Lecture 32 Chapter 34 Electromagnetic Waves EM Waves Review Wavelengths of 108 to 1016 meters 10 1024 Hz Traveling wave of both E and B fields E field is B field Wave moves in direction to both E and B fields E and B vary sinusoidally with same frequency At large distances fields are in phase r r E B E E m sin kx t B Bm sin kx t Review EM waves move at the 8 c 3 10 m s speed of light c in free space vacuum or air v Relate velocity of wave by k Using definition of and 2 wave number k 2 f k Find velocity of wave is Also defined as Em c Bm v c f c 1 0 0 Review r 1 r r S E B Poynting vector S rate of energy transported per unit area Instantaneous energy flow rate 0 S 1 0 Defined intensity I to be time averaged value of S I S avg energy time power area ave area ave I S avg 1 c 0 E rms 2 EB EM Waves 12 Problem Isotropic point light source as power of 250 W You are 1 8 meters away Calculate the rms values of the E and B fields To find Erms need 1 Ps 2 I E rms I 2 c 0 4 r Find intensity I from Erms Ic 0 Erms Ps c 0 2 4 r 250 3 108 1 26 10 8 48 1V m 2 4 1 8 EM Waves 13 Problem Isotropic point light source as power of 250 W You are 1 8 meters away Calculate the rms values of the E and B fields To find Brms need Erms c Brms Brms Brms Erms c 48 1V m 7 1 6 10 T 8 3 10 m s EM Waves 14 Look at sizes of Erms and Brms Erms 48 1V m B rms 1 6 10 7 T This is why most instruments measure E Does not mean that E component is stronger than B component in EM wave Can t compare different units Average energies are equal for E and B EM Waves 15 The energy density of electric field uE is equal to energy density of magnetic field uB uE 0 E 1 2 2 E Bc uE 0 cB 0c B 1 2 2 2 1 2 2 1 1 B 2 uE 0 B 2 0 0 2 0 uE uB 2 c 1 0 0 2 B uB 2 0 EM Waves 16 EM waves linear have momentum momentum as well as energy Light shining on object exerts a pressure radiation pressure Object s change in momentum is related to its change in energy If object absorbs all radiation from EM p wave total absorption If object reflects all radiation back original direction total reflection in U c 2 U p c EM Waves 17 Just defined intensity I as power per unit area A so power is Change in energy is amount of power P in time t P IA U P t IA t Want force of radiation on object For total absorption U p Find force is p F t c p U IA t IA F t c t c t c EM Waves 18 For total reflection back along original path 2 U p c p 2 U 2 IA t 2 IA F c t c t c t Express in terms of radiation pr which is force area SI unit is N m2 called pascal Pa Total absorption I pr c pressure F pr Total reflection 2I pr c A EM Waves 19 Source emits EM waves with E field always in same plane wave is polarized Example television station Indicate a wave is polarized by drawing double arrow Plane containing the E field is called plane of oscillation EM Waves 20 Source emits EM waves with random planes of oscillation E field changes direction is unpolarized Example light bulb or Sun Resolve E field into components Draw unpolarized light as superposition of 2 polarized waves with E fields to each other EM Waves 21 Transform unpolarized light into polarized by using a polarizing sheet Sheet contains long molecules embedded in plastic which was stretched to align the molecules in rows E field component to polarizing direction of sheet is passed transmitted but component is absorbed EM Waves 22 What is the intensity I of the light transmitted by polarizing sheet For unpolarized light separate E field into components Sum of 2 components 1 are equal but only light 2 to polarizer is transmitted One half rule Intensity of unpolarized wave after a polarizer is half of original I I0 EM Waves 23 For polarized light resolve E into components Transmitted component is E y E cos Use definition of intensity I 1 c 0 E 2 1 c 0 E 2 cos 2 I 0 cos 2 Cosine squared rule Intensity of polarized wave changes as cos2 I I 0 cos 2 EM Waves 24 Have 2 polarizing sheets First one called polarizer Second one called analyzer Intensity of unpolarized light going through polarizer is I 1 2 I0 Light is now polarized and intensity of light after analyzer is given by I I 0 cos 2 EM Waves 25 Checkpoint 4 Unpolarized light hits a polarizer and then an analyzer The polarizing direction of each sheet is indicated by dashed line Rank pairs according to fraction of initial intensity which is passed greatest first EM Waves 26 Look at relative orientation of polarization direction between the 2 sheets What is the intensity if the sheets are Polarized all light passes Polarized to each other no light passes For angles in between get more light if closer to a d b c
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