Question

To better understand the polarization consider two components of the electric field:
Ex(t) = 3 Cos (w t) and Ey(t) = 4 Cos (w t-phi). Then determine the functional form of
Ey(Ex) (that is find Ey as a function of Ex at any time t) for the following phase
angles  = 0, 45, 90, -90, 180 degrees. State these functional forms (polarizations)
and sketch them in (Ex, Ey) plane being as specific as you can with maxima and
minima on the graphs.

Answer 1

Given

or

Also given

or

or

when phase phi = 0

The relation is linear. hence this is a linear polarisation.

when phase phi = 45 Degrees

This is an ellipse equation and hence it is an elliptic polarisation.

when angle phi = 90 degrees

This is also an ellipse equation and hence it is elliptic polarisation.

when angle phi = - 90 degrees

This is also an equation of ellipse. This is also elliptic polarisation.

when angle phi = 180 degrees

The relation is linear. hence this is a linear polarization.