The simplest way is to measure Brewster angle, this will give you the refractive index. Absorption is trickier since you probably need to find ellipsometer.
Most UV.vis spectrometers are designed to measure transmission, but if you can find wither one with an integrating sphere, or a mini spectrometer with a bifurcated fibre, you can measure the absorption spectrum by backreflection off the silicon substrate.
Many of the optics suppliers, Thor labs, edmund optics etc. sell spectrometers with reflectance probes (so not just for transmission measurments). They have concentric detection and light source fibres. Though you will pay a premium to go into the UV, where common glass components begin to absorb, and you also require a UV source, though this could be achieved with LEDs). You can buy systems like this:
also, though I would NOT recommend the thin film software they sell - probably easier to put together your own kit to meet your own demands, but this sort of set up can be used.