We are way behind on physics—my son took the AP C: E&M test before we even got to Faraday’s Law. He read through the last 3 chapters of Matter and Interactions in 3 days, rather than the 8 weeks we had originally planned, and he hasn’t done any of the exercises in those chapters yet. Because he is planning to take the SAT 2 Physics test this Saturday, I decided that he should at least have a cursory familiarity with Snell’s Law. Since there wasn’t time or energy for a problem set, we did a lab instead.
I had noticed when playing around with the violet (405nm) laser pointer, that the water in the fish tank fluoresced brightly.
We made some very crude measurements of the angle of the beam coming into the water and of the beam in the water using a protractor. (The beam coming in was invisible in the air, so measuring the incoming angle was very inaccurate.)
Here is the gnuplot script he used for fitting the data (with some editing by me, which he did not entirely approve of):
set angle degrees set xrange [0:90] set yrange [0:60] set title 'Index of Refraction in a Fishtank' set key top left set xlabel 'normal angle in (degrees)' set ylabel 'normal angle out (degrees)' refract(a_in, rfr_ind) = asin(sin(a_in)/rfr_ind) water_rfr = 1.333 fishtank_rfr = 1 # initial guess fit refract(x, fishtank_rfr) 'snell1.gnudat' using (90-$1):(90-$2) via fishtank_rfr plot 'snell1.gnudat' using (90-$1):(90-$2) title 'Measured', \ refract(x, fishtank_rfr) title sprintf('Fitted %f', fishtank_rfr), \ refract(x, water_rfr) title sprintf('Pure Water %.3f', water_rfr)
I’m sure that with more careful measurement, we could get much less scatter around the theoretical curve, but we were tired at the end of the day and couldn’t be bothered to do the measurements right.