sciencecapsules

    We are going to see one of the earliest method used in cryptography to send secret messages.  It was used by Julies Caesar and hence named Caesar cipher.        Here, each letter of the message is shifted forward by 3 places in the alphabet .  That is, A will become D, B will become E and so on. For quick reference;  Plain text:    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Cipher text: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C  So the message 'Welcome to my blog' encrypted as  'ZHOFRPH WR PB EORJ'   This is technically called mono alphabetic substitution cipher.  Here a shift of +3 is used.  But we could use a shift of +1 to +25.  A person who knows the algorithm (method) can only decipher the code and retrieve the message.  Suppose someone wants to break the code and get the message,  Is there a way? Yes, there is.        The appearance of letters in English language has certain frequencies as given below.      The le

    If there are 60  people in a gathering, will any two persons have the same birth day?  We are doubtful. we think if there are more than 365 persons, there may be a possibility of two persons sharing same birthday.  But the statistics' answer is stunning.  Here we go.      In a coin toss, chance of getting head or tail is 50 % or 1/2.  Chance of head is 1/2 and the tail is 1/2.  Hence the total probability is 1.        In a dice throw, chance of getting '1' is 1/6 and the chance of 'not' getting '1' is 5/6 = 1-1/6 .       In a gathering, the chance for a person to have any date in a year as a birthday is 365/365=1=100%.  For another person, the chance of not having a birthday same as first person is 364/365.  For a third person, the chance of not having a birthday same as previous two persons is 363/365.  Hence the probability for not having a match (two persons having same birth day ) among three persons is (365/365) * (364/365)*(363/365)  (ba

Is earth a lonely planet?  Is there any other civilization in our milky way galaxy ?  These questions are answered by Drake equation .  First let us see the variables in the equation. 1. N# - There are roughly 100 billion stars in milky way  galaxy. 2. FP - 20%  to 50% have planetary system. 3. NE- 1 to 5 planets of each star have the capability to sustain life. 4. FL - 0% to 100% of the planets have the capacity to support and evolve life. 5. FI -  In 0 % to 100 % of planets, the intelligent life evolves. 6. FC - 10% to 20% of intelligent life try to communicate. 7. FL - How long the intelligent life survive and communicate? It is tough to guess.  We are communicating using radio waves for last 100 years only.  N - If we multiply all the above factors ,  we may get the probable number of intelligent and communicating civilization in our galaxy. N = N#*FP*NE*FL*FI*FC*FL Let us guess the minimum values, substitute in the equation and find the answer.     = 100 BILLION

Land line :      Here, microphone converts voice into electrical signals, amplified and is sent through wire.  At the other end, electrical variations are converted into sound by the speaker.  Today electrical signals are converted into laser signals and sent through glass fibers.  We know land line is the two way communication (send and receive).    Radio :  Here, electrical signals are superimposed on high frequency radio waves.  Then the radio waves are radiated from tower.  High frequency waves has high energy and they can travel to long distance.  When you put a powerful light on the top of a tower, it will spread to long distance.  Similarly, high wattage radio waves (invisible light) spread to wide area. Wireless communication had begun .  Voice only is sent over the radio.  It is a one way communication, receiving only.  At the receiving end signals are extracted from radio waves and fed to the speaker. TV :        Here, audio and video is converted into electrical

        The calendar mainly based on the motions of celestial bodies.    We know the time taken by the earth to go round the sun once is taken as one year.  We also know the time for the earth to spin is taken as a day.  It happens to be 365+ days in a year.  That is why, a circle is divided into 360 degrees.       Moon takes roughly 29+ days to go round the earth.  Hence 30 days average is taken as the month.  The moon revolves around the earth 12 times a year.        Seven days makes a week.  Because only seven heavenly objects were known then.  Hence the week days were named after them. Sun - Sunday, moon - Monday, mars - Tuesday, mercury - Wednesday, Jupiter - Thursday, Venus - Friday, Saturn - Saturday.      In the past, sundials (measuring time using shadow) were used to measure daytime.  It had 12 equal marks.  So we have "12 hours  day and 12 hours night" system still.      Each hour is split into 60 minutes and a minute into 60 seconds.  Similarly a d

    Light takes 3+  seconds to travel from the moon.  It takes 8 minutes and 17 seconds to travel from the sun. The nearest star alpha centauri is 4.37 light years away. So light propagation is not instantaneous as we experience every day.  It has finite speed 300000000 met/sec in vacuum.        When light travels in denser medium like water or glass,  it slows down.  In glass, it travels at 2*10 ^8 met/sec speed.  The ratio of speed in vacuum to the speed in glass is 1.5 and it is the refractive index of the glass.      Discovery of speed :  Ole roamer observed Jupiter through telescope.  He was able to see the shadow of its moon 'Io" on the face of Jupiter as a blackspot.  When the Jupiter was close to earth, the spot appeared at one place; when the Jupiter was far away  from the earth, the shadow appeared at another place.  From these observations, he was able to calculate the speed of light.      Einstein said: "The velocity of the light is independen

    Cut the trunk of a age old tree.  We can see number of rings in the cross section.  Each ring is formed during a year.  The count of rings gives the age of tree.      Earth rock and meteorites that has fallen on the earth has a composition of potassium-40 and organ-40.  Potassium is the radioactive element.  It emits radiation and decays into organ.   Radioactivity never stops .  The original potassium atoms are slowly converted into organ.  By counting the number of radioactive potassium atoms and stable organ atoms, one can estimate the age of rock using this formula. N = n*e^(-R*T) N - number of radioactive atoms at present (potassium) n- Number of radioactive atoms during the formation of        rock(potassium + organ) R - Radioactive constant of potassium T - Age , time elapsed since the formation of rock. e - Maths constant      This is called radiometric dating.  Since the rock belongs to earth, it will give the age of earth.  The meteorite will give the a

    Water is a peculiar liquid.  But it is very essential for the life to beat.       When liquids are cooled down, they contract and become solid.  Water also contracts and become ice.  But it contracts up to 4 degree c only.  It expands from 4 degree c to 0 degree c due to water molecule bonding.  That is, its density decreases.  That is why ice floats on water.        In a water body like a lake, cooled water comes to the top because it is less denser.  Then the top surface first freezes over.  Since ice and water is poor conductor of heat, the liquid water remains intact below the friezed surface.  Hence the aquatic life can continue to live in the lake in winter also.  Men can walk and play on the lake during winter.   Even truck can move on it, if ice is sufficiently thick.      Iceberg is a ice mountain which has broken away  from glacier and floats on ocean.  1/10 of iceberg  is visible above the surface of ocean.  90 % of the iceberg  remain immersed in ocean due

  We know, if the switches A and B are closed in the above circuit, the bulb will light up.Even if one is open, the bulb is off.  Logically we can say,  if A and B are true, the output is true else the output is false.  In digital logic it can be written, "if A AND B are 1 the output is 1 else the output is 0".      The AND logic can be wired electronically.  Instead of switches we will be using automatic switches like diode and transistor.       Then we have OR  logic.  That is written as; "if either A OR B is 1 then output is 1" . ( If both are 0 then output is 0).    Next NOT  logic; here the input is reversed and given as output(0 to 1: 1 to 0 ).     NOT  and  AND  can be combined and it is called NAND logic.  NOT + OR  is called NOR  logic.      All this logic statements can be hard wired using electronic components and they are used in many devices.  For example :  The AND  logic is used in lift.  " If A door and B door are closed, then

    Water flows from mountain top to valley down.  All fluids flow from high pressure to low pressure.  Heat flows from high temperature to low temperature.  Similarly, the electrons flow from surplus point to starving point.  In chemical reactions of a battery, there are more electrons at negative electrode and there is lack of electrons at positive electrode.  Then the electrons try to flow from negative to positive electrode.  When we connect negative and positive point by a wire, the current (electrons) flow from high electric potential to low electric potential.   (Note: Electrons flow from negative to positive end and the conventional current is taken to flow from positive to negative).        Resistance:  We know the current flows through the metal wire.  The atoms in the metal are never at rest.  They vibrate due to temperature.  The electrons that move through these vibrating atoms get hits.  So the metal atoms offer “ resistance ” to the current. So the ohm’s law

Consider this, 6= 2 * 3 9 = 3* 3 12 = 2* 2* 3 The kind of numbers like 6, 9, 12 are called composite numbers because they can be broken down into smaller numbers.  But numbers like 2, 3, 7, 11 cannot be split up into whole numbers. They are divisible by 1 and by themselves only.  These numbers are called prime numbers.  They behave like "atoms" in the number system.  We can build other composite numbers using them in an unique way.  For example, 28 can be expressed as 7 * 2* 2.  This is the only way to write 28 using primes. Another example:6545448 = 2^3*3^5*7*13*37 The list of prime numbers below 100 is given below. 2, 3, 5, 7, 11, 13, 17, 19, 23 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. There are 25 primes between 1 and 100.  But only 14 primes between 900 and  1000.  There is no formula to find the prime numbers.  There is no pattern in the appearance of primes. Yet, the umber of prime numbers are limitless .  The largest known p

  Earth not only revolves around the sun but also tilts to one side or other every 6 months.   This tilting causes seasons .  The hemisphere which faces the sun is experiencing summer.  The other hemisphere which is away from the sun is having winter.      In summer, we want to cool our body.  Hence we use high speed fans which blow away hot air surrounding the body and brings in cool air.  In winter, we want to keep our body warm.  We wear woolen sweaters.  The hairy wool material traps warm air.  The air cannot easily escape from our body and hence keeps the body warm.      The earth is at right distance from the sun.  Hence it has the right temperature, not too cold or too hot.  The temperature keeps water in liquid form and sustain the life. Science update:  MIT  researchers made micro lenses with droplets.

     We know electron whirls and spins in an atom.  When an electron revolves, the electric fields also circulates.  Consequently a magnetic field is created perpendicular to the plane of rotation(maxwell's equation).       Suppose in a loop of wire, a current (bunch of electrons) flows, a magnetic field will be created through the loop.  One side north pole and the other side south pole.  We will extend this principle further.  If we have a coil of wire (more number of loops).  The magnetic fields are added up and we get a strong magnetic field.  In short, the current carrying coil acts like a bar magnet with north pole at one end and the south pole at the other end.      Now we will do a simple experiment to demonstrate magnetism created by a coil. Wire the circuit as given below.       Here, when the switch is closed, the current flows through the coil only.  Current cannot pass through LED because it is a one way device.  While the current flow

    Let us consider a simple BASIC program which checks marks of each student and count the number of students passed.  Using this program, we will try to learn the nuance of this art .      A program is made of three fundamental components namely 1. sequential flow 2. conditional flow, 3. repetitive flow. 1. Statements from line 10 to 40 are just flowing sequentially .  Line 10 is just a title.  Rem means remark. 20 initiates a counter.  Pass marks is fixed in 30.  In line 40, N stores number of students.  These statements are  executed one by one. 2. Line no. 50 to 80 is executed repeatedly .  That is, the statements 60 and 70 is executed 10 times since N =10.  Each time the control comes to line 60, it READs a value from DATA statement (line 90) and store it in "MARK". 3.  When the control comes to line 70,  it makes a decision .  If the mark is equal to or greater than pass mark, the count is increased by 1.  If the condition is not met, the con

water drop lens     Lens is everywhere.  It is found in telescope, microscope, camera, projector, binoculars and spectacles and so on.  The lens rules the world even today.      Eye lens is natural one.  At one moment, we can see ant moving on the floor.  The next moment we can see the stars in the sky.  Eye lens can change shape automatically and there by alter its focus according to the distance of the object.  That is a natural wonder.  We still struggle to duplicate it.      Eye lens loses its transparency and become opaque due to aging.  That is cataract.  In cataract surgery, the natural lens is replaced by artificial one.  Cataract surgery is one of the highest numbers of surgeries done worldwide. How to see without spectacles?       You need not worry, if you miss the specs.  A pinhole in a camera box (light tight box) acts as the lens and forms the image on the opposite side as shown in figure.  A pinhole can focus the object at any distance.  So

  1 .       Mathematics of the pendulum is complicated. 2 .        Frequency of oscillation of a pendulum depends only on its length. 3 .       Time period or frequency does not depend on mass or material of the bob. 4 .         Pendulum’s energy alternates between potential and kinetic and hence it oscillates . 5 .        Potential energy and kinetic energy have opposite relationship and the total energy is conserved. 6 .         Tension along the string (upwards) and weight of the bob (downwards) are only the two forces acting in the pendulum. 7 .         Mainly gravity is responsible for the pendulum’s swings.  Hence ‘g’ can be measured with a pendulum. 8 .        Pendulum always tries to reach equilibrium (center position).  But overshoots it due to inertia 9 .         Size of the swing does not affect time period or frequency of the pendulum. 10.      99 cm length pendulum takes 2 second for one oscillation. 11.    Pendulum’s

    To add;   3/2+5/3, first we have to calculate the least common divisor which is   2*3 = 6.   then,         3/2+5/3 =  (9+10)/6 = 19/6.  Why do we adopt this procedure?         We cannot add apples and oranges. Similarly 3/2 and 5/3 belongs to different categories .  3/2 has 3 times 1/2 and 5/3 has 5 times 1/3.  Hence we cannot directly add them.  First we should bring them to a common platform .  Here LCD 6 comes to our help.   1/6 happens to be the common factor for both the fractions. 9 times 1/6 gives  3/2               9*(1/6) = 3/2 10 times 1/6 gives 5/3             10*(1/6) = 5/3      So instead of adding 3/2 and 5/3; we can easily add 9/6 and 10/6 and get the answer.                                9/6  +  10/6  =  (9+10)/6  =   19/6                                     Take a white sheet of unit area  and draw the lines as shown in the figure.  Each line goes on halving the area(Note:  Paper size A series is based on this principle). Now I want to add all