k T t T PHYS 2015 Week 13 E-M Waves, Interference Reading Journals Tuesday WebAssign due WEDNESDAY night

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1 PHYS 015 Week 13 -M Waves, Interferene Reading Jurnals Tuesday WebAssign due WDNSDAY night Test Friday: Chap 3 (Magneti indutin); Chap (Indutane, self and mutual, energy, RL iruits). Chap 34 (Waves, eletrmagneti waves, Pynting vetr and energy, intensity, mmentum, and pressure f -M waves, plarizatin t T x A t kx A t x y sin sin ), ( k T f v f T k / / General wave tlbx s far:

2 letrmagneti Waves are traveling eletri and magneti fields. Transverse Wave: and B perpendiular t diretin f travel With diretin f travel given by: Bm k f m f T x

3 letrmagneti Wave Spetrum

4 A red light has a wavelength f abut 650 nm, while a green light has a wavelength f abut 550 nm. Whih light has a higher frequeny? 1. Red. Green 3. Bth the same 4. Nt enugh inf Adapted frm University f Clrad Bulder 0% 0% 0% 0%

5 Quik examples frequenies / wavelengths KUMD FM radi KDAL AM radi 60 Laser in lab 633 nm Mirwave vens, WiFi.4 GHz AC husehld wiring sillates at 60 Hz

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7 nergy in M waves nergy densities: B B u u B B u u B qual ntributins 1 Laser Beam

8 nergy in M waves nergy densities: B B u u B B u u B qual ntributins k t kx B t x B j t kx t x m m ˆ ) sin( ), ( ˆ ) sin( ), ( 1 Laser Beam B B A P A B t U P t A B V u u U ) ( Pwer = energy/time Pwer/area (intensity)

9 Pynting Vetr: instantaneus pwer per unit area (W/m ) arried by -M waves. Osillates rapidly. Intensity = average S (irradiane) (still W/m ) what ur eyes sense f - M waves in the visible part f spetrum I I S avg mb m 1 T T 0 mb m m sin ( kx t) dt Average Pwer = Intensity x Area Intensity = Average Pwer / Area

10 The eletri field f an M wave is shwn at ne pint at ne instant in time. The Pynting vetr is in the z diretin. What s the diretin f the magneti field? 1. - y. + x 3. + z 4. - z 5. - x 6. + y S 0% 0% 0% 0% 0% 0%

11 A pint sure f M waves emits pwer P istrpially (unifrmly in all diretins). Imagine tw spherial surfaes arund the sure. Cmpare the pwer (P) passing thrugh eah surfae and the intensity (I) at eah surfae: P1, P and I1 and I. 1. P < P1 and I < I1. P = P1 and I = I1 3. P = P1 and I < I1 4. P > P1 and I1 = I 5. ther 1 0% 0% 0% 0% 0%

12 A pint sure f radiatin emits pwer P istrpially (in all diretins unifrmly). A detetr f area a d is lated a distane R away frm the sure. What is the pwer P reeived by the detetr? P 4 R a P a R d d R detetr a d P a d R P P R a d Adapted frm University f Clrad Bulder 0% 0% 0% 0%

13 Tw radi dishes are reeiving signals frm a radi statin whih is sending ut radi waves equally in all diretins with ttal pwer P. Dish is twie as far away as Dish 1, but has twie the diameter. Whih dish reeives mre pwer? 1. Dish 1. Dish 3. Same fr bth 4. Need mre inf Dish 1 Dish Adapted frm University f Clrad Bulder 0% 0% 0% 0%

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15 Linear Mmentum arried by M waves Radiatin Pressure, Fre nergy in segment U Pt IAt Arding t Maxwell: linear mmentum in segment is p U Pt IAt Rate f hange r passage f mmentum thru the rsssetin A rrespnds t a radiatin fre F rad p t IA And pressure is fre per unit area, s there is a radiatin pressure P rad F A rad I (Mind yur P s fr pwer, radiatin pressure )

16 A small lump f putty hits and stiks t a muh heavier glider initially at rest n an air-trak. A rubber ball with the same mass and speed as the putty bunes nearly elastially bak ff the glider. In whih ase is des the glider end up mving faster? 1. Putty. Ball 3. Same fr bth 0% 0% 0% Adapted frm University f Clrad Bulder

17 Radiatin fre IA F rad P Radiatin Pressure F A I rad rad Perfetly refleting surfae need the []; Perfetly absrbing surfae, use a [1] Laser tweezers urpean Suthern Observatry s/thumb/8/81/cmetrbit01.svg/50px- Cmetrbit01.svg.png

18 Plarizatin f M Waves The plarizatin f light desribes hw the eletri field in the M wave sillates. Linearly r plane plarized light has the vetr parallel t a single plane Other types f plarizatin f waves: Cirular, elliptial, and mst mmnly randm/ r unplarized

19 Plarized Light Unplarized r randmly plarized light has its instantaneus plarizatin diretin vary randmly with time. One an prdue unplarized light by the additin (superpsitin) f tw perpendiularly plarized waves with randmly varying amplitudes. If the tw perpendiularly plarized waves have fixed amplitudes and phases, ne an prdue different plarizatins suh as irularly r elliptially plarized light.

20 Plarizing sheets / Plarid filters I 0 Only the eletri field mpnent alng the plarizing diretin f plarizing sheet is passed (transmitted); I The perpendiular mpnent is blked (absrbed by lng-hain mleules). (33-15)

21 Intensity f Transmitted Plarized Light Sine nly the mpnent f the inident eletri field parallel t the plarizing axis is transmitted. s transmitted Intensity f transmitted light, plarized inident light: y I I0 s Fr unplarized light, varies randmly in time: s s I I I I 0 avg 0 avg 0 1 Intensity f transmitted light, unplarized inident light: I 1 I 0

22 Intensity f transmitted light, plarized inident light: I I s 0 Intensity f transmitted light, unplarized r randmly plarized inident light: I 1 I 0