May web.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)

May web.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 on what we would like to get back –bring stuff to lab

May web.mit.edu/8.02x/www Poynting Vector Not a typo: John Henry Poynting ( ) 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

May web.mit.edu/8.02x/www Polarization

May web.mit.edu/8.02x/www Polarization

May web.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

May web.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

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

May web.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

May web.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

May web.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

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

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

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

May web.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

May web.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

May web.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)

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

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

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

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

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

May web.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 << )

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