Lecture 13 Electromagnetic Waves Ch. 33• Cartoon• Opening Demo• Topics– Electromagnetic waves– Traveling E/M wave - Induced electric and induced magnetic amplitudes– Plane waves and spherical waves– Energy transport Poynting vector– Pressure produced by E/M wave– Polarization– Reflection, refraction,Snell’s Law, Internal reflection– Prisms and chromatic dispersion– Polarization by reflection-Brewsters angleElectromagnetic WavesEye Sensitivity to ColorProduction of Electromagnetic wavesTo investigate further the properties of electromagnetic waves we consider the simplest situation of a plane wave. A single wire with variable current generates propagating electric and magnetic fields with cylindrical symmetry around the wire. If we now stack several wires parallel to each other, and make this stack wide enough (and the wires very close together), we will have a (plane) wave propagating in the z direction, with E-field oriented along x, E = Ex (the current direction) and B-field along y B=By (Transverse waves)Electromagnetic WaveWave EquationHow the fieldsvary at a PointP in space asthe wave goesbySpherical waves Plane wavesA point source of light generates a spherical wave. Light isemitted isotropically and the intensity of it falls off as 1/r2Let P be the power of the sourcein joules per sec. Then the intensity of light at a distance r is 24 rPI!=What do we mean by Intensity oflight?Spherical Waves17. The maximum electric field at a distance of 10 m from an isotropicpoint light source is 2.0 V/m. Calculate(a) the maximum value of the magnetic field and(b) the average intensity of the light there?(c) What is the power of the source?(a) The magnetic field amplitude of the wave isTcEBsmmVmm98107.610998.20.2!"="==(b) The average intensity isIavg=E2m2µ0c=2.0Vm( )22 4!" 10#7T $Vm( )2.998 " 108ms( )= 5.3 " 10#3Wm2(c) The power of the source is( ) ( )WmIrPmWavg7.6103.510442322=!=="##Radiation pressure: Light carries momentum Pr=IcThis is the force per unit area felt by an object that absorbs light. (Black piece of paper)) Pr=2IcThis is the force per unit area felt by an object that reflects light backwards. (Aluminum foil)Another property of lightPolarization of lightResolved into its y and z-components The sum of the y-components and z components are equalPass though a polarizing sheet aligned to pass only the y-componentPass though a polarizing sheet aligned to pass only the y-componentMalus’s LawIntensity I0One Half RuleHalf the intensity outI =I02I2= I1cos2!I0I1=I02I ! Ey2Ey= E cos"y35. In the figure, initially unpolarized light is sent through threepolarizing sheets whose polarizing directions make angles of !1 = 40o,!2 = 20o, and !3 = 40o with the direction of the y axis. What percentageof the light’s initial intensity is transmitted by the system? (Hint: Becareful with the angles.)Let Io be the intensity of the unpolarized light thatis incident on the first polarizing sheet. Thetransmitted intensity of is I1 = (1/2)I0, and thedirection of polarization of the transmitted light is!1 = 40o counterclockwise from the y axis in thediagram. The polarizing direction of the secondsheet is !2 = 20o clockwise from the y axis, so theangle between the direction of polarization that isincident on that sheet and the the polarizingdirection of the sheet is 40o + 20o = 60o. Thetransmitted intensity is,60cos2160cos20212ooIII ==and the direction of polarization of the transmitted light is 20o clockwisefrom the y axis.I1I2I3I035. In the figure, initially unpolarized light is sent through threepolarizing sheets whose polarizing directions make angles of !1 = 40o,!2 = 20o, and !3 = 40o with the direction of the y axis. What percentageof the light’s initial intensity is transmitted by the system? (Hint: Becareful with the angles.)The polarizing direction of the third sheet is !3= 40o counterclockwise from the y axis.Consequently, the angle between thedirection of polarization of the light incident onthat sheet and the polarizing direction of thesheet is 20o + 40o = 60o. The transmittedintensity isI3= I2cos260oI2= I1cos260oI1=12I0I3I0=12cos460 = 3.125 ! 10"2Thus, 3.1% of the light’sinitial intensity is transmitted.Polarization can be produced by:• Scattering• ReflectionLight scattered from sky is partially polarizedLight scattered from your car hood is polarizedin the plane of the hood.See Brewsters LawLight is also refracted when changing