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228s13-l04

# 228s13-l04 - Physics 228 Today Interference Website Sakai...

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Physics 228 Today: Interference Website: Sakai 01:750:228 or www.physics.rutgers.edu/ugrad/228 We have now Fnished 3 lecture on geometrical optics, and will continue with 4 lectures on interference phenomena, which show the wave nature of light. We studied interference at some level in 124, so this should be in some respects review. Sunday, February 24, 2013

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Inteference Why do we see the colors in the soap bubble? Interference. We will begin to see how this works today, looking at interference of two sources. (Soap bubbles will be on Thursday.) Sunday, February 24, 2013
EM Waves I asked your recitation instructors to show you that Maxwell's equations in a source free region: Divergence of E (and B) = 0? (No charges.) Curl of E = -dB/dt? Curl of B = μ 0 ε 0 dE/dt? (No currents.) have a traveling wave solution. .. ° E = E 0 cos( kz ωt x ° B = B 0 cos( y As long as: kE 0 = ω B 0 E 0 = cB 0 , as c = ω /k, and c = 1/ ( μ 0 ε 0 ) = 1/ (4 π x10 -7 x 8.854x10 -12 ) = 3.0x10 8 m/s Conclusion: one solution to M.E. is a plane wave of E & B Felds traveling at speed c = 1/ ( μ 0 ε 0 ). This is light. Sunday, February 24, 2013

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EM Waves What happens when we have a point source emitting light uniformly in all directions? We get a spherical wave. The wave expands in r, not z, so the argument kz becomes kr. Energy conservation leads to the amplitude decreasing with r, since the area increases as r 2 . ° E ( r, t )= E 0 r cos( kr ωt ) ˆ θ ° B ( B 0 r cos( ) ˆ φ Implicit in these formulas we have a single frequency / wavelength of light. You can add multiple waves with different amplitudes and frequencies as needed, because electromagnetism is linear. Since the θ and φ directions are to the r direction, we arbitrarily put the E Feld in the θ direction and the B Feld in the φ direction. Sunday, February 24, 2013
Coherence When we generate actual light - visible light, radio waves, etc. - the sources can be coherent or incoherent.

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228s13-l04 - Physics 228 Today Interference Website Sakai...

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