Fermat’s Principle, a lecture in Optics. 3

Geometric Optics: When the size of objects that a wave of light interacts with are large compared to the wavelength of light λ, λ can be neglected for practical purposes and the light waves behave like rays of light. Rays of light are geometric line segments from one point of incidence of light to another. Study of optics under the limit of negligible wavelength — λ → 0, is called Geometric Optics.

Geometric Optics can be studied using Fermat’s Principle, much like motion of objects in the realm of classical mechanics are studied using Newton’s laws of motion. To know the basic grounding of Fermat’s Principle follow the links to read two articles which expound the subject matter of Fermat’s Principle, art1 — detailed, historical and long, art2 — conceptual but short. More…

Inherent ability = difficulty * accomplishment. 2

All of Physics is this “Inherent ability = difficulty * accomplishment”. Thats just intuitive but can easily be seen to correspond mathematically with the Principle of least action.

First the edifice: whats the problem? The problem is given you move in straight line when every direction is same around you, which direction will you chose? While you are waiting for a good answer from astrologers intelligent people already give a good hint. Think you have some inherent ability which is fixed.

fixed: which changes only if estimated wrong.

That inherent ability is actually action. Accomplishments are adjusted for difficulties, you waded through a swamp 5 meters you would have accomplished in sand 8 meters with that given inherent ability called action. Because action is abstract we have been sticking to time and path-length, but they are not as fundamental, they are merely specifics. More…

Blackholes and the Action Principle. Reply

This is not an article that purports to establish any link between what I have to say about Blackholes and what I have to say about Action Principle.

First off there are always a connection between action principle and anything else in Physics. Everything in principle can be derived from the action principle. The action principle is the general principle of all sorts of mechanics in Physics and has the weird power of superiority over everything else, at-least in principle. So if you want to claim something is inconsistent in Physics, take a piece of chalk and chalk out how it is that the action principle is inconsistent with anything that you want to discard. The action principle has the key to proving how consistent or inconsistent Physics is.

And I am not stating the action principle much, either. I just wish to mention two ideas that have no explicit connection to be brought out by this article. Hence they are to be read without any purported conjunctions of one with the other. More…

Optical Path and Fermat’s Principle. 7

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, a phenomena known as refraction. Thats because light rays would “bend” inside water (towards a direction where they have to take a shorter path) as their speed must reduce, given to the fact that in the same time in a rarer medium light would have traveled a longer distance in the exact same time, which is no longer possible due to the crowd of molecules and subatomic ghetto that it meets along its way. More…