Write the expressions for two orthogonal plane polarised light waves propagating in z-direction and have equal amplitudes and phase difference of . Obtain the expression for the electric field of the resultant wave arising due to the superposition of these two waves. Determine the trajectory of the tip of the electric field vector associated with the resultant wave.
Let two orthogonal plane-polarised light waves propagate in the $z$-direction with equal amplitudes $E_0$ and a phase difference $\delta$. Assume the first wave is polarised along the $x$-axis and the second along the $y$-axis. The expressions for the electric field components are:
$$
E_x(z,t) = E_0 \cos(kz - \omega t)
$$
$$
E_y(z,t) = E_0 \cos(kz - \omega t + \delta)
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Write the expressions for two orthogonal plane polarised light waves propagating in z-direction and have equal amplitudes and phase difference of . Obtain the expression for the electric field of the resultant wave arising due to the superposition of these two waves. Determine the trajectory of the tip of the electric field vector associated with the resultant wave.