1Phy107 Fall 20061From Last Time…• Electric and magnetic fields• Light, Doppler effect, interferenceToday…Interference, the speed of lightRelativityHW#5: Chapter 10: Conceptual: # 6, 11, 17, 22 Problems: # 4, 6, 8Due: Oct 18thPhy107 Fall 20062The electric and magneticforce and fieldsF =kq1q2r2F = qE• Electric field is from a charge and exerts aforce on other charges• Magnetic field is from a moving charge andexerts a force on other moving charges!F = qvBE =kQr2• Changing electric ormagnetic fields can causemagnetic or electric fieldsPhy107 Fall 20063Properties of EM Waves• Light is a set of electric and magnetic fields where thechanging electric field creates the magnetic field and thechanging magnetic field creates the electric field• Only works when the fields change from up to down andback again at the speed of light• The speed of light is a special value - we’ll see this again inEinstein's relativity.• Has all properties of a wave:v =fc =Phy107 Fall 20064Wave effects in EM radiation• Same properties as sound waves:common to all waves.• Doppler shift:change in light frequency due to motion ofsource or observer• Interference:superposition of light waves can result ineither increase or decrease in brightness.Phy107 Fall 20065Interference of light waves• Coherentbeams fromtwo slits• Constructiveinterference:waves inphase atscreenPhy107 Fall 20066Destructive interference(n +12)2Phy107 Fall 20067Interference: secondary maximanPhy107 Fall 20068Resulting diffraction patternPhy107 Fall 20069Hertz’s measurement:the speed of electromagnetic waves• Hertz measured the speed of the waves from thetransmitter– He used the waves to form an interferencepattern and calculated the wavelength–From v = f , v was found– v was very close to 3 x 108 m/s, the known speedof light• This provided evidence in support of Maxwell’stheory• This idea still used today measure wavelengthswhen studying starsPhy107 Fall 200610Laser pointer interferenceEach clear area onthe slide acts as alight source.Interference withmany light sourcesis sometimes calleddiffraction.Phy107 Fall 200611Complexinterference patternsWhite spaces act as array of sources.The ‘diffraction pattern’ containsinformation about the originalpattern.Phy107 Fall 200612DNA X-raydiffractionpatternX-ray diffraction• X-rays are short-wavelength EM wave.Short wavelengths probe small spacings• Diffraction pattern used to determineatomic structure of complex molecules.– e.g. DNADNA molecularstructure3Phy107 Fall 200613 Visible Light• We see only anarrow range ofthe EM spectrum• 400-700nm• To someone whocould see theentire spectrum,our limitation tothis narrowrange mightseem odd.Phy107 Fall 200614White light is a superposition• Prism can separate the superposition intoit’s constituents.• For example, ‘white’ light is an almostequal superposition of all visiblewavelengths (as well a invisible ones!)• This is a simple analyzer to ‘deconstruct’ asuperposition of light waves (how much ofeach wavelength is present in the light).Phy107 Fall 200615Seeing colors•Rods and cones sendimpulses to brain whenthey absorb light.•Brain processes intocolor information.Cones, 3 typesRods (one type)Phy107 Fall 200616Rods and cones• Rods are responsible for vision atlow light levels. No color sensitivity• Cones are active at higher lightlevels• The central fovea ispopulated only by cones.•3 types of cones– short-wavelength sensitive cones(S)– middle-wavelength sensitive cones(M)– long-wavelength sensitive cones(L)Cones, 3 typesRods(one type)Phy107 Fall 20061700.10.20.30.40.50.60.7400 440 480 520 560 600 640 680ENERGY SENSITIVITYWAVELENGTH ( nm )Eye sensitivity• Eye’s wavelengthsensitivity by cone type.• Sensitivities overlap.S-conesM-conesL-conesFor instance, pure yellow(single wavelength of570nm) stimulates both Mand L cones.M-cone: 0.44L-cone: 0.52S-cone: 0Phy107 Fall 200618Interpreting colors• Each cone sends a signalin relation to its degree of stimulation• A triplet of information (S, M, L) is conveyed.• Brain uses only this information to assign a color• Any light generating same (S, M, L) ‘seen’ as same color0.440.00.52SML4Phy107 Fall 20061900.10.20.30.40.50.60.7400 440 480 520 560 600 640 680ENERGY SENSITIVITYWAVELENGTH ( nm )Red + Green = ?• Combined Green + RedCompare to spectrallypure yellow (S, M, L)=(0,0.44,0.52)Total M-cone stimulus= 0.55+0.02 = 0.57Total L-cone stimulus= 0.49+0.17=0.66Reducing the intensity slightly(by 1.25) gives(S, M, L)=(0,0.45,0.52)Phy107 Fall 200620QuestionSuppose an eye has only two cones with spectral sensitivitiesshown here. It is stimulated by equal intensities of 300and 700 nm pure spectral light. Which single wavelengthmight produce a similar color perception? A. 330 nmB. 430 nmC. 500 nmD. 530 nmPhy107 Fall 200621Relativity and Modern Physics• Physics changed drastically in the early 1900’s• New discoveries — Relativity and Quantum Mechanics• Relativity– Changed the way we think about space and time• Quantum mechanics– Changed our conceptions of matter.Phy107 Fall 200622Special Relativity• From 1905 to 1908, Einsteindeveloped the special theoryof relativity.• Came up completely differentidea of time and space.• Everything is relative.No absolute lengths, times,energies.Showed that our usual conceptions of space andtime are misguided.Phy107 Fall 200623Frames of reference• Frame of reference:– The coordinate system in which you observe events.– e.g. The room around you.– You judge how fast a thrown ball goes by its velocityrelative to some stationary object in the room.– You judge how high athrown ball goes by distancefrom the floor, ceiling, etc.– You judge how fast you aremoving by looking at objectsaround youPhy107 Fall 200624Which reference frameSuppose you are on the bus to Chicago driving at 60 mph,and throw a ball forwards at 40 mph.From your seat on the bus,the speed of ball is the same as in this classroom.To the major league scout on the side of the road,your 40 mph throw has become a 100 mph fastball.Who is correct?You wouldn’t last long in the majors.The important velocity in a baseballgame is the relative velocity of ballwith respect to pitcher or the batter.5Phy107 Fall 200625• Earth spins on its axis– One rotation in (24 hrs)(60 min/hr)(60 sec/min)=86400 sec– Point on surface moves 2RE in one rotation.– Surface velocity =
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