NIGHT HAS THOUSAND EYES

All the illegal activities takes place under the cover of darkness. Police and military requires devices to see in the darkness. There are mainly two principles. Using which night goggles, binoculars, cameras work.

1. AMPLIFICATION
We receive signals of tiny voltage in our smart phones. That signal is strengthen (amplified) by electronic circuits and converted into clear voice, picture and video.

Even in darkness, a small amount of light is present due to stars, moon, distant lights etc. This little light reflected from the objects can be amplified by night vision instruments and present a picture or video to us. Even tiny amount of light is enough because the instrument can amplify it thousands of time. But, if you see a normal light using this night vision equipment, you will be blinded by the amplified heavy intensity of light.

2. INFRA-RED
Buildings, trees, water bodies, man, animals all are always warm-above freezing point. Hence their molecules continuously emit infra-red rays (invisible light) day and night. Using suitable instruments, we can capture these infra-red rays and produce images.

From TV remote, infrared rays goes and activate the TV.
Switch on your smart phone camera. Point the TV remote to the camera lens. You can see a spot of light in the screen. Human eyes cannot see the IR rays, but a camera can. Again note, a highly active man, glow more with infra red rays.

The universe emits lot of Radio waves (again invisible light), using Radio telescope(like dish antenna), we gather lot of info about the universe. The recent "black-hole" photograph was composed using radio waves.

PHILOSOPHY
If you ask, "How to find out what one does is right or wrong"?
The answer: If you do an activity openly and boldly, it is right. If you do something in dark and hiding, mostly it is wrong.
Make no mistake; have no fear for dark.
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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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