[UPSC IFoS 2020] Polarisation and Modern Optics (Q348, 5+5=10M)

(i) Describe the wave given by the expression E = \hat{j} E_0 \sin \left( \frac{2\pi x}{\lambda} - \omega t \right) - \hat{k} E_0 \sin \left( \frac{2\pi x}{\lambda} - \omega t \right) where \hat{j} and \hat{k} are unit basis vectors in Cartesian coordinates. (ii) Write an expression for linearly polarized harmonic plane wave of scalar amplitude E_0, propagating along a line in the xy-plane at 45^\circ to the x-axis and having the xy-plane as its plane of vibration.