The angular distribution of the intensity of the light scattered by director fluctuations in thin LC layers is theoretically considered. The analysis is carried out for a freely suspended smectic-A film and a homeotropically aligned nematic LC cell, It is shown that surface tension, anchoring strength and the splay-bend surface elastic constant (in the case of nematic LC) affect the angular distribution of the scattered light intensity, The correlation function of the fluctuations is written down in a closed explicit form rather than infinite series of natural modes.