University Physics II
University Physics II PHY 146
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This 31 page Class Notes was uploaded by Willard Grady on Monday October 5, 2015. The Class Notes belongs to PHY 146 at Central Michigan University taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/218950/phy-146-central-michigan-university in Physics 2 at Central Michigan University.
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Date Created: 10/05/15
Lecture 48 Electromagnetic waves Chapter 33 Review Radiation pressure Polarization Reflection and refraction Review Electromagnetic waves Maxwell Eqs EEm sinkx al fi27zk27zcacT wave length B Bm sinkx cot amp 3m B Speed of electromagnetic waves 2 299792458 ms C Vzuogo Ex B direction of travel of the wave Poynting vector iEx1 IE LEfms 0 610 Light Pressure Energy transport gt momentum total energy carried by wave Q Momentum speed c ener I ener c momentum IntenSIty gy gt gy timearea c t1mearea t1mearea momentum I FOI CG an Force Q E Rednetuen Preeeure t1me C area Light preeeureg thewgh ight netieeeto e gt te Leuehee ewey frem the em Example The intensity of sunlight in Michigan is approx 10 mWcmz What is the amplitude Emax of the electric field What is the pressure on the black ground pretend it is perfectly absorbing On the white sidewalk pretend it is perfectly reflecting Finally what is the maximum amount of energy a solar cell could absorb in 1 sec assuming an area of 1m2 1 Eliax 2 1W X 100 crzn 2100 Wm2 1000 mW 1m 2 3779 EM 2 pane100 275 NC 275 Vm 1 100 W 2 Black ground Pressure Tm 3310 7 Nm2 6 310 ms solution I 10 mWcm2 gtlt Reflective surface X2 enhancement gt Pressure 610 6 Nm2 Energy average energy density x volume 100 J a V 4 EoEflaX I 7 3 2 8 8 3 gt272 3310 Jm Areaxctzlm 310 ms 152310 In 4 I 5 Dim Polarization Natural light unpolarized Fig 3311 u a W Polarized light elds E B y oscillate in a single plane Fig 3410 E z z T 39avolcngth nm E 700 300 500 1100 b b Visible spectrum 7 Wavelenglh m i 3 7 u I r r I 7 In8 1039 10 10quot 10quot Inquot to2 10 1 10I 101 Io 3 1039quot 10quot int 10quot m h 10 10quot 10 l104110431044III 10quot l I I I l l I I I l I l l l Longwaves Radio waves Infrared IUlevioleL Xrays Gamma rays 1 l l l l l l l l l l l l l I I l I 10 102 104 194 Ion 10 107 10gt 109 101 1911 1012 1013 10le 1015 10m 1017 101 101 102K 1021 1022 102 10 l t Frequency Hz gt i FM radi n I i Maritime Maritime aeronautical t 1 Maritime and AM aeronautical 4 Citizens band 1 l aeronautical uses radio and mobile radio and mobile radio I I I I I I I I 5 104 10quot 10 107 10 10 10 lquot 10 391 Frcquonry I 7 Unpolarized Light We have primarily been considering light that has a definite polarization eg linear or circular Most sources a candle the sun any light bulb produce light that is unpolarized it does not have a definite direction of the electric field there is no definite phase between orthogonal components the atomic or molecular dipoles that emit the light are randomly oriented in the source the intensity of light transmitted through a polarizer is always half the intensity of the unpolarized input regardless of the orientation of the polarizer though of course the output is polarized These are all equivalent ways of describing the same thing Linear Polarization How else can we produce linearly polarized LP em waves Absorpreflect of vector component of wave perp to polarizer TA trans ission axis LP microwave source slotted polarized rag The E eld component parallel to the slots is absorbed andor reflected The E eld component perpendicular to the slots is transmitted Long molecules absorb E eld parallel to molecule Il lll IIIIII ll lll TA iiIIIII transmission axis Absorption produces LP em waves but in so doing it also reduces intensity of the wave How much Polarization Polarizing sheet unpolarized light becomes polarized after passing through Fig 3312 Onehalf rule Incident light ray 1 v UnpolaIized light 1 2 A Polarizing sheet v Vertically polarized light Polarization cont See Fig 3313 Ey 2 E0056 I 0C E2 Cosinesquared rule 121000526 Polarizing direction Polarizer analyzer setup Fig 3314 LP Intensity Reduction TA UP unpolarized light 10 This set of two linear polarizers produces LP light What is the final intensity First LP transmits 12 of the unpolarized light 11 12 10 Second LP projects out the E eld component parallel to the TA a A A E E 9 E2 51 n 210C120 gt 221100829 This result is called the Law of Malus for LP light incident on LP Sample Problem 333 Fig 34l6a shows a system of three polarizing sheets in the path of initially polarized light The polarizing direction of the first sheet is parallel to the y aXis that of the second sheet is 600 counterclockwise from the y aXis and that of the third sheet is parallel to the x aXis What fraction of the initial intensity 10 of the light emerges from the system and how is that light polarized I l I 0 I 1 3 0094 2 2 1 2 0 I0 I I0 cos 9 9 cos2 60 0 1 0 211cosz60 Elojcos260 10 cos2 60 I3 12 cos2 30 210 jcos2 30 2 o 2 o 10 cos 60 cos 30 2009410 2 Polarization by Scattering Suppose unpolarized light encounters an atom and scatters energy absorbed amp reradiated What happens to the polarization of the scattered light The scattered light is preferentially polarized perpendicular to the plane of the scattering For example assume the incident unpolarized light is moving in the z direction Scattered light observed along the xdirection scattering plane xz will be polarized along the ydirection Scattered light observed along the ydirection scattering plane yZ will be polarized along the x direction This bOXW j y which scattef the light beam 3gt Applications Sunglasses The reflection off a horizontal surface eg water the hood of a car etc is strongly polarized Which way A perpendicular polarizer can preferentially reduce this glare Polarized sky The same argument applies to light scattered off the sky Si a Gag 3 Why is that In many cases light is radiatedscattered by oscillating electric dipoles Maximum intensity Intensity lobe l L Less intensity No radiation along direction of motion Start with sunlight with all polarizations amp randomly oriented dipoles m quot f x Dipole oscillates into the paper Horizontal dipoles reradiate Hpolarized light downward Do not respond to incident Vlight Dipole oscillates vertically Vertical dipoles reradiate Vpolarized light to the sides not downward Do not respond to incident Hlightlj Geometric Optics So far EM waves in vacuum What happens to EM waves usually light in different materials we must include K in Maxwell s Equations gt index of refraction n Restriction waves whose wavelength is much shorter than the objects with which it interacts Pretend that light propagates in straight lines called rays Our primary focus will be on the REFLECTION and REFRACTION of these rays at the interface of two materials reflected ray incident ray quotx MATERIAL 1 MATERIAL 2 refracted 15 ray Reflection and Refraction Geometrical Optics light travels in straight line Fig 3317 incident reflected and refracted rays Norlmal Incident Re flCth ray lay Wave ront 9 1 Interface Glass refraction 62 126th Index of refraction Table 331 my I n 3 v Reflection and Refraction Law of reflection Reflected ray lies in the plane of incidence Law of refraction Fig 33181 2 Refracted ray lies in the plane of i n2 sm 62 2 n1 sm 61 Reflection The angle of incidence equals the angle of reflection 6i 9r where both angles are measured from the normal Note also that all rays lie in the plane of incidence Why This law is quite general we supply a limited justification when surface is a good conductor reasonable restriction since reflection is dominant in this case First consider a wave E Excoskz wt hitting a conductor at normal incidence The electrons on the surface of the metal will experience a force FeE gt acceleration gt radiation in i2 MEW 18 Shedding Light on Reflection By superposition which works just as well for oscillating fields the total field incident field reradiated field Etot Ein Ererad But we know Etot 0 inside the conductor Therefore E E rerad 1n The field created by the surface electrons completely cancels the incident field inside the conductor and also is the reflected wave Now consider nonnormal incidence The components ofE parallel to the surface of the incident and reflected waves must cancel for the same reason Ex 2 E0056 Em E cos 9r EixErx 0 Qizg Index of Refraction The wave incident on an interface can not only reflect but it can also propagate into the second material The speed of an electromagnetic wave is different in matter than it is in vacuum 1 Recall we derived from Maxwell s eqns in vacuum 6 l 050 o How are Maxwell s eqns in matter different 50 gt 55 50 K 1 1 yo y go for most materials J W J Therefore the speed of light in matter is related to the speed of light in C vacuum by C v n where n index of refraction of the material n z VIC gt 1 The index of refraction is frequency dependent For example in glass 20 nbme 153 nred 152 Chromatic Dispersion Index of refraction varies with wavelength Fig 3319 3320 blue refracted more than red Normal l Inride R leried white light l l1llE39 Iig it 148 l l H l H1 Q l o l 395 I Glass 112 g 147 92h L1 I 9 H 2r 0 Renamed 5 light 39U E a Normal I Incident 1 Re ected 1 white light white light I 00 O O 400 500 600 700 800 Wavelength nm 21 Dispersion Ultraviolet absorption bands cause a rising index of refraction in the visible Split int Colors 22 Triangular Prism Dispersion in more detail Effects of wavelength dependence of n n03 1 Dg 2 Dense int glass Dispersion n depends on wavelength Light int glass Index of refraction 1 Crystal quartz In many dielectric materials like glass the p i 7 characteristic no is in the f 339 Vitreousquanz ultraviolet 39 39 quot osilicale crown glass nblue gt rIred Wavelength2mm Vblue lt Vred Checkpoint 335 nzsinez n1sin61 Which of the drawings here if any show physically possible re ection a Yes 7 No c No Total Internal Reflection See Fig 3324 Critical angle n1 sinBc 2 n2 sin 900 60 sin 1n 2 n1 Application optical fibers crirtl39cal angle 26 Total Internal Reflection Consider light moving from glass 11115 to air 11210 n1 reflected ray n2 mz gt1 9 gt9 21 1 111 6 1 n2 le light is bent away from the normal as 61 gets bigger 62 gets bigger but 62 can never get bigger than 90 I r I 3 7 39I 1quot I l x l I I v V 1 In general if sin 61 gt n2 111 we have NO refracted ray we have TOTAL INTERNAL REFLECTION For example light in water which is incident on an air surface with angle 01 gt 0c sin11015 4180 will be totally reflected This property is the basis for the optical fibers used in communication 27 Sample Problem 335 Fig 3326 shows a triangular prism of glass in air an incident ray enters the glass perpendicular to one face and is totally re ected at the far glassair interface as indicated If 91 is 45 what can you say about the indeX of refraction n of the glass Total 1 n quot2 1 internal 6 s1n 2 C re ection n1 r11 n QC 2 sin 1 1 lt 45quot n lltsin45 3 n n Polarization by Reflection Unpolarized incident ray Fig 3327 reflected ray perpendicular on incidence plane refracted ray unpolarized Brewster s Law Brewster angle Incident unpolarized Re ected ray ray QB Q 900 n1 sin QB r22 sin 6r 2 n2 sin90 QB r12 cos QB n Qthan 1 2tan 1n n1 Refracted ray 0 Component perpendicular to page 4D Component parallel to page 29 Checkpoint 336 Suppose the prism in this sample problem has the index of refraction n 14 Does the light still totally internally re ect if we keep the incident ray horizontal but rotate the prism a 100 clockwise and b 100 counterclockwise in Fig 3426 Total internal re ection Why is the sky blue Light from Sun scatters off of air particles Rayleigh scattering Rayleigh scattering is wavelengthdependent Shorter wavelengths blue end of the visible spectrum scatter more Haylergh scattering 9quot air mmewl u5 if 3 if a 9 Tee strong wavelength dbpenuenca of it ah I a Fayt igh scattering enhancesme snarl r 4 waivelaughs givmg us The blue Sky 1 The scattering at 40f nm is 94 1mg as great as that at oo nm lor equal Ubseweri incident Intensity This is also why sunsets are red At sunset the light has to travel through more of the atmosphere If longer wavelengths red and orange scatter less The more air sunlight travels through the redder it will appea This effect is more pronounced if there are more particles in the atmosphere eg sulfur aerosols from industrial pollution
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