Consider now that the transition dipole corresponding to the emission of light from the excited fluorophore is parallel to the absorption dipole and that the excited fluorophore cannot rotate during the lifetime of the excited state (for example if the fluorophores are embedded in a highly viscous or frozen medium).
If we were to now measure the polarization of the emission it would be less than +1 since some of the dipoles excited will not be exactly parallel to the direction of the exciting light.
In fact, the number of potential dipoles making an angle q with the vertical axis will be proportional to sin q.  We can then calculate that the upper polarization limit for such a randomly oriented (but rigidly fixed, i.e., non-rotating) ensemble - with co-linear excitation and emission dipole - will be +1/2 (we note that this limit is exceeded for two-photon excitation processes as will be discussed later).
This case, however, assumes that the emission dipole is parallel (co-linear) to the absorption dipole.
Dipole III