SPECTACULAR SPECTRUM

When white light is sent through prism, it is split into colors. A great discovery by Newton. Raindrops acts like a prism and split sun light into seven colors forming the rainbow in the sky.

Let us go deeper into this phenomenon.

Take two carbon pencils (rods) both should be sharpened at one end. Connect positive of high voltage to one rod and the negative to another. Place the two pencils face to face so that there is a little gap between the sharpened ends.
Now powerful white spark will appear in the gap. Actually carbon pencils burn. This set up is called 'carbon-arc lamp' used as a light source in old cinema film projector.

If this light is sent through the prism, it split into spectrum of colors. Since the light comes from carbon atoms, the colors can be called carbon spectrum. (see photo). The pattern of colors is unique to carbon. No other element will give out same arrangement of colors. The spectrum is like finger print of the element carbon.

famous double lines of sodium

We can extract spectrum from all the elements in the periodic table. For example, we know sodium lamp, gives out yellow light. If it is sent through the prism, it split into two yellow colors known as sodium doublet. (yellow in two wavelength). So it is the 'ID' of sodium.

Since light and spectrum is the atomic phenomenon, the colors reveal information about atomic structure of the element(arrangement of electron).

Sunlight gives out spectrum called 'solar spectrum' using which we can study the sun's atmosphere. We can find out the elements present there.

It is possible to form spectra from star light. It can yield info.about the star.

If the source of light moves, the position of colors in the spectrum shifts, called Doppler shift. Using Doppler shift, the speed and direction of any moving source of light, (for example a star) can be calculated.

Next time , when you see colors in a rainbow, in a soap bubble, in a water fall, remember they hold so much knowledge.

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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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