Harmonic Spherical Waves 1

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. More…

Harmonic Plane Waves 2

Optics Series Lecture, Lecture – VIII.

“Harmonic Plane Waves” This lecture was delivered on 13th February in a lecture session of 1 and 1/2 hours. This lecture was delivered to Physics honors students.

In our last lecture, lecture-VII we began by discussing what are electromagnetic waves. We also discussed in good detail what are harmonic waves. Harmonic waves are those waves whose wave-profile is either sine, cosine or in general both sine and cosine combined with each other. Shortly (after within a few lectures) we will discuss what is wave profile and how to transform a wave profile into a traveling wave. A wave profile, wave form or wave shape is simply a time instant view of a more general moving wave. We also discussed what is a plane wave. We applied our harmonic plane waves to the interesting phenomena of interference between two plane waves that are in addition monochromatic that is have same wavelength. Such waves traveling in a homogeneous media do so at a fixed frequency and as long as they are in free-space their speed remains unaltered at the sped of light value c = 3 × 108 m/s.

A plane wave is one traveling wave where the wave fronts are planar points with equal phases all over the plane. In that order a spherical wave front is a locus of uniform phase over spherical configuration and a cylindrical wave front would be a traveling wave where the locus of uniform phase is nothing but a cylindrical surface. In one of the future lecture, shortly, we will discuss in much detail what are spherical waves. More…

How Rainbows are created. Reply

How Rainbows are created. Optics lecture series – IV

Primary and Secondary rainbows, a lecture in Optics.

This lecture was delivered on February 02, 2017.

Sunlight is white in color. That means it comprises of 7 primary colors. VIBGYOR is an acronym for these basic colors: Violet, Indigo, Blue, Green, Yellow, Orange and Red. Each color of light corresponds to a different wavelength. Violet has the shortest wavelength and Red has the highest wavelength. Accordingly Violet has the highest intensity or consequently energy and Red has the lowest intensity or energy. In other words Red is the faintest color in the primary visible spectrum.

Different colors or wavelength of light have different refractive indices, this fact is known as dispersion, that is, different wavelengths of light would travel in different directions upon refraction at any optically denser or rarer media. That means different wavelength or color component of light would travel at different speed and correspondingly different angles, upon incidence on a media whose refractive index differs from the medium from where incidence occurs. More…

How to add speeds; Galileo and Einstein won’t agree. 1

How to calculate the speed of anything, when their speed becomes closer to the speed-of-light.

— To correct the comment I have made earlier ” unless something is completely massless in its rest-frame ” I also add the following. This is a fact which I have realized lately — or rather trapped myself to commit an inconsistent remark, by following the same comment, and better late than never; when something is massless, it will never have a rest-frame, because by Einstein’s transformation rules known as Theory of Relativity to be consistent, a massless particle will always move at the speed of light, no matter which frame we are looking at it from.

This then leads to the velocity addition formula of Einstein. 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…

Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity by Steven Weinberg .. review Reply

A highly sofisticated and an elegant text book on general Relativity and its application. I would say a super book. I have read this book and solved for now a few daunting problems in Physics by applications of the content in this book. My research is available on my website but for context I recommend this book for serious practising physicists. More…