I am currently designing a lighting solution for Phillips as part of my university degree. However I am stuck on a small problem, as stated above. If I was to have a strip of perspex, with the sides matt and the bottom polished, would I achieve more light through the polished surface or the matt surface. And why??
Reading this may help you out: http://en.wikipedia.org/wiki/Fresnel_equations
What you are describing seems to be some sort of light pipe, where you are counting on internal reflection to transport the light along the strip. Whether yor pipe is surrounded by a higher refractive index material, as in optic fiber, or not, as in surrounded by air, to keep all, or at least most, of the light from refracting out of the pipe, you need the incidence angle to be shallow enough.
On a matte surface, rather than having a well defined incidence angle for a ray of light, this will be spread over a range of different angles, due to the irregularities of the surface. This may help understanding that. It will depend on your exact configuration, but if you look at the graphs of the Fresnel formulas above, that is almost certainly going to mean that in a light pipe configuration more light will refract out of a frosted surface than a smooth one.
The new Kindle Paperwhite uses a smooth light pipe, with little protubeances at selected points to guide light out of the pipe, they used to have a nice video explaining it.