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 – XI.
“Fresnel’s Bi-prism: measurement of wavelength of light by it.” This lecture was delivered on 16th February in a lecture session of 1 and 1/2 hours. This lecture was delivered to Physics elective students and later to honors students. This does not strictly pertain to 1 and 1/2 hours of regular lecturing session that we have mostly been employing. Thats because it was created with another part which can be optionally appended to other related subject matter. In the web-version thats what we will do. Our guiding principle is more in line with the honors course, where the subject matter is quite extensive and deep which brings more flexibility and choices into the lecture compositions.
Today we will discuss another interesting interference set-up, now that we have discussed the Young’s double slit experiment, in lecture – IX. A few words about the general mechanism behind interference. There are two kinds of interference basically that we will be discussing in our lectures. We discussed the Young’s DS interference pattern based on our understandings of intensity or irradiance patterns that we studied here: lecture – VII. Interference is sustained and visible if the corresponding sources of light are coherent among themselves, that is, if the sources have phase differences that are not arbitrarily or abruptly changing, as a consequence we can safely assume the phase differences are constant and therefore predictable. Incoherent light makes this impossible. Incoherent light is that light source whose production itself is arbitrary and abrupt and unpredictable, hence nothing can be definitively said on its phase, as a result the coherence is only short lived. If two light sources are so generated that their respective coherence time (or coherence length) are well within each others span, they are said to be coherent light. 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…
Optics Series Lecture, Lecture – VII.
“Conditions of interference, Interference of two plane harmonic waves.” This lecture was delivered on 7th February in a lecture session of 1 and 1/2 hours. This lecture was delivered to Physics elective students but intended as a lecture towards Honors students at a later date.
Light is an electromagnetic wave. In-fact its a transverse electromagnetic wave which means the oscillation of E and B fields produces light which propagates in a direction that is perpendicular to the plane that contains the E and B fields. In other words E, B and k the vector that denotes the direction of light propagation, are mutually perpendicular vectors. We will study these details in a later intended lecture. EM waves are not only transverse waves but also vector waves, that is; E and B are vector fields whose undulation is summarized as light.
Light is a general name for all EM waves but visible light is that particular part of EM waves which has frequency of wave such that the wavelength varies from approximately 400 – 700 nm. In vacuum — only in vacuum, light always moves at a fixed speed: namely 3×108 m/s. Therefore light whose wavelength lies between 400 – 700 nm is called as visible light: we can write in vacuum c = νλ.
Light as a transverse wave phenomenon of vector fields is comprehensively described by four equations known as Maxwell’s Equations. More…
Our previous studies of optical systems were based on two premises.
We assumed a paraxial system.
This means we employed a first order optical theory. Check the article just linked for a good overview of whats paraxial optics and whats first order optical theory. Such assumptions are fraught with various types of aberrations which we studied in detail in lecture-I and lecture-II.
We assumed that our lenses are thin.
This we did for simplicity. In Physics when we assume a simple situation we are not evading the actual complexity of the situation, we are just postponing this to the happy hour, howsoever you define it. Some people go by the Friday happy hour rule. It gives a good substratum on which a disposition can be carried out. Later one develops the nuances and fits it into the substratum and if things are carried out with caution and skill one gets a very effective overview of the pedagogy.
Let us now delve into the complexity of the optical system as a next step from its simple substratum of a thin lens. Our analysis needs to be modified for applying optical principles to optical systems when we consider thick lenses. In our last lecture we studied the method of matrices in understanding optical ray tracing. Let us now apply this method to the case of thick lens and see what power it unleashes. More…