We present 17 transit light curves of the ultra-short period planetary system WASP-103, a strong candidate for the detection of tidally-induced orbital decay. We use these to establish a high-precision reference epoch for transit timing studies. The time of the reference transit midpoint is now measured to an accuracy of 4.8s, versus 67.4s in the discovery paper, aiding future searches for orbital decay. With the help of published spectroscopic measurements and theoretical stellar models, we determine the physical properties of the system to high precision and present a detailed error budget for these calculations. The planet has a Roche lobe filling factor of 0.58, leading to a significant asphericity; we correct its measured mass and mean density for this phenomenon. A high-resolution Lucky Imaging observation shows no evidence for faint stars close enough to contaminate the point spread function of WASP-103. Our data were obtained in the Bessell $RI$ and the SDSS $griz$ passbands and yield a larger planet radius at bluer optical wavelengths, to a confidence level of 7.3 sigma. Interpreting this as an effect of Rayleigh scattering in the planetary atmosphere leads to a measurement of the planetary mass which is too small by a factor of five, implying that Rayleigh scattering is not the main cause of the variation of radius with wavelength.