What experiments could be used to investigate the refraction of light

Other than shining light through a perspex and glass block.

Refraction involves study of light rays behavior when it passes from one medium to another.
If you are not happy with glass or perplex you can try other transparent media like water or any other liquid! For example take a beaker filled with water and pass a light beam (colored) and see where it strikes bottom and measure the angle of deviation and incidence.