## Fermat's Pond

FermatsPond has three panels arranged side-by-side. The middle panel shows a picture of a fisherman who is standing in water that is approximately three feet deep. The fisherman wouldn't look like this, however, because the water would distort his appearance. The right panel shows how the fisherman would actually appear. Notice both the reflection in the water and the way that the submerged part of the fisherman is distorted.

Exactly how the water distorts his appearance depends on your view point. The diagram to the left shows how all this happens. In this diagram the fisherman is standing at the black line separating the diagram from the picture of the fisherman. Your eye is represented by a black dot toward the left side of the diagram. There are several lines representing light rays arriving at your eye -- notice that each light ray coming from the water's surface can come from two different sources. One is shown with a red line that represents a ray reflected by the surface of the water. The other is shown with a blue line representing a ray that is bent as it passes from the water to the air.

The bottom of Fermat's pond is green. Notice in the right panel the bottom appears to be higher than it actually is.

To see how your vantage point changes the appearance of the fisherman, click on the diagram at a new location for your eye. You can also see how the index of refraction of water affects the appearance of the fisherman by clicking on the up and down arrows flanking the display showing the index of refraction of water. (The default value of 1.33 is the index of refraction for water at 20 degress Celsius.)

You can even get a fish's view of the fisherman by clicking at various points below the surface of the water. You may be surprised by what a fish sees. This surprise is the basis for a sample module illustrating one way in which FermatsPond can be used.