AT THE SPEED OF LIGHT

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 independent of light source speed and observer's speed". A car speed is relative to the earth surface or another car speed. But the light speed is absolute, not relative and a constant. This principle is the 'corner stone' of theory of relativity.

Einstein also said: "The light speed is maximum attainable speed in nature". That is, nothing can travel faster than light. Some scientists say this barrier will be broken in future and we will be able to travel faster than light in space.

Light speed plays an important role in Einstein's topmost formula E= mc^2.

So what is speedier than speed of light? One can answer philosophically, it is the speed of thought.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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