interference

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

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.  

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:

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: