2nd & 3th N.U.T.S. Workshops

Gulu University

Naples FEDERICO II University

6 – Interference

6- Interference

2nd & 3th NUTS Workshop ( Jan 2010)

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Soap Bubbles … and Oil Spot

What is producing so nice colours ?

6- Interference

2nd & 3th NUTS Workshop ( Jan 2010)

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Other Examples of Nice Coulours …

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2nd & 3th NUTS Workshop ( Jan 2010)

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It’s just a Phase Difference Pattern!

or a Thin Film Interference Constructive and destructive interference of

light waves is the reason why thin films, such as soap bubbles, show colorful patterns. Light waves reflecting off the top surface of a film interfere with the waves reflecting from the

bottom surface. To obtain a nice colored pattern, the thickness of the film has to be of

the order of the wavelength of light.

Variable thickness of the film give variable wavelength (colour) of the refracted light

constructive interference

What is Interference?

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2nd & 3th NUTS Workshop ( Jan 2010)

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Combined Waveform

wave 1

wave 2

If two waves (same wavelength and frequency) are in phase, both wave crests and troughs align. Constructive interference results increase in the wave amplitude, for

light a brightening of the waveform in that location.

If the two waves are out of phase, then the crests will align with the troughs. Destructive Interference results, a decrease in the amplitude of the combined wave, for

light a dimming of the waveform at that location.

6- Interference

2nd & 3th NUTS Workshop ( Jan 2010)

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SUPERPOSITION of 2 or more Waves in the same region

ONLY UNDER SPECIFIC CONDITIONS

Interference:

Conditions to Have Interference

In the simplest case: Superposition of periodic waves

with same frequency. The waves’ sources oscillate in

phase. i.e. synchronously, or with phase difference constant and known (COHERENT SOURCES)

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2nd & 3th NUTS Workshop ( Jan 2010)

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Example of Incoherent Light Source

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(longitudinal and transversal waves)

Interference for Coherent Sources

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2nd & 3th NUTS Workshop ( Jan 2010)

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Young’s ExperimentThe double-slit experiment, performed by the

English scientist T. Young in 1801, is an attempt to resolve the question of whether light was composed of

particles (Newton's "corpuscular" theory), or rather consisted of waves. The Interference Patterns

observed in the experiment seemed to discredit the corpuscular theory; the wave theory of light remained

well accepted until early 20th century.The original

drawing by T. Young to

illustrate its experiments.

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2nd & 3th NUTS Workshop ( Jan 2010)

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Double-slit Experiment: Schema

To have a constructive interference along the θ direction the path length difference between the wavefronts coming from the two

apertures have to be an integer number of wavelengths: d sin θ= mλ

plane waveforms

to focus on the screen

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2nd & 3th NUTS Workshop ( Jan 2010)

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Another Schema of Young Experiment

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YOUNG Ex conditions for MAX and MIN Intensity

BRIGHT FRINGE :

DARK FRINGE :

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2nd & 3th NUTS Workshop ( Jan 2010)

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Geometry of N-slits Interference

d = spacing between two slits

L = screen distance from the plane of the slits

N = total number of slits = angle between the

direction of incoming beam and the considered out coming one

= wavelength of the incident light

λ

rj

a

x

x′

L

θ

d1

2

j

N

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2nd & 3th NUTS Workshop ( Jan 2010)

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N-slits Interference: the Solution for I

2

0 sinsin

sinsin

)(I

d

Nd

I

Interference of red laser light

2 slits

5 slits

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2nd & 3th NUTS Workshop ( Jan 2010)

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Double-slit Maxima Location

2

0 /sinsin

/sin2sin)(I

d

dI

Maxima when denominator = 0

dnn

d

sin

sinn is the fringe order

- n is a positive o negative integer- there is a nmax (nmax= max integer ≤d/λ) - total number of fringes =2 nmax+1 (from -nmax to +nmax )

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2nd & 3th NUTS Workshop ( Jan 2010)

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5-slits Versus Double Slit

2

0 /sinsin

/sin5sin)(I

d

dI

Maxima 5-slit when denominator = 0

dnn

d

sin

sinsame as 2-slit!!!

only the fringe width is narrower with respect to 2-slit

(the fringe width is proportional to the numerator period!)

Interference of red laser light

2 slits

5 slits

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2nd & 3th NUTS Workshop ( Jan 2010)

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Multi-slits Interference We Will Work on

to build a low cost spectroscope