Matrix formulation in Geometrical Optics. 1

In this lecture, we will discuss about one of the most interesting and powerful methods in Geometrical Optics. As we have discussed, geometrical optics is that segment of optics in which we are limited to a situation when the wavelength of light is negligible eg λ is insignificant compared to the size of the objects light interacts with. As a consequence light can be considered as rays or geometrical straight lines and the nuances of light as wave undulations can be postponed to a happy hour.

Ray Tracing.

Any general optical system has a ray which can be traced through two basic types of traversal of the ray: Translation and Refraction. The law of refraction is thus the central tool for ray-tracing. A ray can be described in an optical system by its coordinates which we will define soon. Our goal is to find the matrix which governs the displacement of the ray from one coordinate to another coordinate of the ray as the ray travels from one geometric point to another. More…

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…

Equivalence from simple notions of Geometry ? Yes. 4

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 — ) More…