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.
Let us recall that the Laplacian in spherical polar coordinate system is given as: