Obtain an expression for elliptically polarised light resulting due to superposition of two orthogonal linearly polarised light waves. Show that plane polarised light and circularly polarised light are special cases of elliptically polarised light

To derive an expression for elliptically polarized light resulting from the superposition of two orthogonal linearly polarized light waves, let's consider two linearly polarized light waves vibrating along the x and y directions respectively. Let \(E_x\) and \(E_y\) represent the electric field vectors of these waves. Then, the superposition of these waves at any given point in space and time can be represented as:

\[E = E_x \cos(\omega t) \hat{i} + E_y \cos(\omega t + \delta) \hat{j}\]

where \(\delta\) represents the phase difference between the two waves.

To find the resultant polarization state, we can express the electric field vector \(E\) in terms of the amplitude and _______ _____ _____ _______ ____.
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