Image Processing. Overview (1): Administrative Details (1):
Overview (): Before We Begin Administrtive detils Review some questions to consider Winter 2006 Imge Enhncement in the Sptil Domin: Bsics of Sptil Filtering, Smoothing Sptil Filters, Order Sttistics Filters
More informationReview Packet #3 Notes
SCIE 40, Fll 05 Miller Review Pket # Notes Prllel Lines If two prllel lines re onneted y third line (lled the trnsversl), the resulting ngles re either ongruent or supplementry. Angle pirs re nmed s follows:
More informationAssembly & Installation Instructions: 920 CPU Holder, 920-X
Assemly & Instlltion Instrutions: 920 CPU Holder, 920-X Prt Inluded, CPU Holder (ll models) A Exterior Housing B Interior Housing C Hrdwre Kit (ll models) D CPU Supporting Plte F Loking Kit (models 920-FL
More informationLight Module Type. Lens Color Description V AC/DC (no-lamp module ) Steady no lamp. 3 Green 24 24V AC/DC. Steady LED.
ulletin 854K 60 mm Control Tower Stk Lights Light Modules 854K 10 TL 4 Stedy LED Module Voltge Light Module Type Lens Color Desription Desription Desription 00 0 250V AC/DC (no-lmp module ) XN Stedy no
More informationClass-XI Mathematics Conic Sections Chapter-11 Chapter Notes Key Concepts
Clss-XI Mthemtics Conic Sections Chpter-11 Chpter Notes Key Concepts 1. Let be fixed verticl line nd m be nother line intersecting it t fixed point V nd inclined to it t nd ngle On rotting the line m round
More informationRed Orange the reflected ray. Yellow Green and the normal. Blue Indigo line. Colours of visible reflection
distance the carrying the moves away from rest position Brightness Loudness The angle between the incident ray and the normal line Amplitude Amplitude of a light Amplitude of a sound incidence Angle between
More informationOrder these angles from smallest to largest by wri ng 1 to 4 under each one. Put a check next to the right angle.
Lines nd ngles Connect ech set of lines to the correct nme: prllel perpendiculr Order these ngles from smllest to lrgest y wri ng to 4 under ech one. Put check next to the right ngle. Complete this tle
More informationOptics and Optical design Problems
Optics nd Opticl design 0 Problems Sven-Görn Pettersson / Cord Arnold 0-09-06 4:3 This mteril is tken from severl sources. Some problems re from the book Våglär och Optik by Görn Jönsson nd Elisbeth Nilsson.
More informationDistance Computation between Non-convex Polyhedra at Short Range Based on Discrete Voronoi Regions
Distne Computtion etween Non-onvex Polyhedr t Short Rnge Bsed on Disrete Voronoi Regions Ktsuki Kwhi nd Hiroms Suzuki Deprtment of Preision Mhinery Engineering, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku,
More informationCS143 Handout 07 Summer 2011 June 24 th, 2011 Written Set 1: Lexical Analysis
CS143 Hndout 07 Summer 2011 June 24 th, 2011 Written Set 1: Lexicl Anlysis In this first written ssignment, you'll get the chnce to ply round with the vrious constructions tht come up when doing lexicl
More informationKULLEGG MARIA REGINA BOYS SECONDARY MOSTA HALF-YEARLY EXAMINATIONS 2012/2013. SUBJECT: PHYSICS Form 4 TIME: 1 HR 30 MIN NAME :
KULLEGG MARIA REGINA BOYS SECONDARY MOSTA HALF-YEARLY EXAMINATIONS 2012/2013 SUBJECT: PHYSICS Form 4 TIME: 1 HR 30 MIN NAME : CLASS : INDEX NO : Track 2 Answer ALL questions in the spaces provided on the
More informationa = 1.25 (31.8) b =.687 (17.4) c =.625 (15.9) a =.813 (20.7) b =.250 (6.4) c =.563 (14.3) d =.031 (0.8) min. of cable dielectric
CONNECTING WITH QUALITY SINCE 959 Route 59 Hillurn, New York 09 offie:(85) 57-750 fx: (85) 57-760 wesite: http://www.zls.om e-mil: info@zls.om UHF ASSEMBLY INSTRUCTIONS #0 UG STANDARD SOLDER TYPE (PL-59)
More informationCreating Flexible Interfaces. Friday, 24 April 2015
Creting Flexible Interfces 1 Requests, not Objects Domin objects re esy to find but they re not t the design center of your ppliction. Insted, they re trp for the unwry. Sequence digrms re vehicle for
More informationDoubts about how to use azimuth values from a Coordinate Object. Juan Antonio Breña Moral
Douts out how to use zimuth vlues from Coordinte Ojet Jun Antonio Breñ Morl # Definition An Azimuth is the ngle from referene vetor in referene plne to seond vetor in the sme plne, pointing towrd, (ut
More informationSystems I. Logic Design I. Topics Digital logic Logic gates Simple combinational logic circuits
Systems I Logic Design I Topics Digitl logic Logic gtes Simple comintionl logic circuits Simple C sttement.. C = + ; Wht pieces of hrdwre do you think you might need? Storge - for vlues,, C Computtion
More information