RAINBOW                       


A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun.
In a so-called "primary rainbow" ,the arc of a rainbow shows red on the outeR part of the arc, and violet on the inner section. This rainbow is caused by light being refracted then reflected once in droplets of water. In a double rainbow, a second arc may be seen above and outside the primary arc and has the order of its colours reversed. This second rainbow is caused by light reflecting twice inside water droplets. The region between a double rainbow is dark and is known as "Alexander's band" or "Alexander's dark band". The reason for this dark band is that, while light below the primary rainbow comes from droplet reflection and light above the upper rainbow also comes from droplet reflection, there is no mechanism for the region between a double rainbow to show any light reflected from water drops. It is impossible for an observer to manoeuvre to see any rainbow from water droplets at any angle other than the customary one (which is 42 degrees from the direction opposite the Sun). Even if an observer sees another observer who seems "under" or "at the end" of a rainbow, the second observer will see a different rainbow further off-yet, at the same angle as seen by the first observer. Thus, a "rainbow" is not a physical object and cannot be physically approached.

A rainbow spans a continuous spectrum of colours. The distinct bands are an artefact of human colour vision and no banding of any type is seen in a black-and-white photo of a rainbow. For colours seen by a normal human eye, the most commonly cited and remembered sequence, in English, is Newton's sevenfold violet, indigo, blue, green, yellow , orange and red  (popularly memorized as VIBGYOR). However, colour-blind persons will see fewer colors. Rainbows can be caused by many forms of airborne water. These include not only rain but also mist, spray and airborne dew.

Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind at a low altitude angle. The most spectacular rainbow displays happen when half the sky is still dark with raining clouds and the observer is at a spot with clear sky in the direction of the sun. The result is a luminous rainbow that contrasts with the darkened background. The rainbow effect is also commonly seen near waterfalls or fountains. In addition, the effect can be artificially created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights. As human visual perception for colour is poor in low light, moonbows are often perceived to be white. It is difficult to photograph the complete semicircle of a rainbow in one frame, as this would require an angle of view of 84°. For a 35 mm camera, a lens with a focal length of 19 mm or less wide-angle lens would be required. Now that powerful software for stitching several images into a panorama is available, images of the entire arc and even secondary arcs can be created fairly easily from a series of overlapping frames. From an aeroplane, one has the opportunity to see the whole circle of the rainbow, with the plane's shadow in the centre. This phenomenon can be confused with the glory but a glory is usually much smaller, covering only 5–20°. At good visibility conditions, the second arc can be seen, with inverse order of colours. At the background of the blue sky, the second arc is barely visible.

          BIOSPHERE                         

The biosphere is the global sum of all ecosystems. It can also be called the zone of life on Earth, a closed and self-regulating system. From the broadest biophysiological point of view, the biosphere is the global ecological system integrating all living beings and their relationships, including their interaction with the elements of the lithosphere, hydros  and atmosphere. The biosphere is postulated to have evolved, beginning through a process of biogenesis or biopoesis, at least some 3.5 billion years ago. In a broader sense, biospheres are any closed, self-regulating systems containing ecosystems including artificial ones such as Biosphere 2 and BIOS-3 and potentially, ones on other planets or moons.
Some life scientists and earth scientists use biosphere in a more limited sense. For example, geochemists define the biosphere as being the total sum of living organisms. In this sense, the biosphere is but one of four separate components of the geochemical model, the other three being lithosphere, hydrosphere and atmosphere. The narrow meaning used by geochemists is one of the consequences of specialization in modern science. Some might prefer the word ecosphere, coined in the 1960s, as all encompassing of both biological and physical components of the planet.

The Second International Conference on Closed Life Systems defined biospherics as the science and technology of analogs and models of Earth's biosphere i.e. artificial Earth-like biospheres. Others may include the creation of artificial non-Earth biospheres—for example, human-centered biospheres or a native Martian biosphere—in the field of biospherics. In the early 1970s, Lynn Margulis, a microbiologist from the United States, added to the hypothesis, specifically noting the ties between the biosphere and other Earth systems. For example, when carbon dioxide levels increase in the atmosphere, plants grow more quickly. As their growth continues, they remove more and more carbon dioxide from the atmosphere.
Many scientists are now involved in new fields of study that examine interactions between biotic and abiotic factors in the biosphere, such as geo-biology and geo-microbiology. Ecosystems occur when communities and their physical environment work together as a system. The difference between this and a biosphere is simple, the biosphere is everything in general terms.

Every part of the planet, from the polar ice caps to the Equator, supports life of some kind. Recent advances in microbiology have demonstrated that microbes live deep beneath the Earth's terrestrial surface and that the total mass of microbial life in so-called "uninhabitable zones" may, in biomass, exceed all animal and plant life on the surface. The actual thickness of the biosphere on earth is difficult to measure. Birds typically fly at altitudes of 650 to 1,800 meters and fish that live deep underwater can be found down to -8,372 meters in the Puerto Rico Trench. There are more extreme examples for life on the planet: Ruppell's Vulture has been found at altitudes of 11,300 meters. Bar-headed Geese migrate at altitudes of atleast 8,300 meters. Yaks live at elevations between 3,200 to 5,400 meters above sea level. Mountain goats live up to 3,050 meters. Herbivorous animals at these elevations depend on lichens, grasses and herbs.

Microscopic organisms live at such extremes that, taking them into consideration puts the thickness of the biosphere much greater. Culturable microbes have been found in the Earth's upper atmosphere as high as 41 km. It is unlikely, however, that microbes are active at such altitudes, where temperatures and air pressure are extremely low and ultraviolet radiation very high. More likely these microbes were brought into the upper atmosphere by winds or possibly volcanic eruptions. Barophilic marine microbes have been found at more than 10 km depth in the Marianas Trench. Microbes are not limited to the air, water or the Earth's surface. Culturable thermophilic microbes have been extracted from cores drilled more than 5 km into the Earth's crust in Sweden, from rocks between 65-75 °C. Temperature increases with increasing depth into the
Earth's crust. The speed at which the temperature increases depends on many factors, including type of crust, rock type, geographic location, etc. The upper known limit of temperature at which microbial life can exist is 122 °C and it is likely that the limit of life in the "deep biosphere" is defined by temperature rather than absolute depth.

Our biosphere is divided into a number of biomes, inhabited by broadly similar flora and Fauna. On land, biomes are separated primarily by latitude. Terrestrial biomes lying within the Arctic and Antarctic Circles are relatively barren of plant and animal life, while most of the more populous biomes lie near the equator. Terrestrial organisms in temperate and Arctic biomes have relatively small amounts of total biomass, smaller energy budgets and display prominent adaptations to cold, including world-spanning migrations, social adaptations, homeothermy, estivation and multiple layers of insulation.

      GEOMETRY

Geometry (Greek: Geo- "earth" -Metria "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Initially a body of practical knowledge concerning lengths, areas and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow. Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. A mathematician who works in the field of geometry is called a geometer. The introduction of coordinates by Rene Descartes and the concurrent development of algebra marked a new stage for geometry, since geometric figures, such as plane curves, could now be represented analytically, i.e., with functions and equations. This played a key role in the emergence of infinitesimal calculus in the Th century. Furthermore, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of projective geometry. The subject of geometry was further enriched by the study of intrinsic structure of geometric objects that originated with Euler and Gauss and led to the creation of topology and differential geometry.

In Euclid's time there was no clear distinction between physical space and geometrical space. Since the 19th-century discovery of non-Euclidean geometry, the concept of space has undergone a radical transformation and the question arose which geometrical space best fits physical space. With the rise of formal mathematics in the 20th century, also space lost its intuitive contents, so today we have to distinguish between physical space, geometrical spaces and abstract spaces. Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean space, which they only approximately resemble at small scales. These spaces may be endowed with additional structure, allowing one to speak about length. Modern geometry has multiple strong bonds with physics, exemplified by the ties between pseudo-Riemannian geometry and general relativity. One of the youngest physical  theories, string theory, is also very geometric in flavour. While the visual nature of geometry makes it initially more accessible than other parts of mathematics, such as algebra or number theory, geometric language is also used in contexts far removed from its traditional, Euclidean provenance.

Geometry originated as a practical science concerned with surveying, measurements, areas and volumes. Among the notable accomplishments one finds formulas for lengths, areas and volumes, such as Pythagorean theorem, circumference and area of a circle, area of a triangle, volume of a cylinder, sphere and a pyramid. A method of computing certain inaccessible distances or heights based on similarity of geometric figures is attributed to Thales. Development of astronomy led to emergence of trigonometry and spherical trigonometry, together with the attendant computational techniques.