Draw a line on a piece of paper and put the block on it as in the figure (the figure is a view from above).
Now shine the laser beam into the block at some angle from perpendicular to the edge. Measure the angle of incidence and the angle of refraction:
Then you can determine the index of refraction since:
nincsinθinc = nrefrsinθrefr
Total Internal Reflection
nincsin(90º) = nrefrsinθrefr
(1)(1) = nrefrsinθrefr
sinθrefr = 1/nrefr
θrefr = arcsin(1/nrefr)
For a beam coming out of the block into the air, this is the maximum angle that it can have from the line perpendicular to the edge of the block and still send some photons out of the block. For angles larger than this, all photons are internally reflected.
Now measure θrefr. The best way to do this is by using the convex lens as in the figure below:
Simply adjust the angle of the beam until the exiting part is about tangent to the curved lens surface. At angles steeper than this, all the light is reflected back to the interior of the lens. It might help here to draw another line perpendicular to the one already on the paper, one that will be tangent to the edge of the lens, so that you can be more sure that you're measuring your refraction angle properly.
Measure the focal length from the focal point to the flat surface of the lens.
Focal Length of the Concave Mirror