Luis Marquez
Physics 211 F10
Snell's Law
 Index of Refraction It's A Trap
 Vapor_Liquid Equilibria   Actual Physics Bibliography

Index of Refraction


A hands on way to use this idea of refraction to estimate the density of a medium can be applied to sugar water. I myself have done this experiment, although it was many years ago for another science class. Essentially, you have a triangular prism where the cross sectional area of the prism is an equilateral triangle. Next, you have a laser  point through the empty prism onto the other side of the wall like so:


http://www.sciencebuddies.org/Files/2646/5/Phys_img190.jpg
Given that the index of refraction would vary depending on the amount of sugar that is put into the water, multiple tests will have to be done at each concentration to find it's index of refraction. On that wall, there should be a marker of some kind, or a meter stick, so that when you fill the prism with a fluid, you know how much the beam got refracted:


http://www.sciencebuddies.org/Files/2647/5/Phys_img191.jpg

If you "use some algebra [and] trigonometric identities" after applying Snell's law twice, you get the equation to find the index of refraction for the sugar water as:
n = Nair × sin[0.5(θmd + θp)] / sin(0.5θp)
Given that the known index of air is 1.00028, θmd is the minimum deviation, and θp is the angle of the prism, which happens to be 60° since its an equilateral triangle, the equation simplifies to:
 n = 2.00056 × sin[0.5(θmd + 60°)]
Once you have found the minimum angle of deviation, you can plug it in to find the index of refraction for that specific concentration of sugar water!