The Zeeman Effect
                                                         

                                                               Pieter Zeeman
 

    The Zeeman effect is the result of an interaction between the magnetic
moment of an atom and a magnetic field, and is useful for determining properties
of the magnetic field causing the effect.
             Suppose we are observing a spectrum from some atoms that are in a
magnetic field. When we are looking at the spectrum parrallel to the magnetic
field we will see that where normally there would be one spectral line, it has
become split into 2 spectral lines. These spectral lines are also circularly
polarized, one clockwise and the other counterclockwise. If we observe the same
spectrum perpendicular to the magnetic field then we would see that the single
spectral line has been split into three spectral lines. These spectral lines are
linearly polarized with the one in the center having the opposite polarization
as the ones on the sides.

                                   
                                                      Illustration of the Zeeman Effect
 

             Now, we can use this information to tell us about the magnetic field.
The change in the frequency of the spectral lines is proportional to the
strength of the magnetic field:

                                     delta(nu)= +/- (e*B)/(4*Pi*m*c)

but we must also determine the direction of the magnetic field to make this more
useful. This is done fairly easily by considering the polarization of the
spectral lines. If we use filters to take out the circular polarization we can
then analyze the linear polarization and see how strong the center line is
compared to the side lines at different linear polarizations.  If we use a
filter to block the linear polarization we can compare the contribution of the
circularly polarized lines. Combined with a measure of the total intensity it is
not difficult to see in principal how we could determine the direction of the
magnetic field from this.
             The four measurements of the spectral lines with different polarizations
known as the stokes parameters, I, Q, U, V. I is a measure of the total
intensity of the lines, Q and U measure the linearly polarized contribution, and
V represents the circularly polarized contribution.
                One could make an instrument with a compensator subjecting the incoming
light to a phase retardance and transmitting the light through a polarizer. With
different combinations of these you could then measure the four Stokes
parameters and determine the direction of your magnetic field. Adding a
spectrometer you could determine the magnitude as well. This is essentially how polarimeters work.