Daily Archives: October 11, 2009

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.

Rod in Glass of water

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.


Sundarbans:Bhatir Desh

Sunderbans, the very name sends the imagination reeling about a amphibian land in the south of Kolkata spread over the maze work of islands created by Ganga, Brahmputra and Meghna rivers. These rivers which seem to abandon their discipline and break up like a fan in this land. It is labyrinth of channels encircling the islands which contain the most fertile soil in their upper crust.

The name seems to be associated with the conspicuous sundari trees which are called Heritiera macrophylla by the botanists. But Mughals, as narrated by Amitav Ghosh in his beautiful novel The Hungry Tide“, called it Bhati  Desh which means Ebb tide country. This became Bhatir Desh over time.

It is the land which is so surreal that there is no line of demarcation between reality and imagination. There are eighteen islands which is why it is also called “Atharo Bhatir Desh”, the land of eighteen lands. There are tigers which can swim miles and miles after their quarries. Crocodiles and dolphins abound here.

There is one chapter in the famous book “Midnights Children” by Salman Rushdie in which three young soldiers of West Pakistan who were sent to East Pakistan and committed heinous crimes like their army, after getting lost, land up in a boat in this Jungle. Rushdie then go on to weave a superb web about the description of the place. He tells that in rainy season, the Jungle seems to grow literally before the eyes. The fruits from the Nipa Palms fall and crack on the ground. In no time the ants swoop on the fruit juice. Since the light never reaches inside many parts, there live snakes which are transparent. Jungle begins to take a complete control of your mind and you forget about the time dimension. Clearly it is the work of great creative imagination of the writer but the author builds these things making base as some real stories.

The Jungle is so dense that if one goes inside, he will forget about the concept of time. The jungle has the power to stop the time. The land is famous for the mangroves which grow copiously and sometimes discard so much dead leaves and wood that they seem to be doing harakiri or suicide, if it were not for the crabs who live there and work as scavengers. They are the janitors who see to it that everything is spic and span or tickety-boo.

The people who live there have adapted themselves to the treacheries of the jungle. They invoke the Goddess “Bonbibi” before going to jungle to gather the honey and wax. The jungle is lorded by Dekkan rai, who stalks in the form of tiger. The legend is that Dekkan rai ruled over the entire Bhatir Desh but he became obsessed with human flesh. According to story, he accosted a convoy of boats which had come there for gathering valuables from jungle, he promised them to give the untold gifts of honey and wax in liu of one human flesh. As planned by the convoy, they left one person behind and when Dekkan rai came to eat him in the garb of tiger, he prayed to Banbibi, who then with the help of her brother fought and defeated Dekkan rai. In the end it was decided that Dekkan rai will rule only the dense jungle.

That is why, whenever inhabitants cross over to jungle, they worship not only Banbibi but also the Dekkan rai, the tiger. It is the place where the womenfolk wear the white saris like widows when there menfolks go to jungle for hunting and gathering honey and wax.

The rivers which have spawned these islands bring with them so much fertile soil from Himalayas that they seem to be playing a game of erecting and erasing the islands at will. Many islands are said to have been buried and no longer exist now. New ones can be born anytime.

There exist so many biomes which harbour myriad kinds of flora and fauna. Storms break where minutes before it was so still that everything looked like a still picture.

It is not far away from Kolkata and yet it is entirely a different world, breathtaking and beautiful and at the same time extremely harsh and unforgiving to the inhabitants.