Imagine that we have a non absorbing glass plate of index n and thickness Δy, which stands...

Imagine that we have a non absorbing glass plate of index n and thickness Δy, which stands between a source S and an observer P.

(a) If the unobstructed wave (without the plate present) is Eu = E0 exp iω(t – y/c) show that with the plate in place the observer sees a wave

(b) Show that if either n ≈ 1 or Δy is very small, then

The second term on the right may be envisioned as the field arising from the oscillators in the plate.