In Figure 4 we depict a light ray hitting a water droplet at point A. Some of the light will be reflected and some of the light will enter the droplet. The light that enters will be refracted as discussed in the previous section. It then hits the other side of the droplet at point B where some of it will exit and the rest will reflect back. Finally at point C some of the light will exit and be seen by an observer.

At the end of this page is a button. When you click on this button you will be able to experiment with "shooting" rays of light into a water droplet. The beam of light enters the water droplet at some height as measured from the droplet's center. This height is called the

- Graph the deflection angle as a function of the impact parameter for
the impact parameter ranging from 0 to 1 on the
graph provided. (Note:
*w*=0 is the center of the droplet whereas*w*=1 is the top of the droplet.) - Numerically approximate the value of the impact parameter for which the deflection angle is a minimum (to within an accuracy of 0.025).
- Note that each value of the impact parameter corresponds to a unique
value of the angle of incidence (
*a*). What is the value of*a*that corresponds to the minimum deflection angle.

- Send in 3 incoming beams of light at:
- impact parameters 0.05, 0.1, 0.15
- impact parameters 0.5, 0.55, 0.6
- impact parameters 0.75, 0.8, 0.85

- Sketch the results
- For which set of impact parameters are the outgoing rays the most concentrated? The most diffuse?
- If an incoming ray has impact parameter
*w*, we define*D(w)*to mean the deflected angle of that light ray. Use the results of the previous experiment to complete the chart you were given.

- How does the angle of minimum deflection change?

- Conjecture how the minimum angle of deflection varies according to the wavelength of light. Specifically, as the wavelength of light decreases, does the minimum angle of deflection increase or decrease? (Make sure your conjecture is supported by your results from Experiment #1 and the first portion of Experiment #3.)

Send in 5 incoming beams of light at impact parameters 0.9. The wavelengths of the incoming beams should be 400, 450, 550, 600, and 700 nanometers.

- What are the corresponding angles of the outgoing rays?

Frederick J. Wicklin <fjw@geom.umn.edu> Stuart Levy <slevy@geom.umn.edu>

This lab is based on a module developed by Steven Janke and published
in *Modules in Undergraduate Mathematics and its Applications*, 1992.

Last modified: Mon Oct 30 13:07:05 1995