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_Andreas
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Homework Statement
An electromagnetic wave is incident upon a planar interface at an oblique angle [tex]\theta_i[/tex], where it is reflected. For the wave vector components parallel to the interface, we have [tex]k_{xi}=k_{xr}[/tex]. Thus, [tex]\theta_i=\theta_r[/tex]. The wave numbers for the incident and reflected waves are equal. Find the relation between the wave vector components normal to the interface for the incident and reflected waves.
Homework Equations
[tex]\cos\theta_i=\cos\theta_r[/tex]
See attached picture.
The Attempt at a Solution
Thus, from the picture, [tex]\frac{k_{zr}}{k}=\frac{k_{zi}}{k}\Longrightarrow k_{zr}=k_{zi}[/tex].
To me this seems to imply that both normal components point in the same direction, in addition to being of the same magnitude. But shouldn't the normal components have opposite signs, since the incident and reflected waves travel in opposite normal directions?