lecture 11 - birminghamepweb2.ph.bham.ac.uk/user/lazzeroni/em2_2017/lecture11_em2.pdf · lecture...
TRANSCRIPT
Lecture 11:
Qualitatively examine light scattered by free electrons
Qualitatively examine light scattered by bound electrons
Examine the cross section for scattering as a function ofthe frequency of EM waveHighlight the regions of Rayleigh, Resonance and Thomson scattering
Explain the blueness and redness of the sky under variousconditions
Thomson scattering
Interaction of oscillating field with free (unbound) electron
We can ignore the magnetic field:
Magnetic force Electric force
Electron velocity
Plane polarized EM wave:
Since E is sinusoidal, electron will oscillate up and downat frequency ωAs a result of the acceleration, electron will radiate at the driving frequency but not in the original direction of polarization
Electron at z=0 experiences acceleration:
Oscillating charge that re-radiates in all directions
Radiation field similar to ideal dipole (also called Hertzian dipole)
Plane through the axis of dipole,For r >>λ
Radiation pattern that shows dependence of field strengthon angle at fixed distance - length of blue arrow is proportional to strength
Solution: with
Mean power radiated by accelerating charge:(derivation beyond the scope of this course)
Note dependenceon mass
Larmor formula
Lecture 9
Here v = c, free space:
Power per unit area of incident wave
Define scattering cross section:
Classical radius
Consider cross section as a target of area σ (not a realmaterial target !). If all the light energy that impinged onthat area were to be spewed out in all directions, then thatis the energy that would be scattered by the electron.
σT is very small - scattering is weak (atomic cross section~10-20 m2) σT is much smaller for proton than electronσT is independent of frequency
Result correct if
For
Cross section for scattering decreases with increasing photon energy - Compton Scattering region
The main difference is that the momentum of the photon is now significant, meaning that the electron has some non negligible recoil due to the scattering
Bound electrons, elastic scattering
Scattering of radiation by neutral atoms without change in frequency (elastic scattering).Classical treatment, similar approach as before.
Atom with a single electron which can oscillate at natural angular frequency ω0, and subject to a plane EM wave:
Dumped simple harmonic oscillator
Loss of energy as EM radiation
Taking oscillating electronas a dipole (Hertzian dipole)it can be shown that:
Steady state solution:
Real part of x:
with
Total power radiated by charge:(Larmor formula)
Incident power per unit area:
Cross section:
Elasticscattering
I. Rayleigh scattering (tightly bound electrons)
ω << ω0
Response is controlled by restoring force
Atmospheric molecules, mostly N2 : natural frequencies are in the ultraviolet so electrons are tightly bound for visible light.
Blue light is scattered far more than the red.
III. Thomson scattering
Response controlled by electron inertia
When a simple harmonic oscillator is driven at frequencymuch higher than resonance frequency, the inertia, not therestoring or dumping force, control the response.So electron behaves as if free - Thomson scattering (or Compton)
Recommended readings:Grant+Phillips: 13.1, 13.2
Next Lecture:
Propagation of EM waves in dielectric materials