waves

Interference of two types

Interference by wave-front and amplitude splitting.

Optics Series Lecture, Lecture – XIV, XV, XVI.

Topics covered in this lecture

A. Color of thin films

B. Newton’s rings

C. Lloyd’s mirror and

D. Phase changes during reflection

We have previously discussed what is interference and what are wave-front splitting and amplitude splitting interference. We have also discussed in much details two wave-front splitting interference viz.

a. Young’s double slit interference, here — Lecture — IX, and

b. Fresnel’s bi-prism, here —  Lecture – XI.

Today we will discuss one more wave-front splitting interference namely Lloyd’s mirror interference before moving onto the amplitude splitting interference of the Newton’s rings.

Also we will discuss two interesting and related concepts;

i. Phase change on reflection and

ii. Color of thin films

Today we will discuss one more wave-front splitting interference namely Lloyd’s mirror interference before moving onto the amplitude splitting interference of the Newton’s Rings.

Also we will discuss two interesting and related concepts;

i. Phase change on reflection and

ii. Color of thin films

Waves

Optics Series Lecture, Lecture – XII and – XIII

“Traveling waves, Differential wave equations, Particle and wave velocities.”

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.

Fresnel’s Bi-prism; measurement of wavelength of light

Optics Series Lecture, Lecture – XI

“Fresnel’s Bi-prism: measurement of wavelength of light by it.”

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.  

Electromagnetic Nature of Light — A brief history of light.

Let us begin this lecture which has roughly two parts;

1. the history of light and its understanding through the centuries

and

2. the electromagnetic nature of light

A brief history of light

Various optical devices and optical phenomena have been known since close to 4000 years. The optical devices of ancient time includes mirrors, burning glasses, lenses and other magnifying devices.

Accordingly various properties and laws of light were understood and developed since these times. E.g.

a. light was understood to propagate rectilinearly and 

b. light was understood to reflect and refract.

Spherical harmonic waves

In our lecture — VIII, we worked out the form of plane harmonic traveling waves. Note that soon we will have to a. address the concept of wave profile and b. 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 work-place. 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 regions that move out with equal phase are the wave fronts in this case, spherical in shape and known as spherical wave fronts.

We obviously need to describe the spherical wave fronts in spherical polar coordinate system, due to the spherical symmetry of problems of 3 – dimensional propagation of light waves.

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