The beam displacement method is not used for measuring a gradient
index of refraction, rather, it is used to measure the index of refraction
of a uniform material.
This method measures the distance that a medium offsets a laser beam. I
introduce the laser to the fishtank at certain angle incriments and record
their corresponding offsets.
Here is a diagram of the setup I used in this experiment :
This is an example of Fermat's Principle in full effect. As I increas
the
incident angle, the light follows the quickest path from the source to
the
plexi-glass.
I was originally discouraged using this method. Looking at the
data from the first trial, the best fit line
was to 1.39 and it was only best fit to an accuracy of 18% error. Since
the accepted value for the index of refraction of water is 1.33, I was
very disappointed. Dr. Noe then suggested
that I use graph paper to record my data as opposed to just making
marker dots right on the plexy glass.
Using the smaller lines, I was able to more accurately measure the displacement of the Laser Beam. These more accurate readings lead to a best fit line of 1.34; with a 1-5% error. This experience taught me that measuring as accurately as possible is one of the most important things one can do in their experiment.
Data plots
First Data (inaccurate)
Second Data (accurate)
I also used this method to measure the index of refraction of corn syrup. the curve was best fir to an index of about 1.48-1.49; which is quite accurate. In conclusion I feel as though the beam displacement method is quite effective in measuring the index of refraction of uniform mediums. Here is a data plot of my corn syrup experiment:
