WHY NIGHT SKY IS DARK? DAY SKY IS BLUE AND TWILIGHT SKY IS RED?

Even in open ground, if you erect light bulbs in all the four corners, the ground will be flooded with light. But universal space has lots and lots of stars (actually suns). Then, why the night sky is pitch dark?

To answer this question, we have to go billions of years back. That is the birth time of the universe. Long, long back, the matter for the entire universe was contained in a tiny atom. The tiny dot has zero size, large mass, infinite density. There was 'big bang', an astronomical explosion. The entire matter was thrown out. The universe was born. The time started to tick. Explosion temperature begins to cool down. Galaxies, star systems formed. They all continue to move and expand like a balloon[due to explosion]. Even today, all celestial bodies continue to move away from us. The expansion of the universe is the greatest discovery of the century.

Next, we have to understand 'Doppler effect'. When a train approaches us, the frequency of whistle sound increases and when it recedes, the frequency decreases. This is called the Doppler shift.
It is applicable to light also. When a star moves away from us, the frequency of light shifts to the infrared side. That is, visible light becomes invisible infrared rays. That is why we loose light from distant stars and space is always dark.

Why the day-sky is blue? The air molecules scatter the blue colour (in the sunlight) more than other colours. It gives the illusion of blue sky. During sunset and sunrise, the light rays have to travel a long distance in the atmosphere. Hence all the colours are scattered away. Mostly red light reaches our eyes. Hence we see blood-red sunset.

So the sky is a misnomer. It is an interplay of colours and just illusion.
Let poets, painters, photographers enjoy the drama in sky theatre. Let us join them too.

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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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