Snell’s Window

How the species under water see the world above? The entire horizon is visible to them through a window, a disc, called Snell’s window named Dutch mathematician Willebrord Snellius. Anything outside this window is not visible. In fact the area outside this window looks dark.

The diameter of disc varies with the depth at which the viewer is located below water. As the depth of eye increases, the disc gets bigger in size.

All this depends upon the strange properties of the light which illuminates this world and which enters our eyes which act as a camera.

We know now that phenomena occurring in the microscopic realm cannot be explained by usual classical science. For example, light is considered as wave as well as discrete bundles called photon. We have to resort to dualism to explain different kinds of observations. This is because assumptions are required to explain when the reality is not known to us. Light may neither be discrete particles or waves which we are unable to fathom as yet.

As we know that light consists of photons which are tiny bundles of light traveling in a stream. This means that light will travel with different speeds in different mediums. In the water for example, the light travels slowly than the air because water molecules offer resistance to the flow of photons. As a viewer, we see the light rays bending towards the normal to the point where light ray strikes the water. This is the other way of saying that light seem to come from a depth which is more than the real depth. This is shown in the following picture.

This was explained by a law known as Snell’s law which states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of velocities of light in two media, or equivalent to the opposite ratio of the indices of refraction.

Refraction of light has many strange and interesting consequences. One of them is how the living species like fish, dolphins & divers look the world outside the water. From the Snell’s law, it is clear that a ray of light making an angle of 90 degrees incidence, meaning grazing parallel to surface, bends at an angle of 48.7 degrees. This clearly means that rays covering the entire horizon will form a disc of light with apex on the eye and cone angle double the angle of refraction, that is 97.4 degrees. Depending upon the depth at which eyes of the species are located, the disc diameter will adjust itself to enclose the entire horizon above. The calculations show this as follows.

So, the entire world above surface will become visible through a disc of light. Outside this disc is all darkness.

This disc is essential to negotiate the space in 3-dimensions. Without this, the species will not be able to know which is upside or downside. They will become disoriented. This can happen to the species which live in the rivers carrying large amounts of clay and are muddied. Here, for survivor, the fish has to adapt other means to survive.

I found this beautiful picture of a turtle in the Snell’s window on the Flickr. Please click the link to see this picture. This site contains very stunning photos. So it will be worthwhile to explore this site.

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