LIGHT RAY FINDS PATH OF LEAST TIME WITHOUT GOOGLE MAP

We know, when a ray of light travels from air to water, it bends according to snell's law. Why should it bend? Why should it follow snell's law?

Say, you are coast guard. Some one cries for help from the sea. You want to reach the person as quickly as possible. Here you have to travel in two media. 1. You have to run in the land (fast). 2. You have to swim in the sea (slow). Hence you need to find the path of shortest time. So you will choose to run a maximum distance on the sand; will reach a particular point on the edge of water; than will swim towards the person in distress.
That path will never be a straight line but looks bent.

Similarly, a ray of light travels faster in air, but slower in water and glass. Hence the light takes a bent path while crossing from air to glass. This is the principle of least time. Also called Fermat's principle.
(Note: When a ray hits a water surface normally (at 90 degree), it will not bend but go straight. (In this case, there is no other path which has 'more least time' than straight line). Next why it should follow snell's law?

sin i/sin r = Refractive index of water = Speed of light in air / speed of light in water- the law
i is angle of incidence and r is angle of refraction as shown in the figure.
The angles depends on the speeds of light in the two media. Hence the speeds determine the angle of bending. Consequently the light ray takes the path of least time.
How the light sense the path of least time? It is because of the wave nature of light. The spherical wave spread from a source of light (a lamp) like a water wave on the sheet of water. These waves senses the nearby paths and finds the quickest path. This principle has been experimentally verified using Radio waves.
There can be many explanations for refraction. This is another way of looking at refraction. Also we get one more idea of 'how the nature works.'

Comments

THE EARTH, A SUPER ORGANISM

JOIN MY COURSE: "Become a programmer in a day with python" A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess. It says, "Earth is a self-regulating organism like a human being. The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment". Hence the earth is still suitable for the life to thrive. Imagine, in a particular place, there are lot of flowers. Some flowers are white and some are darkly coloured. We know, white reflects light and heat while dark absorbs the same. White flowers can thrive in hot climate. But dark flowers requires cold climate. The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist. This is the essence of "Gaia" theory. On our earth, ...

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. ...

DISORDER IS THE "ORDER OF THE DAY"

Imagine a balloon full of air. The air molecules are moving randomly inside the balloon. Let us pierce the balloon with a pin. The air rushes out. Why should not the air molecules stay inside the balloon safely and ignore the little hole? That is not the way the world works. The molecules always "want to occupy as many states as possible". Hence the air goes out in the open to occupy more volume. The things always goes into disorder (entropy) and the disorder increases with time. The above statement is what we call "second law of thermodynamics". Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze. Freezing means bringing things to order and arrangement. It violates the second law. Hence it will never happen. Hence heat must flow from high ...

sciencecapsules

Search This Blog