Diffraction and Interference
Introduction and Theory
When light waves of a single wavelength pass
through a slit and hit a screen, the image is not a
single spot of light but a line of spots of varying
intensity separated by dark regions. This pattern,
the diffraction pattern, occurs because light from
one part of the slit interferes with light passing
through other parts of the slit. This can produce
constructive or destructive interference. If two or
more slits are present, the diffraction pattern is
complicated by the interference between light
passing through the different slits. In this
experiment, you will study the diffraction patterns
produced by one- and two-slit combinations.
function D() = sin2/2 which is plotted in
Figure 2 (a). This pattern is determined by the
width of each slit. The interference pattern is due
to the interference of the light arriving at the
screen from different slits and is described by
cos2 which depends on the distance between the
slits. This function is plotted in Figure 2(b).
Figure 2(c) shows the resulting intensity pattern
when these two functions are combined. This
intensity as a function of angle  is given by the
equation
sin 2 α
I  I0
cos 2 δ ,
(3)
2
α
where I = intensity at angle ,
I0 = intensity at center of pattern,
 = (a/) sin, and
 = (d/) sin.
Figure 1. Laser Diffraction Experiment
Figure 1 shows the geometry of the experiment.
Consider a double slit experiment in which light
of wavelength  is diffracted by two slits each of
width a and separated by a distance d.
Of particular interest is the fact that the minima in
the interference pattern (Fig 2b) are given by
m = d sin, m = 0,  1,  2, ….,  integer. (1)
The minima in the diffraction pattern (Fig 2a) are
given by
m = a sin, m = 0,  1,  2, ….,  integer. (2)
In this case, the intensity at a point on the screen
is actually a diffraction pattern and an
interference pattern superimposed on one another.
The diffraction pattern is described by the
Laser Diffraction
Figure 2. Double Slit Intensity Patterns
1
Figure 4. Experimental setup to obtain light intensity measurements of slit spectrum patterns
If a minimum in the diffraction pattern is located
at the position of a maximum in the interference
pattern, the interference maximum will be
eliminated. This is called a "missing order" in the
interference pattern.
detector by hand along the total length of the
linear translator. Try to move the motion detector
as smoothly as possible. When you examine the
spectrum, it should clearly show the large central
principal peak and at least two secondary peaks
on either side of the center peak. If you don't
have these 5 peaks, make additional runs until
Procedure
you do.Measurements
You may try
changing
the
position of the
Figure 4. Experimental Setup to Obtain Light Intensity
of Slit
Spectrum
Patterns
detector or laser.
The experimental setup that will be used is shown
in Figure 4 on the next page. A light sensor with
Determine the angular position of the minima in
an aperture bracket is mounted on a rotary motion
this spectrum, and use equation 2 to calculate the
sensor that moves along a linear translator bar.
wavelength of the laser. Compare to the given
Set up Science Workshop to record signals from
wavelength. Be sure you have good agreement
the light sensor and rotary motion sensor. The
before you move on.
position of the light sensor can be measured in
radians or distance along the linear translator bar
After you have a suitable spectrum for the single
in cm. Be sure to set this up to measure the way
slit, replace it with the double slit for which a =
you want it to.
0.04 mm and d = 0.125 mm. Keep the setting on
the light sensor at 10. Repeat the process used to
Position the laser so that it is located110-120 cm
obtain the intensity spectrum of the single slit.
in front of the light sensor. With the light sensor
Examine the resulting spectrum. It should clearly
approximately at the center of the linear
show a group of 7 principal peaks at the center.
translator, adjust the laser so that it is shining at
Then there will be two smaller peaks on either
the midpoint of the aperture opening in front of
side of the central group, separated from the
the light sensor. Now put the bracket with the
central group of peaks by a region of zero
single slits just in front of the laser and position it
intensity. You should obtain at least these 11
so that the laser is shining through the slit with
peaks in your spectrum. You may well have
slit width a = .04 mm. Measure the distance L
more peaks beyond this minimum number. If you
between this single slit and the slit in front of the
don't have at least these 11 peaks, make
light sensor. Try to keep L constant throughout
additional runs until you do.
the data collection process.
Using the graph of the double slit data, measure
Move the rotary motion detector along the linear
and record the intensity and position of each of
translator until it is in contact with the "rack
the central 11 peaks, and the minima between and
clamp". Put the setting on the light sensor at 10.
beyond them. Also record data for 22 more
Record angle and intensity data while moving the
2
Laser Diffraction
points, one on each side of the 11 peaks – not at a
maximum or minimum.
Plot a scatter graph of percent maximum intensity
vs. angular distance from the center peak. Since
the central peak has the maximum intensity, it
should be correspond to the point (0, 100).
The theoretical relativity intensity of the peaks is
given by the function in equation 3. Graph this
function on the graph with your data. Be sure to
multiply by 100 to make it a percent instead of a
fraction. If you can justify it, you may assume
the small-angle approximation, so that
sin ≈ 
Observe how closely this function fits your data.
Note whether the fit is better for some peaks than
others. Why might this be?
Laser Diffraction
3