DIFFRACTION OF LIGHT
I. Objectives:
Study the diffraction of light from a double slit, a grating, a two-dimensional array of
holes
II . Equipment:
He-Ne laser, optical bench, component carrier, double slit, grating, square and
hexagonal hole array, ruler.
III. Introduction
In this experiment we will explore the wave nature of light. We will make light go
through apertures and let the transmitted light to combine (“interefere” is the technical
term). Depending on the path difference the various beams have taken, light intensity can
increase (“constructive interference” is the technical term) or go to zero (“destructive
interference” is the technical term). The latter is counterintuitive because we will get the
result: light + light = dark
a. Double slit: The diagram of a double slit is shown in fig.1a. On an opaque screen we
form two long narrow parallel slits separated by a distance d. A schematic of the two-slit
experiment is shown in fig.2. A laser light beam of wavelength  is incident normally on
two long parallel slits on the two slits. The resulting pattern is observed on a screen
placed at a distance L from the slits. Depending on the distance x of the observation point
P form the screen center O, we will get alternating maxima or minima in the light
intensity.
Intensity maxima occur at:
m L
xm 
m  0,  2,  4, ...
2d
(eqs.1)
The integers m are known as “order of diffraction” and are use to label the intensity
maxima and minima. A schematic of the two slit diffraction pattern is shown in fig.3.
b. Grating:
A grating is a repetition of a large number of slits as shown in fig.1b. If we use the setup
shown in fig.2 we get a similar diffraction pattern as in the case of the two slits. The only
difference is that the maxima are very sharp. Light of wavelength  after is passes
through grating propagates (“diffracts” is the technical term) only along certain directions
given by the equation:
d sin   m
m  0, 1, 2, ... (eqs.2)
The integer m is known as the “order of diffraction” .
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c. Two dimensional array of holes. A square array of holes is shown in fig.1c. As in
the case of the grating light after is passes through the hole array propagates only along
certain directions described by the angle  shown in fig.4.
d sin  


mx 2  m y 2 
mx , m y  0, 1, 2, ...
(eqs.3)
In this case we need two integers ( mx and my ) to describe the diffraction pattern which is
more complicated than that of the grating.
A schematic of the diffraction pattern is shown in fig.5. In it we also include the
integers mx and my for each diffraction spot.
IV. Experimental method
The setup for all the diffraction experiments is shown in fig.6. All the components are
mounted on an optical bench. The laser we use has wavelength   632.8 nm.
a. Double slit.
The diffraction pattern of the double slit ( d  0.25 mm) will be recorded on a screen
placed at a distance L  2 m from the slits. You will use a pen to draw a trace of the
diffraction maxima on a piece of paper.
b. Grating
In this case the diffraction spots are observed on a ruler placed at right angles to the
incident beam at a distance L  50 cm from the grating. A top view of the experiment is
shown in fig.7. The laser beam (   632.8 nm) is incident at right angles to the grating.
The spacing d  1.67  103 nm. Five diffracted beams result in five laser spots on the
ruler as is shown in fig.6. These points are: C ( m  0 ), A ( m  1 ), B( m  2 ),
A
( m  1 ) , and B ( m  2 ). We will use spots C, A, and B do determine  by
measuring the distances x1 and x2 of points A and B from point C, respectively.
x 
From triangle GCA we have: 1  tan 1  1 
(eqs.4)
L
x 
From triangle GCB we have:  2  tan 1  2 
(eqs.5)
L
From equation 1 we have:
d sin  2
  d sin 1 (eqs.6)
and also:  
(eqs.7)
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c. Two dimensional array of holes.
The diffraction pattern of the square array ( d  0.1 mm) will be recorded, as in the case of
the double slit, on a screen placed at a distance L  4 m from the hole array.
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V. Procedure
V-1: Double slit.
slit on a paper
Using the setup of fig.6, trace the diffraction pattern of the double
V-2: Grating : Using the setup of fig.7 observe the first (m = 1) and second ( m = 2)
order laser diffraction spots on the ruler (see fig.8). The distance L is setup at 50 cm from
the grating.
Measure the distance x1 of point A from point C and record the value of x1 in the data
sheet.
Measure the distance x2 of point B from point C and record the value of x2 in the data
sheet.
V-3: Two dimensional array of holes. Using the setup of fig.6 trace the diffraction
pattern of the two dimensional hole array on a paper.
VI. For the report
VI-1: Double slit. In this section you will analyze the two-slit data taken in section
V-1. Label the diffraction order m of the intensity maxima on the two-slit diffraction.
Using a ruler measure the distances x3 and x3 of the m = 3 intensity maxima on either
x x
side of the pattern center O. The average distance x3  3 3 . If we solve eqs.1 for d
2
we get:
3 L
dexp 
2 x3
Compare the experimental value dexp with the value given by the manufacturer.
VI-2: Grating
In this section you will analyze the grating data taken in section V-2.
a. Calculate the angle 1 using eqs. 4.
b. Calculate the angle  2 using eqs. 5.
c. Calculate the experimental value 1 for the laser wavelength for m =1 using eqs.6.
d. Calculate the experimental value 2 for the laser wavelength for m = 2 using eqs.7.
VI-3: Two dimensional array of holes. In this section you will analyze the hole array
data taken in section V-3. Using fig. 5 identify spots A, B, C, and D. The indices mx
and my for these points are:
Point A: (1,1), point B: (1, -1), point C: (-1, -1), point D: (-1, 1)
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Measure the distances x A , xB , xC , and xD of points A, B, C, and D respectively from the
x  x  x  xD
center O of the diffraction pattern. Determine the average distance x  A B C
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The experimental value dexp of the separation between the center of the holes can be
calculated using eqs. 3
 2
dexp 
x/L
VII Questions
VII-1: Compare the experimental value of the slit separation dexp from section VI-1 with
xexp  x
 100
x
VII-2: In section VI-2 you measured the wavelength  of the red line of the HeliumNeon laser using the first (m = 1) and second (m =2 ) order laser diffraction spots. The
  1
accepted value for   632.8 nm. Calculate the percentage differencess
100 and

  2
100 between your experimental values and the accepted value. Which

difference is larger?
the value given by the manufacturer. Calculate the percentage difference
VII-3: Compare the experimental value of the hole center separation dexp from section
VI-3 with the value given by the manufacturer. Calculate the percentage difference
xexp  x
 100
x
d
d
d
Fig.1a: Schematic diagram of
the two slits used in this
experiment
d
Fig.1b: Schematic diagram of
the grating used in this
experiment
Fig.1c: Schematic diagram of
the hole array used in this
experiment
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P
d
x
θ
C
O
screen
L
Incident
beam
Fig.2: Schematic diagram of a double slit diffraction experiment
m = -4 -3 -2 -1 0
1
2
3
4
x-axis
x-3
x3
Fig.3: Intensity maxima form the two-slit experiment observed
on the screen of fig.2. The intensity maxima are also called
“bright fringes”
incident
beam
O
θ
hole
array
diffracted
beam
P
Observation screen
Fig.4: Setup for the diffraction of light from a square hole array
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y
A
D
xA
xD
xC
C
O
x
xB
B
Fig.5: Diffraction pattern from the square array of holes as seen on
the observation screen shown in fig.4
diffracted
beam
laser
optical bench
screen
double
slit
L
Fig.6: Experimental setup for the two-slit experiment
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x2
x1
m = -2 m = -1
B'
m=1
m=0
A'
A
C
θ1
L
G
m=2
ruler
B
θ2
Grating
He-Ne
laser
Fig.7: Diffraction of a laser beam by a grating. The diffracted beams
are observed on a ruler placed at right angles to the laser beam
m = -2
m = -1
m=0
B'
A'
C
m=1
A
m=2
ruler
B
x1
x2
Fig.8: Diffraction pattern of the laser beam in fig.7
The diffracted laser spots are observed on a ruler at right
angles to the laser beam
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