Harmonic Spherical Waves 2

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…

Young’s Double Slit Experiment. 2

Optics Series Lecture, Lecture – IX.

“Young’s Double Slit Experiment. Coherent Sources and Conditions of Interference” This lecture was delivered on 14th February in a lecture session of 1 and 1/2 hours. This lecture was delivered to Physics elective students. At a later date this is intended as a lecture to honors students as well. The web-version differs slightly from class delivered lectures, in that: any particular idea is explained without reference to what level it must cater to. That means in class lecture will modulate depending on the actual level of student body and their response. An honors student body who would find a particular discourse difficult will be supplied with further simplified versions of the concepts, verbatim. An elective students body which is well prepared would have no problems grasping the fundamentals at a purported level. Its a happy scenario if that is indeed the case.

The concurrent lecture is particularly divided into two parts. The first part pertains to what are coherent sources and what are the sustainable conditions for interference, for such to be observed. The second part leads us to describe in requisite detail the phenomenon of Young’s double slit interference. Note that we have already discussed the phenomenon of interference in our lecture-VII, which was delivered to honors students. We will only passively mention that there are two kinds of interference the so called wave-front-splitting and the amplitude splitting interference. Later on we will discuss any required details of both kinds. Before we do so we will have several interference phenomenon lectures from both types. Young’s double slit interference is an example of the wave-front splitting interference. What happens here is there are two primary or secondary coherent sources and two separate waves interfere at a given observation vantage. Another example of wave-front splitting interference is Fresnel’s bi-prism set-up which we will study soon, in an imminent lecture. For amplitude splitting interference only one wave produces the interference patterns, because the wave amplitude is partially reflected and partially transmitted — or refracted, and both channels meet up somewhere. More…

Harmonic Plane Waves 3

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…

Interference of two plane harmonic waves. 7

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.

Electromagnetic Waves.

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…

Application of matrix method to thick lens. 1

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…

Matrix formulation in Geometrical Optics. 1

In this lecture, we will discuss about one of the most interesting and powerful methods in Geometrical Optics. As we have discussed, geometrical optics is that segment of optics in which we are limited to a situation when the wavelength of light is negligible eg λ is insignificant compared to the size of the objects light interacts with. As a consequence light can be considered as rays or geometrical straight lines and the nuances of light as wave undulations can be postponed to a happy hour.

Ray Tracing.

Any general optical system has a ray which can be traced through two basic types of traversal of the ray: Translation and Refraction. The law of refraction is thus the central tool for ray-tracing. A ray can be described in an optical system by its coordinates which we will define soon. Our goal is to find the matrix which governs the displacement of the ray from one coordinate to another coordinate of the ray as the ray travels from one geometric point to another. More…