First slide

Electromagnetic waves and its nature

Question

A linearly polarized electromagnetic wave given as $\vec{E} = E_{0} \cos (k z - w t) \hat{i}$ 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

$\bar{E_{r}} = - E_{0} \hat{i} \cos (k z - w t)$
B

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

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

$\bar{E_{r}} = E_{0} \hat{i} \cos (k z - w t)$

Solution

When a wave is reflected from 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 $π$ in the incident wave is introduced. Also, the direction is reversed hence, for the reflected wave we will replace $z b y - z (i n t h e p h a s e) a n d \hat{i} b y - \hat{i}$ .
The incident electromagnetic wave is,
$\vec{E} = E_{o} \cos (k z - w t) \hat{i}$
The reflected electromagnetic wave is
$\vec{E_{r}} = E_{0} \cos [k (- z) - w t + π] (- \hat{i})$
$= - E_{0} \cos [- (k z + w t) + π] \hat{i}$
$= E_{0} \cos [(k z + w t)] \hat{i} [\cos (- θ + π) = - \cos (θ)]$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App