1. May 15 2002web.mit.edu/8.02x/www Electricity and Magnetism Announcements Today –More on wave phenomena Polarization Superposition –Standing waves –Interference (proof that light is a wave) Scattering of light (why is the sky blue)

2. May 15 2002web.mit.edu/8.02x/www Announcements Pset #12 (last one) due today Experiment MW due today Kits (Red Boxes) have to be returned! (if you want a grade) –see e-mail on what we would like to get back –bring stuff to lab

3. May 15 2002web.mit.edu/8.02x/www Poynting Vector Not a typo: John Henry Poynting (1852-1914) Wave: Direction + Magnitude Summarize using vector: Poynting Vector S = 1/  0 E x B Direction: S B, S E Magnitude: S = 1/  0 EB Power/Unit Area

4. May 15 2002web.mit.edu/8.02x/www Polarization

5. May 15 2002web.mit.edu/8.02x/www Polarization

6. May 15 2002web.mit.edu/8.02x/www Polarization Polarization: –Oscillation of fields has well defined direction Polarization only possible for transverse waves In general, light (sun, lightbulb) is unpolarized –Superposition of waves with many different orientations Can be polarized using e.g. polarizer foils

7. May 15 2002web.mit.edu/8.02x/www Superposition of waves We saw many examples of superposition principle Not only true for static fields, but also for time-dependent fields -> Superposition of waves

8. May 15 2002web.mit.edu/8.02x/www Superposition of waves

9. May 15 2002web.mit.edu/8.02x/www Superposition of waves Example: Standing waves z Incoming wave E(z,t) = E 0 sin(kz+  t) Reflecting Surface Conductor

10. May 15 2002web.mit.edu/8.02x/www Superposition of waves Example: Standing waves z Incoming wave Reflected wave E(z,t) = E 0 sin(kz+  t) E(z,t) = E 0 sin(kz-  t) Reflecting Surface Conductor

11. May 15 2002web.mit.edu/8.02x/www Superposition of waves E total = E 0 sin(kz+  t) + E 0 sin(kz+  t) = 2 E 0 sin(kz) cos(  t) Standing wave Superposition of Incoming wave and Reflected wave z E t = 0 0 < t < T  Node

12. May 15 2002web.mit.edu/8.02x/www Standing Wave E  E = 0

13. May 15 2002web.mit.edu/8.02x/www Standing Wave E   E = 0 L = M  2; M = 1,2,3... Microwave oven: ~ 10cm

14. May 15 2002web.mit.edu/8.02x/www Superposition of waves Interference

15. May 15 2002web.mit.edu/8.02x/www Double Slit Experiment d  r1r1 r2r2 E tot = E 0 sin(kr 1 -  t) + E 0 sin(kr 2 -  t) Max. if “constructive interference” kr 1 -  t = kr 2 -  t + M 2  R y

16. May 15 2002web.mit.edu/8.02x/www Double Slit Experiment d  r1r1 r2r2 E tot = E 0 sin(kr 1 -  t) + E 0 sin(kr 2 -  t) Max. if “constructive interference” kr 1 -  t = kr 2 -  t + M 2  y Max = M /d R y Min = (M+1/2) /d R R y

17. May 15 2002web.mit.edu/8.02x/www Interference with Matter Interference can also happen for “matter waves” Bose-Einstein condensate of atoms (Ketterle et al, Nobel Price ’01)

18. May 15 2002web.mit.edu/8.02x/www Scattering of Light

19. May 15 2002web.mit.edu/8.02x/www Scattering of Light Why is the sky blue during day...

20. May 15 2002web.mit.edu/8.02x/www Scattering of Light Why is the sky blue during day...... and red at sunset? Santorini, Greece

21. May 15 2002web.mit.edu/8.02x/www Scattering of Light Red Light ( ~ 700 nm) Blue Light ( ~ 400 nm)

22. May 15 2002web.mit.edu/8.02x/www Scattering of Light Red Light ( ~ 700 nm) Blue Light ( ~ 400 nm) Molecules, dust (size << )

23. May 15 2002web.mit.edu/8.02x/www Scattering of Light Red Light ( ~ 700 nm) Lord Rayleigh: Scattering probability ~ 1/ 4 Blue Light ( ~ 400 nm) Molecules, dust (size << )

24. May 15 2002web.mit.edu/8.02x/www Scattering of Light Red Light ( ~ 700 nm) Lord Rayleigh: Scattering probability ~ 1/ 4 scattering (blue)/scattering(red):   -> 700 4 /400 4 ~ 10 Blue Light ( ~ 400 nm) Molecules, dust (size << )