Simultaneous experimental measurements of copper K-alpha imaging and the maximum target normal sheath acceleration proton energies from the rear target surface are compared for various target thicknesses. For the T-cubed laser (approximate to 4 J, 400 fs) at an intensity of approximate to 2 x 10(19) W cm(-2), the hot electron divergence is determined to be theta(HW HM) approximate to 22 degrees using a K-alpha imaging diagnostic. The maximum proton energies are measured to follow the expected reduction with increasing target thickness. Numerical modeling produces copper K-alpha trends for both signal level and electron beam divergence that are in good agreement with the experiment. A geometric model describing the electron beam divergence reproduces the maximum proton energy trends observed from the experiment and the fast electron density and the peak electric field observed in the numerical modeling. (C) 2013 AIP Publishing LLC.