Lecture 24: TUE 20 APR 2010 Ch.33.6–10: E&M WavesRadiation PressurePowerPoint PresentationSlide 4Slide 5EM waves: polarizationEM Waves: PolarizationExampleReflection and RefractionSlide 10Slide 11Water on Desert Road IllusionSlide 13Chromatic DispersionSlide 15Slide 16Slide 17Total Internal ReflectionSlide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Polarization By ReflectionSlide 27Lecture 24: TUE 20 APR Lecture 24: TUE 20 APR 20102010 Ch.33.6–10: E&M Waves Ch.33.6–10: E&M WavesPhysics 2102Jonathan DowlingQuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.Radiation PressureRadiation PressureWaves not only carry energy but also momentum. The effect is very small (we don’t ordinarily feel pressure from light). If lightis completely absorbed during an interval Dt, the momentum transferred is given bycupΔ=ΔtpFΔΔ=Newton’s law:Now, supposing one has a wave that hits a surfaceof area A (perpendicularly), the amount of energy transferred to that surface in time Dt will betIAU Δ=ΔthereforectIApΔ=ΔIAcIAF =pr=Ic (total absorption), pr=2Ic (total reflection)pr=Ic (total absorption), pr=2Ic (total reflection)Radiation pressure:and twice as much if reflected.[Pa=N/m2]FQuickTime™ and a decompressorare needed to see this picture.Radiation Pressure & Comet TailsQuickTime™ and a decompressorare needed to see this picture.Solar Sails: Photons Propel Spacecraft!QuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.StarTrek DS9NASA ConceptNASA DemoQuickTime™ and a decompressorare needed to see this picture.Radio transmitter:If the dipole antennais vertical, so will bethe electric fields. Themagnetic field will behorizontal.The radio wave generated is said to be “polarized”.In general light sources produce “unpolarized waves”emitted by atomic motions in random directions.EM waves: polarizationEM waves: polarizationWhen polarized light hits a polarizing sheet,only the component of the field aligned with thesheet will get through.)= θcos(EEyAnd therefore:θ20cosII =θ20cosII =Completely unpolarized light will have equal components in horizontal and verticaldirections. Therefore running the light througha polarizer will cut the intensity in half: I=I0/2Completely unpolarized light will have equal components in horizontal and verticaldirections. Therefore running the light througha polarizer will cut the intensity in half: I=I0/2EM Waves: PolarizationEM Waves: PolarizationExampleExampleInitially unpolarized light of intensity I0 is sent into a system of three polarizers as shown. What fraction of the initial intensity emerges from the system? What is the polarization of the exiting light?• Through the first polarizer: unpolarized to polarized, so I1=½I0. • Into the second polarizer, the light is now vertically polarized. Then, I2 = I1cos260o = 1/4 I1 = 1/8 I0. • Now the light is again polarized, but at 60o. The last polarizer is horizontal, so I3 = I2cos230o = 3/4 I2 =3 /32 I0 = 0.094 I0. • The exiting light is horizontally polarized, and has 9% of the original amplitude.Reflection and Reflection and RefractionRefractionLaw of reflection (Light Bounces): the angle of incidence 1 equals the angle of reflection ’1. 1 = ’1Law of reflection (Light Bounces): the angle of incidence 1 equals the angle of reflection ’1. 1 = ’1Law of Refraction (Light Bends):n2sinθ2=n1sinθ1HHSnell's LawLaw of Refraction (Light Bends):n2sinθ2=n1sinθ1HHSnell's LawWhen light finds a surface separating two media (air and water, for example), a beam gets reflected (bounces) and another gets refracted (bends).n is the index of refraction of the medium. In vacuum, nH=H1. In air, nH~1. In all other media, nH>H1.QuickTime™ and a decompressorare needed to see this picture.Plastic GlassSpeed of Light is Slowed n>1v ≡c / nHHHH&HHHHn ≥1HHHHH⇒ HHHHv≤cn=1n>1Hits SandRoadvLvRTurns LeftExampleExampleWater has n=1.33. How much does a beam incident at 45o refracts? n2 sin 2= n1 sin 1 sin 2= (n1 /n2) sin 1 =(1/1.33) sin 45o =0.00982= 32on2 sin 2= n1 sin 1 sin 2= (n1 /n2) sin 1 =(1/1.33) sin 45o =0.00982= 32oQuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.Water on Desert Road Water on Desert Road IllusionIllusionThe index of refraction decreases with temperature: the light gets refracted and ends up bending upwards. We seem to see water on the road, but in fact we are looking at the sky! The index of refraction decreases with temperature: the light gets refracted and ends up bending upwards. We seem to see water on the road, but in fact we are looking at the sky!QuickTime™ and a decompressorare needed to see this picture.Water on the Desert Road MirageChromatic DispersionChromatic DispersionThe index of refraction depends on the wavelength (color) of the light.QuickTime™ and a decompressorare needed to see this picture.The Single RainbowQuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.The Double RainbowTotalInternalReflection!Total Internal ReflectionTotal Internal ReflectionFrom glass to air, the law of refraction uses n2<n1, so 2> 1: it may reach 90o or more: the ray is “reflected” instead of “refracted”.For glass (fused quartz) n=1.46, and the critical angle is 43o: optical fibers!Condition for TIR:n2 sin2= n1 sin1 &2≥ 90n1>1n2~112QuickTime™ and a decompressorare needed to see this picture.Fish Underwater Can’t See Entire Sky!TotalInternalReflection ZoneQuickTime™ and a decompressorare needed to see this picture.The cut of the diamond favors total internal reflection. Most rays entering the top of the diamond will internally reflect until they reach the top face of the diamond where they exit. This gives diamonds their bright sparkle. A fiber optic is a glass "hair" which is so thin that once light enters one end, it can never strike the inside walls at less than the critical angle. The light undergoes total internal reflection each time it strikes the wall. Fiber optic cables are used to carry telephone and computer communications.Fiber Optic
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