A linearly polarized electromagnetic wave given as vecE = E0 hati cos (kz-ω t) 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

Question

A linearly polarized electromagnetic wave given as vecE = E0 hati cos (kz-ω t) 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 (A)  vecEr = -E0 hati cos (kz-ω t) (B)  vecEr = E0 hati cos (kz+ω t) (C)  vecEr = -E0 hati cos (kz+ω t) (D)  vecEr = E0 hati cos (kz-ω t)

Tardigrade Admin · Accepted Answer

As the wall is perfectly reflecting, there is no. change in amplitude

E_{0}

.
Also the wall is optically inactive, so, there is no phase change.
After reflection, the wave travels along -ve z direction,

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

= E_{0} \hat{i} cos (k z + ω t)

(∵ cos (- θ) = cos θ)

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

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

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

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

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

Q. A linearly polarized electromagnetic wave given as E=E0​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

Er​=−E0​i^cos(kz−ωt)

Er​=E0​i^cos(kz+ωt)

Er​=−E0​i^cos(kz+ωt)

Er​=E0​i^cos(kz−ωt)

As the wall is perfectly reflecting, there is no. change in amplitude E0​. Also the wall is optically inactive, so, there is no phase change. After reflection, the wave travels along -ve z direction, ∴Er​=E0​i^cos(−kz−ωt) =E0​i^cos(kz+ωt) (∵cos(−θ)=cosθ)

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

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

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

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

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