Ncert Exercises & Solutions

A linearly polarised electromagnetic wave given as $E = E_{0} \hat{i} \cos (kz - ωt)$ 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:

1. $E_{r} =- E_{0} \hat{i} \cos (kz - ωt)$

2. $E_{r} = E_{0} \hat{i} \cos (kz + ωt)$

3. $E_{r} = - E_{0} \hat{i} \cos (kz + ωt)$

4. $E_{r} = E_{0} \hat{i} \sin (kz - ωt)$

(b) Hint: When a wave is reflected from a denser medium, then the type of wave doesn't change but only its phase changes by 180° or

π

radian.

Step 1: For the reflected wave,

z = - z, \hat{i} = - \hat{i}

and the additional phase of

π

in the incident wave.

Given, here the incident electromagnetic wave is,

E = E_{0} \hat{i} \cos (kz - ωt)

Step 2: The reflected electromagnetic wave is given by,

E_{r} = E_{0} (- \hat{i}) \cos [k (- z) - ωt + π]

= - E_{0} \hat{i} \cos [- (kz + ωt) + π]

= E_{o} \hat{i} \cos [- (kz + ωt) = E_{0} \hat{i} \cos (kz + ωt)]

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