Wave Properties Of Light

Wave Properties Of LightChapter 181Electromagnetic WaveformsThe and fields are perpendicular to each otherBoth fields are perpendicular to the direction of motionTherefore, electromagnetic waves are transverse wavesWith all periodic waves

Since v = c in a vacuum

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2Electromagnetic Waves, SummaryA static electric charge produces an electric field. A uniformly changing (moving) electric field produces an magnetic fieldA uniformly changing (moving) magnetic field produces a electric field**But NONE of these produces an EM WAVE. For this you need an accelerating charge.**3Velocity of Lightc = 3 x 108m/s (In a vacuum)

Slower values in other mediums, even air slows down light, but frequency will stay the same4Frequency, Wavelength and Velocity Wavelength alters along with velocity in order to keep frequency constant

Objects COLOR is determined by frequency, NOT wavelength

Wavelengths normally listed in the EM spectrum for the visual range are VACUUM wavelengths (in space)

As light passes from that vacuum of space into a medium with a higher index of refraction, its velocity is reduced, and thus wavelength must also reduce in order to preserve frequency and color5Electromagnetic-Photon Spectrum6The Spectrum of EM WavesForms of electromagnetic waves exist that are distinguished by their frequencies and wavelengthsc = Wavelengths for visible light range from 400 nm to 700 nmThere is no sharp division between one kind of em wave and the next7The EM SpectrumNote the overlap between types of wavesVisible light is a small portion of the spectrumTypes are distinguished by frequency or wavelength

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RadiowavesRadio WavesUsed in radio and television communication systemsWavelengths range from 100s of meters to less than a cm9Radio Telescopes

Large dish focuses the energy of radio waves onto a small receiver (antenna)Amplified signals are stored in computers and converted into images, spectra, etc.010Radio Interferometry

Just as for optical telescopes, the resolving power of a radio telescope is amin = 1.22 l/D.For radio telescopes, this is a big problem: Radio waves are much longer than visible light Use interferometry to improve resolution!011MicrowavesMicrowavesWavelengths from about 1 mm to 30 cmWell suited for radar systemsMicrowave ovens are an application

12InfraredInfrared wavesIncorrectly called heat waves1mm down to 700nmProduced by hot objects and moleculesReadily absorbed by most materials

13Visible LightVisible lightPart of the spectrum detected by the human eyeMost sensitive at about 560 nm (yellow-green)

14UltravioletUltraviolet lightCovers about 400 nm to 0.6 nmSun is an important source of UV lightMost UV light from the sun is absorbed in the stratosphere by ozone

15X-raysX-raysMost common source is acceleration of high-energy electrons striking a metal targetUsed as a diagnostic tool in medicine

16Gamma RaysGamma raysEmitted by radioactive nucleiHighly penetrating and cause serious damage when absorbed by living tissue

17Interference, Diffraction and Polarization18.218Proving Light Is A WaveThomas Young, in 1807, used Diffraction to prove that light experiences both Constructive and Destructive Interference.

19DiffractionThe shape of a wave front is altered (bent) as it passes through a hole or slit in another medium.A Diffraction Grating is a screen with a series of slits which create constructive/destructive interference patternsA Spectrometer uses a diffraction grating to create a spectrum measuring the wavelengths on incoming light. This can be used to identify materials emitting that light20Diffraction

21PolarizationLight travels as a transverse wave, and it can thus displace within a plane with a specific orientation.White Light consists of all wavelengths essentially travelling in all polarizations it is UNpolarized.Polarization of a light wave is defined by the orientation of the Electric Wave

22PolarizersFilter out all light wave polarizations EXCEPT one

The light transmitted through a polarizer is now polarizedit has a single polarization

Can be used to block out some portion of sunlight (sunglasses), create images on an LCD screen by filtering certain values of RGB light and even to identify mineral composition of rocks viewed in thin section23

24Relativity18.325Foundation of Special RelativityReconciling of the measurements of two observers moving relative to each otherNormally observers measure different speeds for an objectSpecial relativity relates two such measurements**Rests on the foundation that the speed of light (c) is the same for ALL observers, regardless of either THEIR motion or any motion of the light SOURCE.**26Consequences of SRTime DilationLength ContractionIncreased Mass of particlesLoss of Simultaneity**But FIRST---a little historical perspective.**27Galilean RelativityChoose a frame of referenceNecessary to describe a physical eventAccording to Galilean Relativity, the laws of mechanics are the same in all inertial frames of referenceAn inertial frame of reference is one in which Newtons Laws are validObjects subjected to no forces will move in straight lines28Galilean Relativity ExampleA passenger in an airplane throws a ball straight upIt appears to move in a vertical pathThis is the same motion as when the ball is thrown while at rest on the EarthThe law of gravity and equations of motion under uniform acceleration are obeyed

29Galilean Relativity ExampleThere is a stationary observer on the groundViews the path of the ball thrown to be a parabolaThe ball has a velocity to the right equal to the velocity of the plane

30Galilean Relativity ExampleThe two observers disagree on the shape of the balls pathBoth agree that the motion obeys the law of gravity and Newtons laws of motionBoth agree on how long the ball was in the airConclusion: There is no preferred frame of reference for describing the laws of mechanics31Galilean Relativity LimitationsGalilean Relativity does not apply to experiments in electricity, magnetism, optics, and other areasResults do not agree with experimentsThe observer should measure the speed of the pulse as v+cActually measures the speed as c

32Luminiferous Ether19th Century physicists compared electromagnetic waves to mechanical wavesMechanical waves need a medium to support the disturbanceThe luminiferous ether was proposed as the medium required (and present) for light waves to propagatePresent everywhere, even in empty spaceMassless, but rigid mediumCould have no effect on the motion of planets or other objects33Verifying the Luminiferous EtherAssociated with an ether was an absolute frame where the laws of e & m take on their simplest formSince the earth moves through the ether, there should be an ether wind blowingIf v is the speed of the ether relative to the earth, the speed of light should have minimum (b) or maximum (a) value depending on its orientation to the wind

34Michelson-Morley ExperimentFirst performed in 1881 by Michelson Repeated under various conditions by Michelson and MorleyDesigned to detect small changes in the speed of lightBy determining the velocity of the earth relative to the ether35Michelson-Morley EquipmentUsed the Michelson InterferometerArm 2 is aligned along the direction of the earths motion through spaceThe interference pattern was observed while the interferometer was rotated through 90The effect should have been to show small, but measurable, shifts in the fringe pattern

36Michelson-Morley ResultsMeasurements failed to show any change in the fringe patternNo fringe shift of the magnitude required was ever observedLight is now understood to be an electromagnetic wave, which requires no medium for its propagationThe idea of an ether was discardedThe laws of electricity and magnetism are the same in all inertial framesThe addition laws for velocities were incorrect37Lorentz-FitzGerald ContractionProposed in 1892 by G. Fitzgerald to retain the aether wind.Every object moving at speed v contracts along the direction of motion by a factor equal to

Where b = v/cRe-emerged over a decade later as part of Einsteins Special Theory of Relativity

38Albert Einstein1879 19551905 published four papers2 on special relativity1916 published about General RelativitySearched for a unified theoryNever found one

39Einsteins Principle of RelativityResolves the contradiction between Galilean relativity and the fact that the speed of light is the same for all observersPostulatesThe Principle of Relativity: All the laws of physics are the same within all inertial framesThe Constancy of the Speed of Light: the speed of light in a vacuum has the same value in all inertial reference frames, regardless of the velocity of the observer or the velocity of the source emitting the light40The Principle of RelativityThis is a sweeping generalization of the principle of Galilean relativity, which refers only to the laws of mechanicsThe results of any kind of experiment performed in a laboratory at rest must be the same as when performed in a laboratory moving at a constant speed past the first oneNo preferred inertial reference frame exists!!!It is impossible to detect absolute motion!!!

41Consequences of Special RelativityRestricting the discussion to concepts of length, time, and simultaneityIn relativistic mechanicsThere is no such thing as absolute lengthThere is no such thing as absolute timeEvents at different locations that are observed to occur simultaneously in one frame are not observed to be simultaneous in another frame moving uniformly past the first42Time DilationThe vehicle is moving to the right with speed vA mirror is fixed to the ceiling of the vehicleAn observer, O, at rest in this system holds a laser a distance d below the mirrorThe laser emits a pulse of light directed at the mirror (event 1) and the pulse arrives back after being reflected (event 2)

43Time Dilation, Moving ObserverObserver O carries a clockShe uses it to measure the time between the events (tS)tS is the proper time (see forward 5 slides for proper time)She observes the events to occur at the same placetS = distance/speed = (2d)/c

44Time Dilation, Stationary ObserverObserver O is a stationary observer on the earthHe observes the mirror and O to move with speed vBy the time the light from the laser reaches the mirror, the mirror has moved to the rightThe light must travel farther with respect to O than with respect to O

45Time Dilation, ObservationsBoth observers must measure the speed of the light to be cThe light travels farther for OThe time interval, tM, for O is longer than the time interval for O', tS46Time Dilation, Time Comparisons where

Observer O measures a longer time interval than observer O'

d47Time Dilation, SummaryThe time interval t between two events measured by an observer moving with respect to a clock is longer than the time interval tS between the same two events measured by an observer at rest with respect to the clockA clock moving past an observer at speed v runs more slowly than an identical clock at rest with respect to the observer by a factor of -148Identifying Proper TimeThe time interval tS is called the proper timeThe proper time is the time interval between events as measured by an observer who sees the events occur at the same positionYou must be able to correctly identify the observer who measures the proper time interval

49Alternate ViewsThe view of O that O is really the one moving with speed v to the left and Os clock is running more slowly is just as valid as Os view that O was movingThe principle of relativity requires that the views of the two observers in uniform relative motion must be equally valid and capable of being checked experimentally50Time Dilation Generalization All physical processes slow down relative to a clock when those processes occur in a frame moving with respect to the clockThese processes can be chemical and biological as well as physicalTime dilation is a very real phenomena that has been verified by various experiments51Example 1A college physics laboratory is under observation by aliens traveling on an asteroid. An undergrad seen measuring the period of a mass oscillating on a spring gets a value of 2.00 s. Given that the aliens are cruising by at a constant speed of 0.50c, what period will they determine?Given: v = 0.50c and the proper time measured by the student, tS = 2.00 s.Find: The period determined by the aliens tM 52Example 1Solution: Time dilation problemUse Eq. (26.2)

53Time Dilation Verification Muon DecaysMuons are unstable particles that have the same charge as an electron, but a mass 207 times more than an electronMuons have a half-life of tS = 2.2s when measured in a reference frame at rest with respect to them (a)Relative to an observer on earth, muons should have a lifetime of tS (b)A CERN experiment measured lifetimes in agreement with the predictions of relativity

54The Twin Paradox The SituationA thought experiment involving a set of twins, Speedo and GosloSpeedo travels to Planet X, 20 light years from earthHis ship travels at 0.95cAfter reaching planet X, he immediately returns to earth at the same speedWhen Speedo returns, he has aged 13 years, but Goslo has aged 42 years55The Twins PerspectivesGoslos perspective is that he was at rest while Speedo went on the journeySpeedo thinks he was at rest and Goslo and the earth raced away from him on a 6.5 year journey and then headed back toward him for another 6.5 yearsThe paradox which twin is the traveler and which is really older?56The Twin Paradox The ResolutionRelativity applies to reference frames moving at uniform speedsThe trip in this thought experiment is not symmetrical since Speedo must experience a series of accelerations during the journeyTherefore, Goslo can apply the time dilation formula with a proper time of 42 yearsThis gives a time for Speedo of 13 years and this agrees with the earlier resultThere is no true paradox since Speedo is not in an inertial frame

57Example 2The nearest galaxy to ours is the shapeless star-island known as the Magellanic Cloud (about 1.70 x 105 ly distance). Assuming you can get up to a speed of 0.99999c in a negligible amount of time, how long would you say the trip to that galaxy will take?Given: v = 0.99999c, LS = 1.70 x 105 ly (as measured by an imaginary, stationary ruler).Find: tS (proper time flight time of travelers clock)58Example 2Solution: LM is the length as seen by someone moving with respect to the physical system in which the proper length is LSThe proper time tS is

59Length ContractionThe measured distance between two points depends on the frame of reference of the observerThe proper length, LS, of an object is the length of the object measured by someone at rest relative to the objectThe length of an object measured in a reference frame that is moving with respect to the object is always less than the proper lengthThis effect is known as length contraction60Length Contraction EquationLength contraction takes place only along the direction of motion

LS61Example 3A flying saucer descending straight toward the Earth at 0.4000c is first observed by an astronomer on the planet when it passes a satellite at an altitude of 3000 km. At that instant, what will be the ships altitude as determined by its navigator?Given: the proper length as measured by someone on Earth, LS = 3000 km and v = 0.4000cFind: The measure altitude62Example 3Solution: An observer in motion will see a measured distance as shorter (length contraction.)Using Eq. (26.5):

63Example 4A starship is headed for a galaxy that, according to astronomers, is 200 light-years away from Earth. Flying a direct course, the ship quickly reaches a cruising speed of 0.999c. What will be the Earth-galaxy distance as then determined by the navigator?Given: proper distance, LS = 200 ly and v = 0.999c.Find: The navigators distance64Example 4Solution: Proper length or distance is measured by an observer at rest. The distance measure by an observer in a moving space ship will be shorter (length contraction.)

65SimultaneityIn Special Relativity, Einstein abandoned the assumption of simultaneityThought experiment to show thisA boxcar moves with uniform velocityTwo lightning bolts strike the endsThe lightning bolts leave marks (A and B) on the car and (A and B) on the groundTwo observers are present: O in the boxcar and O on the ground66Simultaneity Thought Experiment Set-upObserver O is midway between the points of lightning strikes on the ground, A and BObserver O is midway between the points of lightning strikes on the boxcar, A and B

67Simultaneity Thought Experiment Results The light signals reach observer O at the same timeHe concludes the light has traveled at the same speed over equal distancesObserver O concludes the lightning bolts occurred simultaneously

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Simultaneity Thought ExperimentBy the time the light has reached observer O, observer O has movedThe light from B has already moved by the observer, but the light from A has not yet reached himThe two observers must find that light travels at the same speedObserver O concludes the lightning struck the front of the boxcar before it struck the back (they were not simultaneous events)69Simultaneity Thought ExperimentTwo events that are simultaneous in one reference frame are in general not simultaneous in a second reference frame moving relative to the firstThat is, simultaneity is not an absolute concept, but rather one that depends on the state of motion of the observerIn the thought experiment, both observers are correct, because there is no preferred inertial reference frame70