Mathematics

Optical Path and Fermat’s Principle.

Mirror and Fermat’s principle: We can see ourselves in the mirror and take our mirror reflected selfie as a consequence of Fermat’s Principle, the topic of discussion of the blog.

Snell’s Law governs refraction which is adjustment of optical paths in in-homogeneous media because light can no more travel at its speed in free-space.

Snell’s Law and Refraction.
The above expression comes from Fermat’s optical theorem, called as “Fermat’s least time principle” which can in turn follow either from;

a. Huygens’s Principle; that light travels like spherical wave-fronts hence satisfies geometric rules or,

b. Principle of least or stationary action ( or Hamilton’s action principle ).

So in the beginning of our understanding we thought “Light travels a path which is shortest, or the least-path”. This is due to Heron of Alexandria, who lived between 10 AD and 70 AD. Then this path which is traversed by light was redefined to something called optical path, which led us to our understanding that “light travels the path of least time”.

All physical laws are derivable mathematically –with appropriate physical understanding, from Hamilton’s Action variation or Principle of Action, made to provide the least or stationary time. Then time is replaced by definition of action as the most general formulation of the law.

So all in all, path/distance >> Time >> Action . That is crudeness goes towards abstract physical understanding. This can be recognized as an attribute of unification and tells us why Mathematics reigns supreme in Physics.

In the last few weeks I am trying to understand why light traverses straight lines and why it refracts. The other day, I saw a little mug, floating inside a bucket full of water. Inside water any object would look shortened, this is known by a phenomenon called as refraction.

Lets envisage the phenomenon or observation, via this quickly reproducible trick. Lets dip our favorite pencil in a glass of water and another in a glass filled with air. This is how it looks, I quickly made this arrangement to which my 3 year old niece just glued with rapt attention.

Equivalence from simple notions of Geometry ? Yes.

Now it may also be related that light bends in a denser media compared to a rarer media because an additional rotational force is working. In other words, the definition of straight line has to change in the medium, that is of different density, because path of light is changing. Light is the guy who suffers the least when something tries to buzz it, because its inertial property of mass is zero. The curvature of light or the bending or deflection known as Refraction is thus a measure of the sideways force or energy.

Thus speed of light in different media is a measure of this bending or curvature and is known as Snail’s law ( — Pun intended, its actually; Snell’s Law — ) . Automatically when distance and time have to readjust, to produce an angle or bending, known as refraction ( — possible because distance and time can produce an angle if they are equivalents — ) the speed must also change.

All these are inter related. Light refracts and its speed changes, in relative change in density of media because there are rotational or non-inertial effects.

( — or additional energy is available, or a force is acting to bring a curvature in light’s path, perhaps the electromagnetic effects of the molecules? Its not only distance or time that are equivalents, read one article of mine “All You Need To Know About Relativity” to understand; how energy and time and distance and in short all Physical Variables are equivalents of each other — )

A Question a day, Q4 (series)

Question:

Liliana has a bag of marbles. The bag contains 18 black,
15 red, 11 blue, and 8 white marbles. Liliana randomly takes
a red marble from the bag and leaves the marble on a table.
What is the probability that she will next take a red or a white
marble from the bag?

The approach to unify Language.

The thought of Sun theory of language is “äny word is an alphabet.” Therefore there are infinite number of languages and infinite number of rules of language and infinite number of alphabet. Therefore humanity has only learned to produce new alphabets, and a word is the way to do it. If I say damn, it says: d, a, m, n is an alphabet. alphabet; literal meaning is miniaturization. {therefore quantization} because alpha means less/ap/ab {ap as in apapsis, alpa as in Indianic: alpayu} and bat/bet is adjective-suffix of alpa. {as English: LY in nicely}

You know Einstein was very clever. (Information Theory in Physics )

Then he goes S = Int{Ldt}, action is the total amount of specified definitions of energy over all of time, and action is a kind of information if we are dealing with a statistical system of L {energy} because Energy is not known precisely, or rather action is not, this fact is brought in by saying the time is an information or a PLAN, because things are not known precisely although depend on other well defined factors. Then he sees that since interactions of different chunks of Energy with each other which are not known very precisely gives rise to heat or temperature, temperature here serves as information or PLAN. Then this is still called S, akin to action because S again is information or imprecise or statistical. Then they call it Entropy. {Perhaps for INTERnal-Energy = Intropy} But this other factor temperature also is denoted by same initial T. Since T has to be a fundamental parameter as are Energy and Entropy it can go anywhere, in denominator or numerator and sitting below sometimes feels good so they give T the chance to do that. Its better to heat from below. Heat works that way. But Time T sits on top, see: S = Int{Ldt}.