Question

A propagating wave in a lossless medium along z-direction has x and y electric field components both sinusoidal of same amplitude and in phase with each other. The wave is ________.

• A. Linearly Polarised along X-axis
• B. Right circularly polarised
• C. Linearly polarised at 45$^\circ$ to X-axis
• D. Elliptically polarised

Hint:

Equal magnitude and in-phase x and y components produce linear polarization at 45$^\circ$ to x-axis.

Answer 1

The Correct Option is C

Given:
Electric field in x and y: equal amplitude, in phase.
Propagation along z-axis.
Linear Polarization at 45°:
Equal amplitudes and same phase ⇒ resultant vector lies along 45$^\circ$.
$E_x = E_0 cos(\omega t)$ and $E_y = E_0 cos(\omega t)$.
So, net E-field = $\vec{E} = E_0 (\hat{i} + \hat{j}) cos(\omega t)$ ⇒ angle = 45$^\circ$ to x-axis.