# Reflected electromagnetic wave relation

If incident electromagnetic wave is given as:

\begin{align*}E_i&=A_e \cos(\omega t + bz)\\ H_i&=A_h \cos(\omega t + bz)\end{align*}

What would be relation for REFLECTED wave?

Does it go like this? \begin{align*}E_r&=A_e \cos(\omega t - bz)\\ H_r&=A_h \cos(\omega t - bz)\end{align*}

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This needs some cleaning up. The indident wave and your guess for the reflected wave are both traveling in the same direction, namely the $-z$ direction. In fact, the two are identical! One should have $wt-bz$ rather than $wt+bz$. Also, electric and magnetic fields are vectors. You probably want to indicate that explicitly somehow. Are the quantities $A_e,A_h$ vectorial quantities? Or are they equations for particular components (in which case you need to say which components)? – Ted Bunn Aug 20 '11 at 15:45
I formatted the math using LaTeX, but I agree with Ted that this needs to be clarified before we can properly answer it. – David Z Aug 20 '11 at 16:49
Before LaTeX formatting, there was "- bz" for reflected waves. (I had corrected this...) Yes, both of these are vectors, Ae and Ah are some constants. Direction of these vector should also be given for this to be complete, but I didn't bother with that, because I just want to know does the sign before z ("- bz" and "+ bz") always changes for reflected wave? – domagojk Aug 20 '11 at 17:53
@domagoj: yes, it changes by the very definition of the reflection since reflected wave means wave moving into the opposite direction. – Marek Aug 20 '11 at 18:04
If $A_e$ and $A_h$ are vectorial, then exactly one of them needs to flip its sign on reflection. Otherwise the wave wouldn't obey the right-hand rule relating the fields to the direction of propagation. Which one flips its sign depends on the type of surface doing the reflecting, which defines a boundary condition. In general the reflected wave will also have a lower amplitude. – Ben Crowell Aug 20 '11 at 18:33