# 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…

# How Rainbows are created. Reply

How Rainbows are created. Optics lecture series – IV

Primary and Secondary rainbows, a lecture in Optics.

This lecture was delivered on February 02, 2017.

Sunlight is white in color. That means it comprises of 7 primary colors. VIBGYOR is an acronym for these basic colors: Violet, Indigo, Blue, Green, Yellow, Orange and Red. Each color of light corresponds to a different wavelength. Violet has the shortest wavelength and Red has the highest wavelength. Accordingly Violet has the highest intensity or consequently energy and Red has the lowest intensity or energy. In other words Red is the faintest color in the primary visible spectrum.

Different colors or wavelength of light have different refractive indices, this fact is known as dispersion, that is, different wavelengths of light would travel in different directions upon refraction at any optically denser or rarer media. That means different wavelength or color component of light would travel at different speed and correspondingly different angles, upon incidence on a media whose refractive index differs from the medium from where incidence occurs. More…

# Fermat’s Principle, a lecture in Optics. 3

Geometric Optics: When the size of objects that a wave of light interacts with are large compared to the wavelength of light λ, λ can be neglected for practical purposes and the light waves behave like rays of light. Rays of light are geometric line segments from one point of incidence of light to another. Study of optics under the limit of negligible wavelength — λ → 0, is called Geometric Optics.

Geometric Optics can be studied using Fermat’s Principle, much like motion of objects in the realm of classical mechanics are studied using Newton’s laws of motion. To know the basic grounding of Fermat’s Principle follow the links to read two articles which expound the subject matter of Fermat’s Principle, art1 — detailed, historical and long, art2 — conceptual but short. More…