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 the 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. Cylindrical waves are left to the advanced and willing students to work out by themselves. If time permits sometime in the future we can fall back and make a case for cylindrical wave fronts as well. But no promise at this point.
Note that waves are simply motion of phase points as a function of space or location and time instant. A phase is nothing but the angular argument of the wave described in terms of harmonic functions.
Let us begin studying Plane waves in detail. Here are some of its features.
1. A plane wave is the simplest example of a 3-dimensional wave.
2. These are so called, because plane wave wave fronts are planar in shape.
A wave-front is a locus of points on which the phase of the wave is same. Its a surface of wave-disturbances which move together, at the same speed.
3. Optical devices are often tuned to produce plane waves.
This necessitates the study of plane waves as base examples, where more complicated features can be assigned when they become pertinent.
4. Wave fronts are always perpendicular to the direction of wave propagation.