Constructive Interference

Destructive Interference

Coherence

Coherence is a measure of the correlation between the phases measured at different (temporal and spatial) points on a wave.

If two waves have a definite phase relationship then they are coherent.

Otherwise, they are incoherent (ex: two light bulbs).

Effectively, this means that the waves do not shift relative to one another as time passes.

Lasers are coherent sources of light, while incandescent light bulbs and fluorescent lamps are incoherent sources.

Temporal Coherence:

If the Phase difference between any two points along the direction of propagation is independent of time then the wave is said to be temporally coherent.

It is a measure of the correlation of light wave’s phase at different points along the direction of propagation – it tells us how monochromatic a source is.

Correlation of phase at the same point but at different times

Spatial Coherence:

If the phase difference between any two points located transverse to the direction of propagation is independent of time then the wave is said to be spatially coherent.

It is a measure of the correlation of a light wave’s phase at different points transverse to the direction of propagation - it tells us how uniform the phase of a wavefront is.

Waves in phase in time, but at different points in space

Example of Coherence Length

Sodium vapour lamp yellow "D" line

λ = 589 nm and linewidth 5.1x10¹¹ Hz

L_coh = cτ_coh = 2.98 x10⁸ (1.96 x10⁻¹² )= 5.88x10⁻⁴ m = 0.59mm

He-Ne laser in multimode operation

λ = 632.8 nm and linewidth 1500 MHz

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If single mode HeNe operation linewidth goes to 1 Mz and cohrence time is 1 microsec, cohrence length 300 m

Methods to Produce Coherent sources

a). Division of Wavefront:

Two coherent sources are produced by splitting of a wave front at an obstruction.

Examples: Young’s double slit, Llyod’s mirror, Fresnel’s biprism etc.

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b). Division of Amplitude:

The amplitude of the incoming beam is divided into two parts through the process of reflection or refraction to produce coherent sources.

Examples: Thin films, Newton’s rings exp, Michelson interferometer.

THOMAS YOUNG’S EXPERIMENT

Young’s Interference Pattern

Bright fringe

Bright fringe

Dark fringe

Change of Phase in Reflection

The positions of the fringes are reversed compared to Young’s experiment

An EM wave undergoes a phase change of 180° upon reflection from a medium that has a higher index of refraction than the one in which it is traveling.

String Analogy

Interference in Thin Films

• A wave traveling from a medium of index of refraction of n₁ towards a medium with index of refraction of n₂ undergoes a 180° phase change upon reflection if n₂ > n₁ and no phase change if n₂ < n₁.
• The wavelength of light λ_n in a medium with index of refraction n is given by, λ_n = λ / n.

For constructive interference

m = 0,1,2,…

For destructive interference

m = 0,1,2,…

Soap film interference pattern

Newton’s Rings

For constructive interference

For destructive interference

NEWTON’S RINGS Exp. Arrangement

DARK AND BRIGHT RINGS

Diffraction

Wave bends as it passes an obstacle

28-6 Diffraction Gratings

Diffraction can also be observed upon reflection from narrowly-spaced reflective grooves; the most familiar example is the recorded side of a CD. Some insect wings also display reflective diffraction, especially butterfly wings.

Double Refraction

When light is refracted into two rays each polarized with the vibration directions oriented at right angles to one another, and traveling at different velocities. This phenomenon is termed "double" or "bi" refraction

Blue Sky

The blue color of the sky is caused by the scattering of sunlight off the molecules of the atmosphere. This scattering, called Rayleigh scattering, is more effective at short wavelengths

Sunset

As incoming sunlight passes through a more dense atmosphere, shorter wavelengths of light (violet and blue) are efficiently scattered away by particles suspended in the atmosphere. This allows predominantly yellow and red wavelengths of light to reach the observer's eyes, producing a yellowish-red sunset