Stick a pin in a flat cork circle and put it by the pin down on the surface of the water in the bowl. If the tube is not too wide, no matter how tilted you head, you will not be able to see the pins - although it would seem that it is long enough that the tube did not keep it from you.
Figure 1. Experience with the pin, invisible in the water.
Why light rays do not come from a pin to your eyes? Because they undergo what in physics is called "total internal reflection". Recall, what is this phenomenon. Figure 2 you can follow the paths of rays passing from air to water (generally from among more than refracting in the environment less refracting) and back. When the rays going from air into water, they are approaching the perpendicular fall"; for example, the beam incident on the water at an angle b to the perpendicular to the plane of incidence, enters into it at an angle andwhich is less than b.
Figure 2. Different cases of refraction of the beam at the transition from air to water. In case II the beam falls under the limit angle to a perpendicular fall in and out of the water, gliding along its surface. III depicts the case of total internal reflection.
But what happens when an incident beam, sliding on the surface of the water that falls on the water surface is almost at a right angle to the perpendicular? He enters the water at an angle less than a straight line, namely at an angle of 48.5 degrees. At a large angle to the perpendicular, than 48.5 degrees, the beam to enter the water cannot; this is water "limit" angle. You need to understand these simple ratios to understand the future, completely unexpected and extremely interesting investigation of the law of refraction.
We have now learned that the rays falling on the water under vsevozmojnymi angles are compressed under water in a very narrow cone with an angle of a solution of 48.5 + 48,5 = 97°. Watch now over the course of rays coming back from air to water (Fig. 3).
Figure 3. The rays emanating from point P at an angle to the perpendicular fall more marginal (pods - 48.5 degrees), do not go into the air from the water, and completely reflected inside.
According to the laws of optics, the path will be the same, and all the rays of the prisoners mentioned in the 97-degree cone, will be released into the air from different angles, spread across 180-degree space above the water.
But where it is underwater beam that is outside the above-mentioned cone? It turns out that it will not work at all out of the water, and will be reflected entirely from its surface, as from a mirror. In fact, every underwater beam met the surface of the water at an angle, large "marginal" (i.e., large 48.5 degrees), not refracted, and reflected: he suffers, as physicists say, "total internal reflection*".
Figure 4. The arc of the outer world in 180° is reduced to an underwater observer to the arc at 97°; the reduction is stronger, the next is part of the arc from the Zenith point (0°).
If the fish studied physics, the main Department of optics would be for them the doctrine of "internal reflection", because in their underwater vision it plays a primary role.
In connection with the peculiarities of the underwater view is, in all probability, the fact that many fish have silvery color. According to zoologists, this painting is the result of the adaptation of fish to color spread over them the water surface: when observed from below the surface of the water, as we know, seems to mirror due to the "total internal reflection"; and against this background, silver-colored fish remain invisible to hunting them aquatic predators.
* Reflection is called in this case full because it reflects all the incident rays, meanwhile, as even the best mirror (polished magnesium or silver) reflects only part of the incident rays, absorbs the rest. Water under specified conditions is the perfect mirror.