Actually, measuring the index of refraction for *your* prism is an experiment, one that is done all the time for lots of reasons. Not all prisms are created equal, so you can measure it for 2 prisms and compare the 2. Doing an experiment for your own samples is still worthy, even if it's not the first time the experiment has ever been done.
Also, experimenting to give "proof" of the wavelength-dependence of the index of refraction, with actually real numbers comparing multiple prisms, is proving a scientific concept that is central to a lot of areas of science, and something all people know and so few realize they know it. It makes rainbows; and, why does crystal glassware cost more and look prettier than regular glass? Because the added lead increases the index of refraction, and increasing the index of refraction generally also increases the wavelength-dependence of the index. Increasing the index not only makes it reflect more light, making it "shinier", it also make the glass more prismatic. Same for diamonds: changing the index of refraction makes it prettier and more sparkly, and you can prove that higher index makes things more prismatic with lasers and prisms. Scientific, physics proof of something that any self-respecting female knows and takes pride in, her crystal stemware. I'd almost guarantee that would impress most female science fair judges, and is still very science-y for anyone not worrying about stemware.
The actual thinking is coming up with the experimental design to actually measure the index of refraction, measure the wavelength-dependence of the index of refraction, and relate those things back to an observed phenomenon in order to prove it. It's a beautiful experiment, really. It's not just demonstrating that refraction happens, it's measuring the actual phenomenon in order to explore it.
