How to find the critical angle in an experiment
A simple experiment that can show you the critical angle of glass into air is to use a hemi cylindrical glass block, a laser light and a protractor. See below:
The light initially enters the glass hemi cylinder perpendicular (at right angles) to the glass (point A) and because of this no bending of the light occurs.
Up to the critical angle light will refract out the back of the glass.
At the critical angle light will travel along the boundary. You can read off the angle this makes to provide you with the critical angle.
After the critical angle total internal reflection occurs. This same experiment can be tried with a similar hemi cylindrical dish which you can fill with water.