W9_parallel_resonance.eps

372 Week 11: Light

• Linear Polarization:
  Linear polarization occurs whenever the electric field vector oscillates consistently
  in a single vector direction in the plane perpendicular to propagation.


• Circularly Polarized Light:
  Circularly polarized light has the same electric field magnitude in the twoinde-
  pendent polarization directions but the waves in these directions areπ/2 out of
  phase:

E~(z, t) =

√

2

2

E 0 xˆsin(kz−ωt±π/2) +

√

2

2

E 0 yˆsin(kz−ωt)

E~(z, t) =

√

2

2 E^0 (±ˆxcos(kz−ωt) +yˆsin(kz−ωt)) (908)

There are two independenthelicitiesof circularly polarized light: right (clock-

wise/+) and left (anticlockwise/-) when facinginthe direction of propagation).

• Elliptically Polarized Light:
  If the amplitudes of the two waves are (potentially) differentandthe two waves are
  (potentially) out of phase, the most general polarization state is that ofelliptical
  polarization:

E~(z, t) =E 0 xxˆsin(kz−ωt+δx) +E 0 yyˆsin(kz−ωt+δy) (909)

In this expression,E 0 xandE 0 ymay or may not be equal, and the phasesδxand

δymay or may not be zeroorequal.

• Polarization by Absorption (Malus’s Law):
  For an ideal polaroid filter that is otherwise fully transparent:

Itransmitted=

Iincident

2

(910)

The transmitted light is fully linearly polarized in the direction of thetransmission

axisof the filter.

If the light that is incident on the filter is already polarized, then only thecomponent

of the electric field vector that isparallelto the transmission axis is transmitted:

Etransmitted=E~·tˆ=Eincidentcos(θ) (911)

whereθis the angle between the direction of linear polarization of the incidentlight

and a unit vector along the transmission axis. This implies that the transmitted

intensity is given by:

Itransmitted=Iincidentcos^2 (θ) (912)

This result is known asMalus’s law.

• Polarization by Scattering:
  Rays scattered more or less at right angles to an atom, molecule, orspeck of dust
  are linearly polarizedperpendicular to the plane of scattering.


• Polarization by Reflection:
  Light that is reflected at a non-normal angle from a dielectric surface is (partially
  or completely) polarizedparallel to the surface, which is alsoperpendicular
  to the plane of reflection. Light transmitted into the new medium is partially
  polarized the opposite way (by subtraction).
  The reflected light iscompletelypolarized when the light is incident at theBrewster
  angle, where the reflected and refracted rays are perpendicular to each other, given
  by:
  tan(θb) =

n 2

n 1 (913)