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Question #45149 posted on 05/26/2008 3:01 a.m.
Q:

Dear Laser Jock, Physics Chick, and the 100 Hour Board,

I recently purchased a cheap "5mW" green laser. (So cool.)

Anyway. I was playing around with it just now, taking some pictures of the beam in some water, when I noticed something kind of odd. I was getting three reflections off of the wall of the container. I was expecting two, based on past experience and physics classes.

Here is the setup. I shone the laser through a plexiglass wall, and reflected it off of the plexiglass containers bottom. The container is filled with tap water. I expected either one or two reflections. One if I accomplished total internal reflection, two if not. Obviously I did not get total internal reflection. Anyway, I expected two reflections, since there should be a reflection at each interface, so one off of the water-plexiglass surface, and one off of the plexiglass-air surface. But I got three. Even more interesting, when I stuck a piece of the plexiglass completely into a big barrel of water, I only got two reflections. This says to me that it probably has something to do with there not being water on both sides of the plexiglass.

You can see a picture of this strangeness here: http://fredjikrang.petfish.net/board/laserconun.jpg

So, why does this happen? It is blowing my mind at the moment. :D

Thanks!

- Fredjikrang

A: Dear Fredjikrang,

First, you're right about what would happen if you got total internal reflection off of the water/plexiglas interface: you'd see one reflected beam. However, if you didn't get total internal reflection you would see more than two beams. The reason is that at the first boundary (water/plexiglss) you would get some light reflected, and some transmitted. At the second (plexiglas/air) you would likewise get some reflected and some transmitted. The reflected light, heading back toward the water, would have to pass through the plexiglas/water interface again—and again, some would be reflected back into the plexiglas, and some would be transmitted into the water. So what you get is a series of reflections back into the water that grow successively weaker. The reason you're seeing only three is that they're so faint that the fourth isn't easy to see. (However, I think I am seeing a fourth in that picture as well.) This diagram (from the Wikipedia article on Fabry–Pérot interferometers) shows what I'm describing.

When you submerged the tank of water in more water, you were changing the index of refraction on the outside of the plexiglas from 1.00 (air) to 1.33 (water). The refractive index of plexiglas (PMMA), on the other hand, is 1.49. The amount of light that gets reflected at an interface partially depends on the difference in the refractive indices of the two materials. Since water is much closer than air to the refractive index of plexiglas, much more of the light was transmitted, and the resulting reflections were much weaker (and harder to see). Fun question, and keep enjoying your new laser pointer!

—Laser Jock