Thanks for your question, and welcome to Science Buddies. What I think you are asking is determining the Phase Velocity of the electromagnetic wave propagation through a medium other than a vacuum. We all know that the speed of light in a vacuum is ~ 3x10^8 m/s (denoted by the symbol, c). That same wave (say a light beam) moving through matter moves at a speed less than c due to the wave being absorbed and reemitted by the atoms of the matter over and over again, like small speed bumps. This slowing of the beam as it transitions from one medium to another causes the beam to bend in a measurable way. This science buddies experiment details how the speed of light in a medium can be measured: http://www.sciencebuddies.org/science-f ... p009.shtml
To apply it to your experiment, you will need to find a way to accurately detect and measure an invisible infrared beam. However, once all the angles are measured, you can use Snell's law to determine the index of refraction (n2) of your solutions. From there, the relationship n2=c/v2; where n2=index of refraction, c=speed of light in a vacuum, v2=phase velocity through your solution. Rearranging, we get v2=c/n2 to solve for the phase velocity. The difference between c and v2 is the absorption and transmission propagation rate of the wave through the solution. You can further use the relationship v2=c/n2=lambda/T; where lambda=wavelength, T=time to determine the time it takes to propagate.
As far as the intensity of the beam as it enters/exits the material goes, this doesn't account for the reflection properties of the medium. To take it the next step, you can use Fresnel equations of reflection to solve for the reflection (Rs/p) and transmission (Ts/p) coefficients to identify the fraction of the beam that is reflected away vs. what is absorbed vs. what fraction makes it through the medium to be detected on the other side. Basically:
E_in = E_out + E_attenuated
This doesn't take into account scattering, but would solve for the total attenuation within the material itself.
E_attenuated = E_scattered + E_absorbed
I haven't worked with Maxwell's equations in quite awhile, so if anyone has anything to add, please do. I hope this answers the question.
I hope this helps.
"As the circle of light increases, so does the circumference of darkness around it."
~ Albert Einstein