Solution
= Solution
In the lower solid $l^2+m^2=\omega^2/c_S^2$. Put $m'^2=\omega^2/c_S'^2-l^2$ and $Z=\mu'm'\cot(m'h)$. Matching displacement and shear stress at $y=0$, with zero displacement at $h$, gives
$$
R=-\frac{Z+i\mu m}{Z-i\mu m}.
$$
For real propagating parameters $|R|=1$: the rigidly backed lossless layer transmits no mean energy, so all incident energy is reflected (though with a phase shift).