We coupled a home-made rotating analyzer ellipsometer to the Fourier-spectrometer of the U4IR beamline at the National Synchrotron Light Source in Brookhaven. The set-up is designed to operate in the spectral range from 30 to 700 cm(-1). The higher brightness of the synchrotron compared to conventional light sources allows us to measure on small surfaces (approximate to 1 x 1 mm(2)). Furthermore. the opening angle of the light focused on the sample can be kept at a minimum, which is a requirement for ellipsometric measurements with high accuracy. We apply this new technique to determine the out-of-plane response of the high-T-c system La2-xSrxCuO4 with dopant concentrations ranging from the underdoped to the overdoped regime (x = 0.1; 0.12; 0.15; 0.18 and 0.2), The out-of-plane response of these compounds contains contributions from the c-polarized infrared active phonons as well as from free charge carriers. No anomalies attributed to superconductivity are seen for any of the observed phonons. The low frequency plasmon appearing in the superconducting state is discussed in terms of a Josephson-plasmon in a layered superconductor.