This paper describes a technique for measuring refractive index and thickness of transparent plates using a fibre-optic low-coherence interferometer. The interferometer is used to independently measure quantities related to the phase and group refractive indices, np and ng, of the material under investigation. Additionally, the dispersion of the phase index dependent quantity is measured by taking advantage of the range of wavelengths available from a broadband source. These three quantities are related to simultaneously yield np and ng as well as the geometrical thickness t of the sample. Measurements are presented for a range of transparent materials including measurements of the ordinary and extraordinary refractive indices of a birefringent sapphire window. The mean percentage errors across all the samples tested were 0.09% for np, 0.08% for np, and 0.11% for t.