Low temperature photoluminescence measurements were carried out on pseudomorphically strained InxGa-1-xAs-Al0.28Ga0.72As ternary-on-ternary heterostructures grown by molecular beam epitaxy to investigate the change in the transition energy, linewidth and intensity as a function of InGaAs well thickness at two different indium compositions, x = 0.10 and x = 0.15 respectively. Sharp exciton peaks as narrow as 4-6 meV were observed from the InGaAs wells grown at 530-degrees-C with 1 min of growth interruption at the top and bottom heterointcrfaces. The linewidth decreases as the well thickness is increased up to 300 angstrom. In addition, there are signs of linewidth broadening and a sharp decrease in the photoluminescence intensity at higher well thicknesses which may indicate the onset of plastic relaxation. Relatively small variations in the transition energy were observed at well thicknesses up to almost-equal-to 3 times the theoretical critical layer thickness calculated by the Matthews-Blakeslee model (J. Cryst. Growth, 27 (1974) 118), suggesting that the small density of dislocations which may be present may not have a significant effect on the band structure of the well. Good agreement between experimental and calculated transition energy vs. well thickness data was obtained, from which the conduction band offset DELTAE(c)/DELTAE(g) was estimated to be 0.65 +/- 0.05 for x = 0.10-0.15, consistent with the results from other techniques reported in the literature.