Animate
The blue, red, and gray areas represent media of different indices of refraction. The path of a light ray incident from the blue medium is shown in yellow. The angle of incidence is given as an output. Playing the applet forward or reverse will increase or decrease the initial angle of incidence. In order to increase the precision with which the incident angle can be read, decrease the Angle Increment. Also change the Starting angle to something very near the angle you're looking for so that you don't have to step through many angles.
The problem is to find the relative indices of refraction n1:n2:n3. That is, find the ratios n2/n1 and n3/n2. For good results, measure angles to the nearest tenth of a degree.