A beam ofunpolarizedlight is shown to be split into three distinctpolarizedbeams when it passes through the core region of a smectic liquid crystal which is oriented so that its planes form concentric cylinders. InN‐p‐cyanobenzylidene‐p‐octylozyaniline (CBOOA) the angle between two adjacent exit beams is ∼22° whereas forN‐p‐cyano‐p‐octylbiphenyl (COB) it is ∼14°. Knowing this angle, we are able to deduce the ratio of the extraordinary to ordinary index of refraction,ne/no, for CBOOA and COB.