Lect15 handout

Download Lect15 handout

Post on 18-Dec-2014

151 views

Category:

Technology

0 download

Embed Size (px)

DESCRIPTION

 

TRANSCRIPT

<ul><li> 1. Electromagnetic Waves and Polarization Physics 102: Lecture 15 </li> <li> 2. Today: Electromagnetic Waves <ul><li>Energy </li></ul><ul><li>Intensity </li></ul><ul><li>Polarization </li></ul></li> <li> 3. Preflight 15.1, 15.2 1 2 3 In order to find the loop that dectects the electromagnetic wave, we should find the loop that has the greatest flux through the loop. x z y E B loop in xy plane loop in xz plane loop in yz plane </li> <li> 4. </li> <li> 5. Propagation of EM Waves <ul><li>Changing B field creates E field </li></ul><ul><li>Changing E field creates B field </li></ul><ul><li>E = c B </li></ul>If you decrease E, you also decrease B! x z y This is important ! </li> <li> 6. Preflight 15.4 Suppose that the electric field of an electromagnetic wave decreases in magnitude. The magnetic field: 1 increases 2 decreases 3 remains the same E=cB </li> <li> 7. Energy in EM wave <ul><li>Light waves carry energy but how? </li></ul><ul><li>Electric Fields </li></ul><ul><li>Recall Capacitor Energy: </li></ul><ul><li>U = C V 2 </li></ul><ul><li>Energy Density (U/Volume): u E = 0 E 2 </li></ul><ul><li>Average Energy Density: </li></ul><ul><li><ul><li> u E = ( 0 E 0 2 ) </li></ul></li></ul><ul><li><ul><li> = 0 E 2 rms </li></ul></li></ul><ul><li>Magnetic Fields </li></ul><ul><li>Recall Inductor Energy: </li></ul><ul><li><ul><li><ul><li>U = L I 2 </li></ul></li></ul></li></ul><ul><li>Energy Density (U/Volume): </li></ul><ul><li>u B = B 2 / 0 </li></ul><ul><li>Average Energy Density: </li></ul><ul><li><ul><li><ul><li>u B = ( B 0 2 / 0 ) </li></ul></li></ul></li></ul><ul><li><ul><li><ul><li>= B 2 rms / 0 </li></ul></li></ul></li></ul></li> <li> 8. </li> <li> 9. Energy Density <ul><li>Calculate the average electric and magnetic energy density of sunlight hitting the earth with E rms = 720 N/C </li></ul>Example </li> <li> 10. Energy Density <ul><li>Calculate the average electric and magnetic energy density of sunlight hitting the earth with E rms = 720 N/C </li></ul>Use Example </li> <li> 11. Energy in EM wave <ul><li>Light waves carry energy but how? </li></ul><ul><li>Electric Fields </li></ul><ul><li>Recall Capacitor Energy: </li></ul><ul><li>U = C V 2 </li></ul><ul><li>Energy Density (U/Volume): u E = 0 E 2 </li></ul><ul><li>Average Energy Density: </li></ul><ul><li><ul><li> u E = ( 0 E 0 2 ) </li></ul></li></ul><ul><li><ul><li> = 0 E 2 rms </li></ul></li></ul><ul><li>Magnetic Fields </li></ul><ul><li>Recall Inductor Energy: </li></ul><ul><li><ul><li><ul><li>U = L I 2 </li></ul></li></ul></li></ul><ul><li>Energy Density (U/Volume): </li></ul><ul><li>u B = B 2 / 0 </li></ul><ul><li>Average Energy Density: </li></ul><ul><li><ul><li><ul><li>u B = ( B 0 2 / 0 ) </li></ul></li></ul></li></ul><ul><li><ul><li><ul><li>= B 2 rms / 0 </li></ul></li></ul></li></ul><ul><li>In EM waves, E field energy = B field energy! ( u E = u B ) </li></ul><ul><li>u tot = u E + u B = 2u E = 0 E 2 rms </li></ul></li> <li> 12. </li> <li> 13. Intensity (I or S) = Power/Area <ul><li>Energy (U) hitting flat surface in time t </li></ul><ul><li><ul><li><ul><li>= Energy U in red cylinder: </li></ul></li></ul></li></ul><ul><li><ul><li>U = u x Volume </li></ul></li></ul><ul><li><ul><li> = u (AL) = uAct </li></ul></li></ul><ul><li>Power (P): </li></ul>A L=ct <ul><li><ul><li>P = U/t </li></ul></li></ul><ul><li><ul><li> = uAc </li></ul></li></ul><ul><li>Intensity (I or S): </li></ul><ul><li> S = P/A [W/m 2 ] </li></ul><ul><li><ul><li>= u c = c 0 E 2 rms </li></ul></li></ul>23 U = Energy u = Energy Density (Energy/Volume) A = Cross section Area of light L = Length of box </li> <li> 14. Polarization <ul><li>Transverse waves have a polarization </li></ul><ul><li><ul><li>(Direction of oscillation of E field for light) </li></ul></li></ul><ul><li>Types of Polarization </li></ul><ul><li><ul><li>Linear (Direction of E is constant) </li></ul></li></ul><ul><li><ul><li>Circular (Direction of E rotates with time) </li></ul></li></ul><ul><li><ul><li>Unpolarized (Direction of E changes randomly) </li></ul></li></ul>x z y </li> <li> 15. Linear Polarizers <ul><li>Linear Polarizers absorb all electric fields perpendicular to their transmission axis. </li></ul></li> <li> 16. </li> <li> 17. Unpolarized Light on Linear Polarizer <ul><li>Most light comes from electrons accelerating in random directions and is unpolarized. </li></ul><ul><li>Averaging over all directions: S transmitted = S incident </li></ul>Always true for unpolarized light! </li> <li> 18. Linearly Polarized Light on Linear Polarizer (Law of Malus) <ul><li>E tranmitted = E incident cos( ) </li></ul><ul><li>S transmitted = S incident cos 2 ( ) </li></ul> is the angle between the incoming lights polarization, and the transmission axis E Transmitted E absorbed =E incident cos( ) TA Transmission axis Incident E </li> <li> 19. ACT/Preflight 15.6 Unpolarized light (like the light from the sun) passes through a polarizing sunglass (a linear polarizer). The intensity of the light when it emerges is <ul><li>zero </li></ul><ul><li> 1/2 what it was before </li></ul><ul><li> 1/4 what it was before </li></ul><ul><li> 1/3 what it was before </li></ul><ul><li> need more information </li></ul></li> <li> 20. </li> <li> 21. ACT/Preflight 15.7 Now, horizontally polarized light passes through the same glasses (which are vertically polarized). The intensity of the light when it emerges is <ul><li>zero </li></ul><ul><li> 1/2 what it was before </li></ul><ul><li> 1/4 what it was before </li></ul><ul><li> 1/3 what it was before </li></ul><ul><li> need more information </li></ul></li> <li> 22. Law of Malus 2 Polarizers Cool Link 1) Intensity of unpolarized light incident on linear polarizer is reduced by . S 1 = S 0 S = S 0 S 1 S 2 2) Light transmitted through first polarizer is vertically polarized. Angle between it and second polarizer is =90. S 2 = S 1 cos 2 (90) = 0 Example </li> <li> 23. How do polaroid sunglasses work? incident light unpolarized reflected light partially polarized the sunglasses reduce the glare from reflected light </li> <li> 24. </li> <li> 25. Law of Malus 3 Polarizers 2) Light transmitted through first polarizer is vertically polarized. Angle between it and second polarizer is =45. I 2 = I 1 cos 2 (45) = I 0 cos 2 (45) 3) Light transmitted through second polarizer is polarized 45 from vertical. Angle between it and third polarizer is =45. I 3 = I 2 cos 2 (45) I 2 = I 1 cos 2 (45) = I 0 cos 4 (45) = I 0 /8 I 1 = I 0 Example </li> <li> 26. ACT: Law of Malus A B 1) S 2 A &gt; S 2 B 2) S 2 A = S 2 B 3) S 2 A &lt; S 2 B S 1 = S 0 cos 2 (60) S 2 = S 1 cos 2 (30) = S 0 cos 2 (60) cos 2 (30) S 1 = S 0 cos 2 (60) S 2 = S 1 cos 2 (60) = S 0 cos 4 (60) Cool Link E 0 E 0 TA TA S 1 S 2 S 0 TA TA S 1 S 2 S 0 </li> <li> 27. </li> </ul>