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. More…
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.
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…
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…