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March 9, 2021

What is the angle of the transmitted wave in the lower halfspace, and what kind of wave is it (radiating or evanescent)?

Consider the reflection of a plane wave from an isovelocity fluid layer of thickness H overlying an isovelocity fluid halfspace for which c₂ <>₁<>₃ and p₁ <>p₂ <>p₃:

a. What is the critical grazing angle for waves incident from medium 1?

b. If k₂H 1, show that to leading order the plane-wave reflection coefficient reduces to the plane-wave reflection coefficient without the layer present.

Now, suppose that P₁ = p₃ <>p₂ and c₁= c₃ <>₂, and that the plane wave is incident at grazing angle <> (c₁=c₂).

c. What is the angle of the transmitted wave in the lower halfspace, and what kind of wave is it (radiating or evanescent)?

d. What is the form of the solution in the layer?

e. Derive the expression for the reflection coefficient in the upper halfspace and the transmission coefficient in the lower halfspace.

f. By your intuition, what happens when Verify your answer by examining the leading order behavior of the reflection and transmission coefficients.

Computer Science

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