Discussion
Two infinite plates made up of perfect conducting material are held parallel to each other with finite separation between them. In the gap region, an electromagnetic radiation is so introduced that it strikes the plates with angle of incidence θ. The energy propagates with the speed :
Answer: C
The energy propagates with the speed \( c \sin\theta \).
Between the plates the wave travels in a zig-zag at speed \( c \), reflecting from each plate with angle of incidence \( \theta \), measured from the normal. Only the component of its velocity parallel to the plates carries energy down the guide, and that component is \( c\sin\theta \), the group velocity.
The wave fronts sweep along the plates faster, at the phase velocity \( \frac{c}{\sin\theta} \), whose product with the group velocity is \( c^{2} \). That value exceeds \( c \) and carries no energy. The cosine forms would follow only if \( \theta \) were measured from the plates.
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