wave equations – "Invariance" from M Dash Foundation

Waves.

March 25, 2017 Mohan, mdashf

Optics Series Lecture, Lecture – XII and – XIII.

“Traveling waves, Differential wave equations, Particle and wave velocities.” These lectures were delivered on 17th and 20th February 2017, in two lecture sessions of 1 and 1/2 hours each. The web version has been named “Waves.” and the lectures were delivered to Physics honors students.

In one of our earlier optics session lecture I had hinted at having waves defined by their pulse shape called as wave profile — or alternatively wave shape or wave form, and transcribing them into forms that represent actual wave motion. The later are then called as traveling or progressive waves. The former, the so called wave shape or wave profile are then time-snapshots of the full fledged time varying waves that we just called traveling waves. Remember that stationary or standing waves are not wave profiles or any snapshots of a single traveling wave, they are rather the superposition of an advanced and a retarded wave — that is one traveling wave moving forward and another exactly shaped traveling wave moving in the reverse direction. We studied advanced and retarded waves, here. We have also already dealt with traveling waves in much detail, eg, here and here. This lecture will justify what we have been espousing all along.

Electromagnetic Nature of Light — A brief history of light

March 17, 2017 Mohan, mdashf

“Electromagnetic Nature of Light — A brief history of light” This lecture was delivered on 16th March, yesterday, in a lecture session of 1 and 1/2 hours. The second part of this lecture was delivered to Physics honors as well as Physics elective students.

As I promised in the last lecture, lecture-X we have our one of the interesting historical and technical perspective about light that is also one of my favorite, as I discovered yesterday, or shortly before that, the night before, when I was composing the lecture from scratch. We will name this lecture with its proper number, only after its clear to us what chronological number it must be associated with it. Its like an advanced wave, it reached us before in time, before it was intended to be taken up for its web-version.

Let us begin this lecture which has roughly two parts, 1. the history of light and its understanding through the centuries and 2. the electromagnetic nature of light. The second part is intended as the course material for honors as well as elective students but you will be in amusement if you also cover the first part.

A brief history of light.

Various optical devices and optical phenomena have been known since close to 4000 years. The optical devices of ancient time includes mirrors, burning glasses, lenses and other magnifying devices.

Accordingly various properties and laws of light were understood and developed since these times. Eg light was understood to propagate rectilinearly, light was understood to reflect and refract. There were various laws that were known since these times which catered to the need for explanation of these phenomena. eg Reflection was understood to be a phenomena explained by the principle of shortest path — follow link to know this and other related ideas and their history: Hero of Alexandria. Laws of refraction were understood either partially or completely as the centuries or even millennia passed.

Apart from rectilinear propagation of light it was understood that light moves at infinitely large speed. Advanced optical devices such as telescopes were developed based on partial and faulty understanding of light which was gradually refined to accommodate better credits of advancement.

Harmonic Spherical Waves

March 16, 2017 Mohan, mdashf

Optics Series Lecture, Lecture – X.

“Harmonic Spherical Waves” This lecture was delivered on 16th February in a lecture session of 1 and 1/2 hours. This lecture was delivered to Physics honors students.

In our lecture ( lecture-VIII ) we worked out the form of plane harmonic traveling waves. Note that soon we will barge into the concept of wave profile and how to convert a wave profile into its corresponding time-dependent or traveling form. But before we do that here is yet another general form of a traveling wave which we often meet in the Physicists Den. The traveling spherical wave fronts. Let us work out its details.

Spherical Waves.

When a stone is dropped in water it sends out circular waves. Similarly a sphere or a glob of matter that oscillates inside of a water body would send out 3-dimensional waves or ripples. Sources of light wave, which we will study in great detail, in this course, to fulfill our insatiable hunger for understanding the nature of optical phenomena, similarly, send out oscillations which propagate radially and uniformly in all directions. These are the spherical waves and the points or region that move out with equal phase are the wave fronts in this case, spherical in shape, called as spherical wave fronts.

We evidently need to describe the spherical wave fronts in spherical polar coordinate system, owing to the spherical symmetry in problems of 3-dimensional propagation of light waves.

Least action principle and principle of equivalence …

June 15, 2012 Mohan, mdashf

This article is written in the flow of my intuition which is in a chronological order without any flip-flops. So first I came up with the idea Principle of equivalence means nature of potential energy and kinetic energy are same hence they are equivalents not gravitational mass and kinematic mass as represented through all texts [read other articles linked in this article for this idea] Then I came with the idea it actually follows from Prinicple of Least action in a round about way [which could be spurious and incorrect but leads to the answer] and in a direct and simple way in two lines.