18.4 Apparent Depth

If you look at a swimmer standing in a clear pool, her legs may seem somehow bent compared to the rest of her body. Stick a pencil into a glass of water, as sketched in Figure 18.11, and the formerly straight pencil suddenly looks bent at the water's surface.

Figure 18.11 Long objects immersed in water seem to be bent at the water's surface.

A very striking example of this is shown in Figure 18.12 where a coin has been placed on the bottom of a bowl. The coin is not visible at first. But if water is poured into the cup the coin appears to be raised higher and, thus, is visible.

Figure 18.12 A coin on the bottom of this empty bowl can not be seen from this angle of view. Pouring water into the bowl makes an image of the coin appear above the actual coin and, thus, the coin's image is visible from this angle of view.

Another example of this which you may have already noticed is illustrated in Figure 18.13. There a fish is swimming in an aquarium. When viewed through the top, the fish seems closer to the top than it really is; when viewed through the front, the fish seems closer to the front than it really is. This means you can see two fish although there is really only one. If you position yourself carefully you may even be able to see three fish! You are seeing three images of the same fish.

Figure 18.13 Fish in an aquarium appear closer to the surface than they really are.

How does a plane surface like this produce an image? Figure 18.14 shows an object O located at a distance do below the surface of the water. One ray of light is shown going straight up. This ray of light strikes the water-air interface normal or perpendicular to the surface and passes into the air without being bent. A second ray strikes the water-air interface a horizontal distance x away with an angle of incidence of i and is refracted so that it leaves with an angle of refraction of r. This ray and the first one now appear to have originated from position I-the image-located at distance di below the surface. This image distance di is the apparent depth of the thing we are looking at.

Figure 18.14 The change of index of refraction in passing from water into air is responsible for the apparent depth.

As you can see from the figure, the apparent depth or image distance is going to be less than the actual depth or object distance. For rays at other angles or for other values of x, the image is not located at the same place. You can even notice this in looking at fish in an aquarium. At some angles the images of a fish received by your two eyes may not coincide precisely and the fish may appear blurred or simply "strange" or you may even feel slightly dizzy. This lack of a well-defined position for the image is an example of astigmatism.

Q: When you look at a fish in an aquarium, it is closer to the glass or farther from the glass than it appears to be?

A: The fish is farther away than it appears to be.