Living underwater has many consequences for fish. Not only do fish need to be able to breathe and move and feed underwater, but this denser-than-air medium also has a large impact on how fish see their surroundings.
One of the most important aspects of light, as far as anglers are concerned, is how it behaves when passing between air and water. When a person looks at a tree, or a bass looks at a minnow, light behaves in much the same way for each. However, if the person looks down into the water at the minnow—or the bass looks up at the tree—the situation suddenly changes. When light travels through the air and suddenly strikes the water, it is bent (or refracts) and now moves at an angle to its original path. This refraction can be easily observed by placing your rod tip underwater: suddenly, the rod no longer appears straight, but appears to be bent at the point where it enters the water.
The same principle applies to an angler and a bass warily keeping an eye on each other at the local fishing hole. Because of the refraction of light, the angler can actually see over the edge of the bank and spot the bass (solid line in illustration below), even though without refraction the bank would actually block his straight-line-of-sight to the bass (dashed line below). Similarly, the bass can also see the angler along the same angle of refracting light, even though without refraction the bank would also block the fish's view of the man.
Light refraction in water
Thanks to refraction, this angler can see the bass over the edge of the bank even though it would otherwise be blocked from his line-of-sight. And the bass can see him too!
One important point to note here is that even though the light is being bent, it doesn't look bent to the angler. Without a little knowledge of physics, the angler would assume that he is looking in a straight line directly at the fish. But the fish is actually closer than it appears. For this reason, if an angler is trying to present a bait or a lure directly in front of a fish, he should cast slightly short of what appears to be the intended target.
WARNING: Objects in water are closer than they appear!
There is an exception to this general rule. If an angler is looking straight down on a fish (from a bridge or pier for example), then that fish is exactly where it appears to be. The light from the fish is striking the surface of the water at a right angle and perpendicular (⊥) to the water's surface, and under these conditions it penetrates straight down into the water with no refraction at all.
By a similar line of thought, if you move far enough away from that same fish there is another point at which light is not refracted down into the water and to the fish, but instead of penetrating is reflected off the surface of the water. This point varies with water conditions and the directional source of the light, but is illustrated below. In this simplified example, the standing angler is visible to the fish because light above our theoretical dividing line is refracted and enters the water. However, the crouching angler is not visible, because light below the line strikes the water at such a sharp angle that it is reflected off the surface of the water and away from the fish.
Stay low to hide from fish
The moral of the story: Take a hint from trout anglers and stay low to remain hidden from fish!
The precise point where light is reflected from the water rather than penetrating would be difficult to calculate in the field, but the basic principle remains that staying low will reduce your chances of being seen. Of course, if the fish cannot see the angler, then the angler cannot see the fish either.
All of this discussion assumes a smooth water surface under ideal observation conditions. Choppy water or waves makes it correspondingly more difficult for angler (or fish) to see from air into water or vice-versa. Other factors, such as direct sunlight versus cloudy weather and directional source of available light, also play a role in how much an angler can see of a fish, and how much a fish can see of the angler.