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A linearly polarized electromagnetic wav...

A linearly polarized electromagnetic wave given as `vec(E )=E_(0)cos(kz-omega 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

A

`vec(E )_(r )=E_(0)(kz-omega t)hat(i)`

B

`vec(E )_(r )=E_(0)cos(kz + omega t)hat(i)`

C

`vec(E )_(r )=-E_(0)cos (kz + omega t)hat(i)`

D

`vec(E )_(r )=E_(0)sin (kz-omega t)hat(i)`

Text Solution

Verified by Experts

The correct Answer is:
B
When wave is reflected from denser medium its type do not change but its phase change by `180^(@)` or `pi` rad.
`therefore` Reflected wave `vec(E )=E_(0)cos {kz - omega t}hat(i)`
Reflected wave propagates in negative x - direction hence reflected wave
`vec(E )_(r )=-E_(0)cos{k(-z)-omega t+pi}hat(i)`
`=-E_(0)cos{-(kz+omega t)+pi}hat(i)`
`=+E_(0)cos(kz+omega)hat(i)`
`[because cos(-theta)=cos theta " and " cos(pi+theta)=-cos theta]`
`therefore vec(E )_(r )=E_(0)cos(kz+omega t)hat(i)`
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