Question

Two plane polarised light waves are propagating along the positive z-direction 

such that their electric field vectors are mutually perpendicular. These waves are 

superposed. Obtain the condition under which the resultant wave will be circularly 

polarised.

Answer 1

$E_x=A_1\cos(\omega t),$

$E_y=A_2\cos(\omega t+\delta),$

$A_1=A_2,$ $\delta=±\frac{\pi}{2},$

$\tan \varphi=\frac{E_y}{E_x}=\frac{A_2\cos(\omega t±\frac{\pi}{2})}{A_1\cos(\omega t)}=\mp\frac{\sin(\omega t)}{\cos(\omega t)}=\mp \tan(\omega t).$