# fundamentals of optics

## 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:

## Young’s double slit experiment

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 was delivered 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.

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. Just to mention it for the time being, Newton’s Ring Interference patterns are example of amplitude splitting interference. Later we will study the details of all sorts of interference phenomena such as the ones just mentioned.

Coherent sources and conditions for interference:
Let us now discuss the first part of our lecture. Let us for the time being define coherence as the attribute of a light source such that there is no arbitrary and unexpected changes in the phases of different light waves such that when these waves at an observation point meet, we can apply the results of our interference analysis that we discussed in lecture-VII.

## Interference of two plane harmonic waves

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 c = 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. The Maxwell’s Equations are a summary of important and fundamental laws of electricity and magnetism — together called as electromagnetism, such as Gauss Law and Ampere’s Law. These equations produce the wave equation of motion, a linear, homogeneous, 2nd order differential equation that we will study a few lectures afterwards.

If you are quite serious and technically well equipped though, you can have a glimpse of it all — and may be work out to your satisfaction, by following the link to my slide-share presentations. There are many other important Physics concepts that are worked out in great detail, in those slide-share presentations by me. eg check: Electromagnetic Waves.

Let us therefore write the wave equation of motion, where the 3 components of E field — such as Ex, Ey or Ez or the 3 components of B field such as Bx, By, Bz, are denoted as ψ chosen anyone at one time. eg we can chose Ex = ψ. In general we have: