What you see is explained in the same way as are the things that took place in the other experiments in refraction, or bending of light. The light from the part of the pencil above the water comes straight to your eye, of course; so you see it just as it is. But the light from the part of the pencil in the water is bent when it comes out of the water into the air on its way to your eye. This makes it come to your eye from a different direction and makes the lower part of the pencil seem to be in a place to one side of the place where it really is. The pencil, therefore, looks broken.
Fig. 67. The bending of the light by the water in the glass causes the pencil to look broken.
Whenever light passes first through something dense like water or glass, and then through something rare or thin like air, it is bent one way; whenever it passes from a rare medium into a dense one, it is bent the other way. Light passing from a fish to your eye is bent one way; light passing from you to the fish's eye is bent the other way, but the main point is that it is bent. And when light is bent before reaching your eyes it usually makes things seem to be where they are not.
Fig. 68. The light is bent when it enters a window pane and is bent again in the opposite direction when it leaves it.
If light goes through a perfectly smooth, flat pane of glass, it is bent one way when it goes into the glass and back the other way when it comes out; so it seems to be perfectly straight and we see things practically as they are through a good window. But if the window glass has flaws in it, so that some parts are a little thicker than others, the uneven parts act like prisms and bend the light to one side. This makes anything we look at through a poor window seem bent out of shape. Of course the things are not bent any more than your pencil in the water was bent, but they look misshapen because the light from them is bent; the reflected light is all we see of things anyway.
The air itself is uneven in a way. The parts of the air that are warm, as you already know, are thinner and more expanded than are the cold parts. So light going from cold air into warm or from warm air into cold, will be bent. And this is why you see what are called "heat waves" above a stove or rising from a hot beach or sidewalk. Really these are just waves of hot air rising, and they bend the light that comes through them so as to give everything behind them a wavy appearance.
Stars twinkle for much the same reason. As the starlight comes down through the cold air and then through the warm air it is bent, and the star seems to be to one side of where it really is; but the air does not stand still,—sometimes it bends the light more and sometimes less. So the star seems to move a little back and forth. And this is what we call "twinkling." Really it is the bending of light.
Application 35. Explain why an unevenness in your eye will keep you from seeing clearly; how glasses can help this; why good mirrors are made from plate glass, which is very smooth, instead of from the cheaper and more uneven window glass; why fishes in a glass tank appear to be where they are not.