  From measurements of the far-infrared reflectivity at grazing angles of
incidence with p-polarized light we determined the c-axis Josephson plasma
frequencies of the single layer high T_c cuprates Tl_2Ba_2CuO_6 and
La_{2-x}Sr_xCuO_4. We detected a strong plasma resonance at 50 cm^{-1} for
La_{2-x}Sr_xCuO_4 in excellent agreement with previously published results. For
Tl_2Ba_2CuO_6 we were able to determine an upper limit of the unscreened c-axis
Josephson plasma frequency 100 cm^{-1} or a c-axis penetration depth > 15 \mu
m. The small value of $\omega_J$ stands in contrast to recent a prediction
based on the inter-layer tunneling mechanism of superconductivity.
