# How much can a thin layer of hi-speed material within a low-speed volume block a wave due to total internal reflection?

Consider a block of isotropic material with compression wave velocity associated with it, $v_1$. Consider a thin flat layer of high compression wave velocity $v_2, v_2>v_1$ that is buried within the block.

It is known that if the wave hits the layer at an angle of incidence above a critical angle, the phenomenon of total internal reflection occurs.

What is the estimate of the reflection coefficient for that phenomenon? How near it approaches $1$? How it depends on the hi-speed layers thickness in relation to compression wave length? Is it reasonable to say that the transmission of wave energy through the hi-speed layer occurs only within the cone with apex at the wave source and the apex angle equivalent to critical angle?

In the picture below f is the thickness, in pale red is the low-speed volume, in purple is the hi-speed layer, in blue is the total internal reflection raypath, V1 and V2 are velocities.

• Presumably you would get an evanescent wave just as you do for TIR of light. Your layer would need to be thick enough for the evanescent wave to decay to a negligable amplitude. – John Rennie Feb 18 '14 at 10:19