Two Source Interference

Interference

For electromagnetic wave [Maxwell’s equation in free space]

Optical Interference Optical interference corresponds to the interaction of two or more light waves yielding a resultant irradiance that deviates from the sum of component irradiance.

Light waves interfere with each other much like mechanical waves do All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine LINEAR SUPERPOSITION!

Resultant

Interference Animation © 2006 Walter Fendt http://www.walter-fendt.de/ph14e/interference.htm

Irradiance

Interference term

The interference term

The phase difference arising from a combined path length and initial phase difference.

For maximum irradiance Total constructive interference

For minimum irradiance Total destructive interference

Components out of phase Constructive Interference

Components 90o out of phase

For I1=I2

For the spherical wave emitted by two sources, in-phase at the emitter

Photo shows an interference pattern by two holes 

Two-Slit Experiment with Laser Light http://www.colorado.edu/physics/2000/applets/twoslitsa.html

Moire Pattern

Moire pattern in folded net

Moire pattern formed in the atomic image of nanocrystals

Conditions of Interference

White Light Interference

Coherent Sources Constant phase difference Such sources may or may not be in step but are always marching together

Coherence Time of Radiation Temporal coherence The interval over which the light wave resemble a sinusoid is the measure of it temporal coherence. Coherence Time of Radiation The average time interval during which the light wave oscillates in a predictable way is known as coherence time of radiation.

Spatial extent over which the light wave oscillates in a regular predictable way is the coherent length

Temporal Coherence © SPK

Spatial Coherence © SPK

P3 P2 P1 © SPK

Interference of light from two bulbs?

Wavefront splitting interferometer Amplitude splitting interferometer (i) Fringes of equal inclination (ii) Fringes of equal thickness

Twin Source Interference Pattern

Condition for reinforcements Condition for destruction

Path difference represents the equation of a family of confocal hyperbolae with S and S as the common foci

Confocal hyperboloids of revolution in 3D

Transverse section –Straight fringes P S x q q O d N S D

Path difference The distance of mth bright fringe from central maxima Fringe separation/ Fringe width

Longitudinal section –Circular fringes P rn N O q S S d D

For central bright fringe Path difference = d

For small qm Radius of nth bright ring

Summary Interference by two plane polarized light wave For constructive interference For destructive interference

For sustained interference between two sources of light to be observed, there are two conditions which must be met The sources must be coherent. They must maintain a constant phase with respect to each other The waves must have identical wavelengths

Reference 1. Optics Author: Eugene Hecht Class no. 535 HEC/O Central library IIT KGP