2nd & 3th N.U.T.S. Workshops
Gulu University
Naples FEDERICO II University
6 – Interference
2nd & 3th NUTS Workshop ( Jan 2010)
Soap Bubbles … and Oil Spot
What is producing so nice
colours ?
6- Interference
2
2nd & 3th NUTS Workshop ( Jan 2010)
Other Examples of Nice Coulours …
6- Interference
3
2nd & 3th NUTS Workshop ( Jan 2010)
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
6- Interference
4
2nd & 3th NUTS Workshop ( Jan 2010)
What is Interference?
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
5
2nd & 3th NUTS Workshop ( Jan 2010)
Interference:
SUPERPOSITION of 2 or more Waves in the same region
ONLY UNDER SPECIFIC CONDITIONS
6- Interference
6
2nd & 3th NUTS Workshop ( Jan 2010)
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)
6- Interference
7
2nd & 3th NUTS Workshop ( Jan 2010)
Example of Incoherent Light Source
6- Interference
8
2nd & 3th NUTS Workshop ( Jan 2010)
Interference for Coherent Sources
(longitudinal and transversal waves)
6- Interference
9
2nd & 3th NUTS Workshop ( Jan 2010)
Young’s Experiment
The 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.
6- Interference
10
2nd & 3th NUTS Workshop ( Jan 2010)
Double-slit Experiment: Schema
plane waveforms
to focus on the screen
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:
dsinθ= mλ
6- Interference
11
2nd & 3th NUTS Workshop ( Jan 2010)
Another Schema of Young Experiment
6- Interference
12
2nd & 3th NUTS Workshop ( Jan 2010)
YOUNG Ex conditions for MAX and MIN Intensity
BRIGHT FRINGE :
DARK FRINGE :
6- Interference
13
2nd & 3th NUTS Workshop ( Jan 2010)
Geometry of N-slits Interference
N
rj
x′
j
θ
a
L
2
λ
d
1
6- Interference
x
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
14
2nd & 3th NUTS Workshop ( Jan 2010)
N-slits Interference: the Solution for I
 Nd sin 

 sin

I ( )  I 0 
 sin  d sin 









2
2 slits
5 slits
Interference of red laser light
6- Interference
15
2nd & 3th NUTS Workshop ( Jan 2010)
Double-slit Maxima Location
 sin  2 d sin  /   

I ( )  I 0 
 sin  d sin  /   
Maxima  when denominator = 0
 d sin 

 n   sin   n

2
n is the fringe order
d
- 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 )
6- Interference
16
2nd & 3th NUTS Workshop ( Jan 2010)
5-slits Versus Double Slit
 sin 5 d sin  /   

I ( )  I 0 
 sin  d sin  /   
Maxima 5-slit  when denominator = 0
 d sin 

same as 2-slit!!!
 n   sin   n

d
2
only the fringe width is narrower with respect to 2-slit
(the fringe width is proportional to the numerator period!)
2 slits
5 slits
Interference of red laser light
6- Interference
17
2nd & 3th NUTS Workshop ( Jan 2010)
Multi-slits Interference We Will Work on
to build a low cost spectroscope
6- Interference
18