First slide

Electromagnetic waves and its nature

Question

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

Moderate

A

$\vec{E_{r}} = - E_{o} \hat{i} \cos (k z - w t)$
B

$\vec{E_{r}} = E_{o} \hat{i} \cos (k z + w t)$
C

$\vec{E_{r}} = - E_{o} \hat{i} \cos (k z + w t)$
D

$\vec{E_{r}} = E_{o} \hat{i} \cos (k z - w t)$

Solution

When a wave is reflected from a denser medium, the reflected wave is without change in type of wave but with a change in phase by $180^{0}$ or $π$ radian. Therefore, additional phase of $π$ is introduced in the incident wave . For the reflected wave direction is reversed means reflected wave travels in $- \hat{i}$ . As a result in the phase $+ k z i s r e p l a c e d b y - k z$ .
The incident electromagnetic wave is
$\vec{E} = E_{o} \cos (k z - w t) \hat{i}$
The reflected em wave will be ,
$\vec{E_{r}} = E_{o} (- \hat{i}) \cos [- k (z) - w t + π]$
$= - E_{o} \hat{i} \cos [- (k z + w t) + π]$
$= E_{o} \hat{i} \cos [- (k z + w t)]$
$[\cos (θ + π) = - \cos θ] = E_{o} \hat{i} \cos (k z + w t) [\cos (- θ) = \cos θ]$

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