Lab #3 Gradient Index (GRIN) Optics

Follow the bouncing laser

Please make either a analytic or computational model of the Gradient Index (GRIN) systemseen in lab a few weeks ago. This system consists of a tank of water (index of refractionn = 1.33) with dissolved sugar in it such that the sugar solution increased in concentrationtoward the bottom of the tank. The gradient index in this experiment come from the factthat sugar-water solutions have a higher index of refraction than pure water increasing withconcentration.

For a few fixed points you may wish to take the following values:

Substance nWater 1.33

30% sugar solution 1.3880% sugar solution 1.49

Your analytic or numerical model should be used to predict how far the laser beam willtravel before it is bent into the bottom of the tank. You have control over the followingvariables: Sugar concentration profile (and hence the profile of the gradient index) and theentry height, and small incidence angle of the laser beam.

In the actual experiment the laser entered the tank at normal incidence (hence no pathrefraction from the glass). The true profile of the sugar solution was non-uniform in scaleheight, allowing for an effective angle of incidence to be introduced. For your model youmay start the beam at a nominal angle of incidence, and ignore the glass tank.

Physics 432 3 1 Optics