Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
Topics
 Slit width and slit separation dependence of diffraction pattern for single
and double slits in the Fraunhofer (far-field) regime.
 Babinet’s principle: Determine the thickness of your hair.
 Diffraction pattern for circular apertures.
 Quantitatively measuring the intensity distribution of the diffraction
patterns of single and double slits in the Fraunhofer (far-field) regime and
fitting data to theory.
 Determination of the ration of slit-width a and slit separation-distance d
from the double slit diffraction pattern.
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
VII.A Experiments with the Observation Screen
 Look at single slit diffraction pattern for different slit widths.
 Determine the laser wavelength from the diffraction pattern minima from a
single slit.
x
Q
I(x)
L
a
Minima occur when :
sin Q   ,  2 ,  3 ...

 a

sin 2  sin  


I ( )  I 0
2
 a

 sin  


Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
Babinet’s Principle
The diffraction pattern in the far field due to a given screen is the same
as the diffraction pattern due to it’s complement.
Translation for our experiment:
A slit of width a produces the same diffraction pattern as a hair of the same width.
x
Q
I(x)
L
a
Minima occur when :
sin Q   ,  2 ,  3 ...

 a

sin 2  sin  


I ( )  I 0
2
 a

 sin  


Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
VII.A Determine the Thickness of your Hair
Tape hair to
component
holder
View from the front
Laser beam should hit the hair
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
VII.A Diffraction pattern of a small circular aperture
View from the front
Use the slide that contains
circular apertures of sizes
0.04mm and 0.08mm (those
you should use). It also
contains a big square and a
big round hole with patterns
inside.
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
VII.A Diffraction pattern of a small circular aperture
For circular aperture (a hole) of diameter q the diffraction
pattern is an “airy disk”.
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
Mathematical Description of the Diffraction Pattern
of a Circular Aperture in the Far-Field
  2a

 2 J1   sin Q  

I Q  I 0  
 2a sin Q 



2
J1 = “Order One Bessel Function”
Minima when I Q   0
 2a

J1 
sin Q 
 
 0

2a
sin Q


2a

sin Q  3.832 , .....
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
Mathematical Description of the Diffraction Pattern
of a Circular Aperture in the Far-Field
2a

sin Q  3.832 for thefirst dark ring
 qQ


 3.832  Q  1.22

q
(q  diameterof aperture)
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
Angle of first minimum (dark circle) (measured from axis that goes
through center of the central bright disc):
Small angle approximation (Q in radians)
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
Mathematical Description of the Diffraction Pattern
of a Circular Aperture in the Far-Field
More maximaand minima:
m
sinQ 
, where q  diameterof aperture
q
Minima
Maxima
m
0
m
m
m
1.220
2.233
3.238
1.635
2.679
3.69
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
VII.B Experiments with Linear Translator,…….
Observe the diffraction pattern intensities at your setup using
the linear translator, photometer, and oscilloscope.
Record patterns using translator, photometer, noise filter, 750
interface, and Data Studio at the front table and email the
results to yourself.
Process the measured intensity pattern with Excel and
generate a theoretical intensity pattern in Excel.
Compare measured and theoretical pattern in a graph in
Excel.
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
VII.B Example of Processing Single Slit Data in Excel
Time
Voltage
Time-tc
0
1.1
-25
1
1.1
-24
2
1.1
-23
3
1.2
-22
…..
…..
……
From Data Studio
Calculate from “Time”-column
(Time-tc=0 at peak of pattern)
Voltage-Voffset
I(t)
Calculate the
theoretical Intensity
distribution.
Calculate from “Voltage”-column
(so that Voltage-Voffset goes to zero at the edges of the pattern.
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
VII.B Calculating I(t)
a
 sin( Avt) 
I (t )  I (0)
 , where A 
D
 Avt 
2
You can read that off your
data (Voltage-Voffset at the
maximum intensity)
D = distance from the slit to
the fiber optic cable
a = slit width
=632.8nm
v = 10mm/min
t = Time - Toffset
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
VII.B Hints for getting the ratio of slit width a and slit
separation d for the double slit from the diffraction pattern.
Double slit maxima
mdouble=1,2,3
Single slit minimum
msingle=1
Modern Optics Lab
Lab 7: Diffraction and Interference Experiments
Double slit maxima
mdouble=1,2,3
Single slit minimum
msingle=1
m double 
Double slit maxima : sinQ 
d
Single slit minima: sinQ 
msingle 
a