My Science School

          The Greek letter ‘pi’ is a unique number and is defined as the ratio of a circle’s circumference to its diameter. This number is independent of the size of a circle and for all practical purposes its approximate value is taken as 22/7 or 3.1416. In fact, the fraction 22/7 is slightly greater in value than ‘pi’.

          For many centuries mathematicians have been fascinated by its unique characteristic. The strangest thing about this number is that nobody has been able to calculate its exact value. Computer scientists have now computed pi to over one million decimal places.

          At one time the scientists tried to prove that ‘pi’ was a fraction. When any fraction is written in a decimal number, the same digits always appear over and over again in a special pattern. If ‘pi’ were a fraction, there would be a repeating pattern to its digits. But strangely enough a repeating pattern in ‘pi’ could not be found. Finally in 1761, a Swiss mathematician named Johann Heinrich Lambert settled the matter once and for all. He proved that pi is not a fraction.

          Now the question arises what is the significance of ‘pi’ in our daily life? Suppose you have an automobile tyre whose diameter is one metre. If you want to find its circumference, you can find it out by measuring with a tape. Another way of finding the circumference is to multiply the diameter by this strange number ‘pi’. This number is used to calculate the circumference of all the circular objects.

          The mathematicians are still engaged in research in this direction to see if the digits are arranged in any special way. 

            The contact lenses are worn directly on the cornea of the eyes to correct any defects of vision. All the defects that are corrected by regular eye glasses or others that cannot be corrected thus can be rectified by contact lenses.

            The first contact lenses to be used as an eye aid were made by A.E. Fick in 1887. These early lenses were first made by blowing the glasses and then by grinding and polishing bottoms of glass test tubes. These lenses were not successful and for a long time remained just a subject of academic study. However, concrete progress in this direction was made in 1938 when the plastic (methyl methacrylate) contact lenses were developed. From 1938 to 1950 many lenses were made by taking impressions of the eye and forming the lens on this mould. Such lenses had a fluid under them and covered most of the eye. 

            After 1950 smaller lenses were used that covered only the cornea which is the front surface of the eye and floated on a layer of tears. In this case it is not necessary to make an impression of the eye as the curvature of the cornea can be measured by optical instruments. Such lenses are usually 7 to 11 millimeters in diameter and 0.1 to 1 mm in thickness and can be worn all day without removing.

            To fit the contact lenses, the eyes are first tested for the vision defects just as they would be in case of spectacles. Then the radius of curvature of the eye surface is found out by using a device called keratometer. After deciding the diameter and power of the lens, the prescription goes to the manufacturer for making the lens.

            To make the contact lens the plastic rod is first sawn into sections and then turned on a lathe to make button-shaped tablets known as bonnets. Then they are given the right curvature with the help of machines for obtaining the desired power and then polished finally. The lenses are then examined to see whether they fit the eye well, or not. Finally they are worn on the cornea. With increasing acquaintance these lenses can be worn comfortably by most people for 12 hours at a stretch.

            Besides being invisible, contact lenses provide a much wider field of vision than the ordinary spectacles. They are more useful in active sports since they are not easily lost or broken and can even be tinted to protect against the sun. But contact lenses are not effective in all cases of eye trouble. They are also expensive and some people find difficulty in wearing them.

            As the research continues, even smaller and more flexible lenses are being developed in order to make them less irritating to eyes. Soft lenses of hydroxyethyle are used in modern contact lenses. 

          Paint is a mixture of one or more coloured powders and a liquid. The coloured powder is called a pigment. The liquid is called a vehicle or binder. The vehicle carries the pigment and allows it to spread over the surface. Many vehicles contain a solvent or thinner.

          There are basically two types of pigments – prime pigment and inert pigment. Prime pigments give the paint its colour, and inert pigments like calcium carbonate, clay, mica or talc make the paint durable.

          Vehicles include oils, varnishes, latex and various types of resins. When a vehicle comes in contact with air, it dries and hardens. This makes the pigment bind with the surface. 

          There are various types of paints in common use today. The paints often used on walls and roofs are oil-based. Such paints serve to protect wood and metals. Latex paints include wall paints and masonry paints. Many masonry paints are produced with substances like polyvinyl acetate or acrylic emulsions. Lacquers are often used to paint the automobiles. It is made up of a solution of resins in a solvent. The solvent dries up after the laquer is put on. Now we also have fire-retardant paints that protect against any likely damage due to fire. Heat resisting paints are used to cover warm and hot surfaces.

          Then there are cement water paints that add colour to cement surfaces, such as a basement floor. In the metallic paints, aluminium or bronze powder is used as an ingredient. Enamel paints contain small amounts of prime pigments. They are often used in bathrooms and kitchens.

          Paint is manufactured in the following process in the paint factories. A small amount of the vehicle is put into a large mechanical mixer. Then powdered pigment is slowly added to the vehicle. Thus a heavy paste of these two items is made. Now the paste is put into a grinder to break-up the pigment particles, and scatter them throughout the vehicle. This operation is followed by ‘thinning’ and ‘drying’. Now, the paint is poured until the solution is thin enough for use. Tinting is the next process. A tinter adds a small amount of pigment to give the paint the exact colour and shade desired. The final steps include straining and packaging. The paint is strained through a filter to remove any solid bits, dust or dirt. It is then poured into a filling tank, and finally into metal cans in which it is sold.  

               

 

               A shadow is formed when light is incident on an opaque object and cannot penetrate into the space immediately beyond it. In other words, a shadow is that part of an illuminated surface which is shielded from oncoming light rays by an object through which the light cannot pass. This infers that it is a dark patch or area on the ground or on any other surface created by cutting off passage of light. 

 

 

 

               The extent and the shape of a shadow mainly depend on the size of the source of light. If the source of light is very small the outline of the shadow will be sharp and well-defined and their shapes will that of the object producing it. But if the source is large, the shadow will be very dark in the middle, and lighter on the outside with indistinct outlines. The dark part of the shadow is called umbra, i.e. the region of complete darkness and the lighter portion is called as penumbra region.

               The shadows cast by the sun always have a penumbra and the shape of the shadows cast varies with the position of the sun in the sky and the angle of rays. An upright pole will cast a long shadow in the morning when the sun is rising but will grow shorter with approaching noon. As the sun declines in the sky, the shadow grows longer again.

               The human shadows have often had a mystical or magical significance. 

                    A range finder is an instrument used to measure long distances for a number of purposes, especially, by surveyors and the army. They are mainly of two types: optical range finder and laser range finder. Radar is also a form of non-optical range finder. It measures the time lapse of an electromagnetic echo and translates the time into distance. 

                    The military range finders are usually long tubes with eyepieces at the centre. The lenses and prisms are located at each end of the tube. The operator looks through the eyepiece and adjusts the prisms so that the target can be sighted through both the ends of the tube. The difference in the direction of the two lines of sight from the ends of the tube is called the parallactic angle. The angle depends upon the distance of the target. The angle is measured on a dial from which the distance of the target can be read directly.

                    There are two types of optical range finders, coincidence and stereoscopic. In the coincidence range finder, the operator looks through a single eyepiece and sees two images of the target. By turning a knob, these two images move together. When this happens, the distance to the target can be read on a dial. 

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            A siphon is a device used to transfer a liquid from one container to another. It is shaped like a bent tube with arms of unequal length.

            A rubber or plastic tube is normally used as a siphon. Shaped like ‘U’ it has arms of unequal length. One end of the arm is placed in a container and the liquid is sucked up into the tube through the other end. A finger is quickly placed on the open end of the tube to keep the liquid in it. Keeping one end of the tube in the liquid, the open end is then placed in a second container, which should be necessarily at a lower level than the first container. You will find that soon the liquid starts flowing from the first container to the second.

            Now the question arises what makes the liquid flow from one container to the other?

            It is the air pressure which forces the liquid to flow from the first container to the second, provided the level of the liquid in the first container is higher than that in the second one. Because of the difference in the lengths of the arms, a pressure difference causes the liquid to flow. The liquid flows from one container to the other till the level of the liquid in the two containers becomes the same. Since the upper liquid is usually exposed to the atmosphere, the maximum elevation over which a water siphon will function is about 9 m (30 ft) which is the water equivalent of atmospheric pressure. 

          When we throw a ball up into the air, we observe that after its initial pick-up, the speed retards gradually and becomes zero for a fraction of a second before it starts falling back to the ground. While falling down, it should be noted that the initial speed is low but picks up later.

          The ball falls to the ground because it is pulled towards the earth by the force of gravity. The earth attracts all objects towards its centre with a force known as the force of gravity. Due to this force of gravity, all falling objects acquire an acceleration which is called the acceleration due to gravity. It is denoted by ‘g’.

          The acceleration due to gravity accelerates the ball roughly by 9.8 m per sec. per sec. (32 feet per second per second). This means that each second the object would move 9.8 metres faster than the previous second. The speed of the ball at different intervals of time varies as follows. 

          To begin with, the ball or the falling object is stationary or its speed is zero metre per second when it starts falling. At the end of the 1st second it travels 9.8 m per second. At the end of 2 seconds it moves 19.6 m per second and at the end of 3 seconds, 29.4 m per second and so on. In fact, every second the object falls 9.8 m faster than its speed in the previous second.

          The acceleration of a body or object falling freely in a vacuum varies slightly from place to place due to slight variations in the gravitational pull as the distance of the places from the centre of the earth varies to some extent. At London its value is 9.807 m per second per second, at North Pole 9.8 m per second per second, and at equator 9.79 m per second per second. At the sea-level in Washington it is 9.8008 m per second per second. Acceleration due to gravity is defined as the rate of change of velocity of the falling object with respect to time due to the force of gravity. Because it is a measure of rate of change of velocity, it is expressed in metres per second per second.

          One of the important points to note about the falling objects is that however heavy they might be, they all fall at the same rate. However, air resistance may have some effect on the speed of falling objects. This fact was demonstrated by the famous scientist Galileo by dropping a heavy cannon ball and a light musket ball at the same time from the Leaning Tower of Pisa. Both the objects arrived at the ground at the same time.

          The resistance of the air is the main reason why some objects fall faster than the others. A feather, for example, floats slowly downwards because it faces more air resistance due to its relatively large surface for the air to act on. A smooth, pointed bullet will fall faster than a feather because it experiences less resistance of air. In the vacuum both will fall with the same speed because the air resistance would not be there. 

                    The ‘refraction of light’ is defined as the change in direction of a ray of light as it passes from one medium to another, say, air to glass or vice versa. Refraction occurs because light travels at different speeds through transparent materials. For example, light moves at about 300,000 km per second through air but at a much lower speed through water. When it enters water it slows down, which makes it change direction. The ray of light can bend either towards or away from the normal. The normal is defined as the perpendicular line to the interface of the two media. When a ray of light passes from air into glass, it bends towards the normal. When it passes out into air again, it bends away from the normal. In other words, when a ray of light passes from a rarer to a denser medium, it bends towards the normal and when it is the other way round, it bends away from the normal. Also when a ray passes from one medium to another, its speed also changes. If the ray goes from a rarer to a denser medium its speed decreases and vice versa. 

                    There are two basic laws of refraction. The first law states that the ray that hits the surface, called the incident ray and the ray that travels in the second medium called the refracted ray, and the normal – all lie in the same plane. The second law is called the Snell’s law which states that the ratio of the sine of the angle of incidence to the size of the angle of refraction is constant. The size of the constant depends on the two materials through which the light is passing. It is termed as the refractive index between the two materials. 

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               A parachute is an umbrella like device used for slowing down the descent of a body falling through the atmosphere. Originally it was conceived as a safety measure against a probable plane crash or some malfunctioning in a flying aircraft. The parachutes have now found wide applications in times of war and peace; for safe dropping of supplies of essential items in times of emergency as well as for landing of personnel. The first man to demonstrate it was Louis-Sebastian Lenormand of France in 1783. Andre-Jacques Garnaria was first to use a parachute on regular basis demonstrating a number of exhibition jumps including one from a height of about 2400 m in England in 1801.

               Early parachutes were made of canvas and later silk also came to be used. Captain Albert Berry of the U.S. Army made the first successful descent from an aeroplane in 1912. In World War II, parachutes were used for a variety of purposes; landing of special troops for combat, infiltrating agents into every territories and dropping of weapons etc. The modern man-carrying parachutes are made of nylon and are about 7 to 9 m wide when open. The cargo parachutes may be as wide as 30m when open.

               Now the question arises how does a parachute work?

               A parachute operates on a simple principle involving the force of gravity and air resistance — the two forces that act upon any falling object. The parachutes start falling towards the ground due to the pull of the force of gravity but the speed of the fall is checked substantially due to the resistance of air. At low speeds the pull of gravity is stronger than the resistance of air and at higher speed, the air resistance becomes more. Also, large flat surfaces offer more resistance than sharp surfaces. At a certain point the object reaches a speed called terminal velocity when air resistance and the pull of gravity are evenly balanced and, thereafter, the object starts falling at a constant speed. Therefore, an object shaped like a saucer reaches its constant velocity sooner. So it falls more slowly than one shaped like a needle.

               As soon as the parachute canopy opens fully, the resistance of air slows down the descent of the parachutist so suddenly that he is jerked sharply. Now even parachutes with holes or slots in their canopies have been developed to reduce the force of these opening shocks.

                The parachutes descend at a rate of about 5 m (15 ft) per second or slightly faster. But if dropped from less than 150 m above the ground, it can prove dangerous because this height does not allow the parachutes to open. The parachutists can control the direction of their descent by pulling on the shrouds and other operational devices.

               Nowadays new parachutes have been developed which enable one to escape from supersonic planes. Parachute-jumping has become a popular sport in the United States and Europe. Today there are many clubs who organize national and international jumping events in which parachutists try to land on small targets on the ground.  

 

          Any positive integer which is greater  than one and divisible by only itself is called a prime number. For example 2,3,5,7,11,13,17,19,23,29, etc. are all prime number – numbers that cannot be split by division by any other number except 1 and the particular number itself.

          The prime numbers lie at the very roots of arithmetic and have always fascinated those dealing with figures. We can take the sequence of the above given series of prime numbers as far as we like, but we will never find a prime number divisible by another. Over the centuries, the world’s greatest mathematicians have tried to do so and always fail, although they have also been unable to prove that no such number exists.

          Every positive integer greater than one can be expressed as the product of only a single set of prime numbers. Despite the fact that prime numbers have been recognized since at least 300 B.C. when they were first studied by the Greek mathematician Euclid and Eratosthenes. Still these numbers have not yet unfolded certain mysteries relating to them.

          There is infinity of prime numbers and in theory anything may happen in infinity. But so far theorists have not been able to even find any particular rule or theory governing the gaps between prime numbers, which still remains a great mathematical mystery.

          However, the highest known prime number was discovered in 1992 by analysts at AEA Technology’s Harwell Laboratory, Oxon. The number contains 227832 digits, enough to fill over 10 fullscap pages. 

               In ancient times, man had no idea of electrical energy. They took the flash of lightning during a thunder storm to be a signal for an impending destruction from the heavenly Gods. With the passage of time, science in its own way explained the mystery of this great energy called electricity.

               Today, we cannot imagine the normal life without electricity. Commonly we know it as a form of energy, that powers almost all machines or mechanical devices — trains, radios, television sets, freezers and so on. Electricity is a phenomenon involving electrical charges and their effects, when at rest as well as when in motion.

               Electricity that we use flows through wires as electric current. In a nutshell, when an electric current flows through a conductor of finite resistance, the heat energy is continuously generated at the expense of electrical energy. The particles of a matter may be positive, negative or neutral. We know that electricity has its two important particles — protons and electrons. Electron is negatively charged while proton is charged positively to an equal extent. The object containing an equal number of protons and electrons is electrically neutral. For example, anode is a positive electrode while cathode is a negative one. Bulk of the electricity we use is produced in power stations. In the generator of a power station, coils of wire are made to rotate between powerful magnets in order to rotate electric current through the coils. Electricity travels through substances like copper, aluminium and iron. These are called conductors. However, electricity cannot pass through some materials like rubber and glass and these are called insulators. 

               Electricity which flows in one direction and then in the opposite is called Alternate Current (A.C.). Each movement of A.C., back and forth, happens very quickly – about 50 times a second. The electricity that flows in our houses is mostly A.C. Steady flowing current in one direction only is known as Direct Current (D.C.). For instance, battery current is D.C.

               Soon after the invention of electric cell by Alessandro Volta, people came to know that heat, light, chemical reactions and magnetic effects could be produced from electricity.

               As early as 600 B.C. Greeks discovered electricity by rubbing Amber with cloth which enabled it to attract small pieces of papers. In fact, the word electric originated from the Greek word Electron. Based on the theory of “Electro-Magnetic Induction” of Michael Faraday in 1831, first successful generator or Dynamo was made in Germany in 1867. USA produced; electricity by running turbines with the help of falling water in 1858.

               Subsequently hydel and thermal power stations came into existence all over the world. During the 20th century many nuclear power stations were established to meet the growing demand of electricity. 

          A pyrometer is an instrument used for measuring high temperature – especially those which can’t be measured through ordinary thermometers. For example, pyrometers are used to measure temperature in a furnace. 

          There are two main kinds of pyrometers: the radiation pyrometer and the optical pyrometer. In a radiation pyrometer, the radiation from the hot object is focussed onto a thermopile which is a collection of thermocouples. When the thermopile gets heated due to the intercepted radiation, it produces a voltage. The amount of voltage developed depends upon the temperature. Proper calibration permits this electrical voltage to be converted into the temperature of the hot object.

          Sometimes a bolometer is used instead of a thermopile. A bolometer has two strips of the platinum metal. When the platinum strips heat up, the electrical resistance of the strips changes. The change of resistance can be used to measure the temperature. 

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            The solar wind is the constant flow of charged particles from the sun. These particles include protons, electrons and some nuclei of heavy elements. They are accelerated by high temperatures of the solar corona or outer region of the sun, to velocities high enough to allow them to escape from the sun’s gravitational field. Recent researches using satellites have shown that the solar winis made up of plasma, i.e. ionized gas, mostly hydrogen and helium, containing nearly an equal number of protons and electrons.

            The solar wind streams from the sun though outer space at a speed of about 480 km (300 miles) per second. It takes the particles about 3 days to reach Earth.

            In 1958, the American physicist, Egune Norman Parker, called this outward system of protons — the solar wind.

            The solar wind causes the tails of comets to change direction and point away from the sun. It also causes magnetic storms which may disrupt radio communications on Earth. The solar wind causes ionization of the gases in an upper atmosphere, resulting in the coloured light phenomena known as auroras.

            When the solar wind encounters Earth’s magnetic field a shock wave results, the nature of which is not fully understood. That part of the solar wind which does not interact with Earth or the other planets continues to travel at supersonic speeds upto a distance of approximately 20 astronomical units (one astronomical unit is about 1.5 x  kms). As it passes through a similar shock phenomenon it loses this supersonic characteristic. Here the gas cools off and eventually diffuses into the galactic space.

 

               Some stars that have been shining steadily for millions of years suddenly undergo a fantastic change. This change comes in a very unpredictable and violent way. Within a few hours or a couple of days their brightness increases by 10,000 times or more. An ordinary observer might think that a new bright star has appeared in the sky. The increase in brightness occurs when an explosion throws up a small amount of the star’s matter—probably less than a hundred thousandth of its matter. This matter is actually a shell of gas that expands brilliantly in the outer space as soon as the ignition and explosion take place. A nova reaches its maximum brilliance in a few hours or a few days, and then after a few weeks or months it returns to its normal brightness. The decline of the brightness begins at various rates which often fluctuate. After a few years the brightness of the novae remnant becomes steady and a gas cloud may be observed around it which expands at a rate of hundred kilometres per second. Some novae have been known to erupt more than once and are termed as recurrent. All recurrent novae flare up at long intervals. About 20 or 30 novae are believed to occur in our galaxy every year. 

               It has been found that the novae reach absolute visual luminosities to the extent of about 10,000 to 1,000,000 times than that of the sun. The total energy emitted during a large novae outburst is of the order of  ergs, equal to the radiation from the sun in 10,000 years. Should the sun ever become novae, the earth would be destroyed in a few hours or days. However, Sun is unlikely to become so.

               A supernova is a much more spectacular event than a nova. In a supernova explosion, there is a complete self-destruction of the star or at least one-tenth of its matter is thrown off. This may result in an increase in brightness which reveals an entire galaxy as the increase is a billion times more.

               The remains of a supernova that occurred in 1054 A.D is still seen today as the crab nebula which has become one of the most fascinating objects in the sky. Some supernovae including the above were bright enough to be seen in the broad daylight. It seems that a supernova occurs once in about every 300 years. All supernovae are shattered to pieces in their explosions, collapsing into neutron stars.

 

          ‘Every action has an equal and opposite reaction’ – Newton enunciated this principle long ago which is commonly known as Newton’s third law of motion. And a jet engine works on this principle. Its working can be compared to the action of a swimmer who swims forward by pushing water backwards. To put it in the Newtonian law, here the action is pushing of the water backwards and the opposite reaction is the forward movement of the swimmer. In a similar fashion a jet engine ejects (pushes backward) gases at the rear with a great speed and the resulting opposite reaction to this action is the moving of the aircraft in the forward direction in an equal speed. But where does this gas come from and how is it released with such a great force?

          All jet engines have fuel inside them which when burnt in the engine produces a great amount of hot gases almost instantly. It is like an explosion. These hot gases blast out of the back with a great force and the engine reacts by being pushed forward with an equal force. This forward force is called thrust. To get an idea of this movement, we can observe the motion of an air-filled balloon when the air is released suddenly. The balloon zips away rushing out the air in one direction. The rushing out of air is responsible for pushing the balloon in the opposite direction with a thrust.

          The rockets also work on the same principle. The main difference between jets and rockets is the source of oxygen to burn the fuel. A jet engine takes in oxygen from the air around it through an intake nozzle. But a rocket carries its own oxygen which may be in the form of Liquid oxygen in a tank or may be part of a solid fuel the rocket burns. The jet engines have compressors to compress or squeeze the sucked air together before it is mixed up with the fuel and burned in the combustion chamber thereafter. The compression is done to increase the force of explosion within the engine.

 

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