228s13-l04

E0 e r t coskr t r the wave expands in r not z

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Unformatted text preview: itrarily put the E field in the θ direction and the B field in the φ direction. E0 ˆ ￿ E (r, t) = cos(kr − ω t)θ r The wave expands in r, not z, so the argument kz becomes kr. ˆ ￿ (r, t) = B0 cos(kr − ω t)φ B r Energy conservation leads to the amplitude decreasing with r, since the area increases as r2. 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. Sunday, February 24, 2013 Coherence E0 ˆ ￿ E (r, t) = cos(kr − ω t)θ r B0 ˆ ￿ B (r, t) = cos(kr − ω t)φ r When we generate actual light - visible light, radio waves, etc. the sources can be coherent or incoherent. E.g., when we oscillate electrons back and forth in an antenna, and at a fixed point look at the light broadcast from it, the electric and magnetic fields are basically fixed in direction and oscillate back and forth as cos(ωt). For light bulbs, the photons are emitted incoherently independently in time and space. So at a fixed observing location, the direction and magnitude of the electric and magnetic fields vary (somewhat) in time. LEDs are also incoherent, but LASERs are coherent. For intereference, we need coherent light sources. Sunday, February 24, 2013 Spherical Wave The two sources emit light ``in phase’...
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