First slide

Electromagnetic waves and its nature

Question

A linearly polarized electromagnetic wave given as $E = E_{0} \hat{i} \cos (k z - ω t)$ is incident normally on a perfectly reflacting wall $z = a$ . Assuming that the material of the optically inactive, the reflected wave will be given as

Moderate

A

$E_{r} = E_{0} \hat{i} \sin (k z - ω t)$
B

$E_{r} = E_{0} \hat{i} \sin (k z + ω t)$
C

$E_{r} = - E_{0} \hat{i} \cos (k z + ω t)$
D

$E_{r} = E_{0} \hat{i} \cos (k z + ω t)$

Solution

When a wave is reflected from a denser medium (or) perfectly reflecting wll made with optically inactive material then the type of wave doesn’t change but only its phase changes by $180^{0}$ or $π$ radian
Given here the incident electromagnetic wave is $\bar{E} = E_{0} \hat{i} \cos (k z - ω t)$
This wave is incident normally on a perfectly reflecting infinite wall at $z = a$ . Here the reflected wave in the direction of travelling of wave will be reversed and additional phase of $π$ in the incident wave
$\bar{E_{r}} = E_{0} (\hat{i}) \cos [k (- z) - ω t + π]$
$\bar{E_{r}} = - E_{0} \hat{i} \cos [- (k z + ω t) + π]$
$\bar{E_{r}} = E_{0} \hat{i} \cos [- (k z + ω t)]$
$\bar{E_{r}} = E_{0} \hat{i} \cos (k z + ω t)$

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