= Solution
For a P-to-S converted <seismic head wave>, set the transmitted S-wave angle to $90^\circ$, giving $\sin i_c=V_{P,\rm incident}/V_{S,\rm transmitted}$. At the limestone–sandstone boundary, $2500/1200>1$, so \b[no transmitted S-wave head wave is possible] for incidence from limestone.
At the sandstone–salt boundary, using the stated interpretation $V_{S3}=3000\ \mathrm{m\,s^{-1}}$,
$$
\sin i_c=\frac{2000}{3000},\qquad \boxed{i_c=41.81^\circ}.
$$
The P-transmission <seismic critical angle> is lower, $30^\circ$, but this does not forbid the converted S branch: at $41.81^\circ$ the transmitted P field is evanescent while the S field reaches grazing incidence.
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