Laser Diffraction
Figure 1. Schematic of Experimental Arrangement.
Figure 2. Single-slit diffraction pattern.
Introduction and Theory
When light waves of a particular wavelength pass through
a slit and hit a screen, the image seen is not a single spot
of light but a line of spots separated by dark regions. This
pattern, the diffraction pattern, occurs because light
emitted from one part of the slit interferes with light emitted
from other parts of the slit. Depending on the relative
phases of the light waves, this can produce constructive or
destructive interference. If there are several slits, the
diffraction pattern is complicated by the interference
between the light emitted from different slits. In this
experiment, you will study the diffraction patterns produced
by single, double, and triple slit.
The minima are labeled by integers n. Let b be the width
of the slit and xs be the separation between adjacent
minima. Then,
b=
D
.
2
xs
(Note that the separation between the minima n = -1 and
n = 1 is actually 2xs). Thus, a measurement of the
separation between the minima in a diffraction pattern
allows the calculation of the width of the slit.
Figure 1 shows the geometry of the experiment. Dark
regions, or minima, in the diffraction pattern occur where
the light waves interfere destructively. At these positions,
the lengths of the paths followed by different waves differ
by half of a wavelength. From this condition, it follows that
 = K sin  =
Kx
2
D + x
2

Kx
.
D
1
The last equation assumes that the small-angle
approximation is valid, or that D is large compared to x.
The value of K depends on the number of slits.
Figure 2 shows the intensity of light as a function of
position in the diffraction pattern produced by a single slit.
Figure 3. Double-slit diffraction pattern.
Figure 3 shows the diffraction pattern produced by double
slit. Let d be the spacing between the slits. Then, again
Laser Diffraction
letting xs denote the separation between adjacent minima
in the diffraction pattern, we have that
d=
D
light.
Procedure
.
3
Turn on the laser and place the single slit in the laser
beam. Tape a strip of paper to the wall approximately 5-8
meters from the laser. Sketch the diffraction pattern.
xs
You will need to use four minima on either side of the
central maximum. Mark the center of each minimum on
the sheet of paper. These positions are the xi referred to in
the figures. Measure and record the positions of these
minima. Estimate the uncertainty -- note that there is
uncertainty in making the marks, as well as in measuring
the marks once made. Try to take both into account.
Measure and record the distance D between the slit and
the wall, as well as the uncertainty in that measurement.
Figure 4. Triple-slit diffraction pattern.
Finally, Figure 4 shows the diffraction pattern produced by
triple slit. Note that adjacent minima are separated by
either xs or by 2xs. Compare the separation between n=1
and n=2 with that between n=2 and n=4. In this case, the
spacing between adjacent slits is
d=
D
3 xs
.
4
Repeat the sequence of measurements for the double slit
and for the triple slit. The width b of the single slit and the
spacing d of the double slit and of the triple slit are printed
on the slit holder. Record these numbers.
Analysis
For the helium-neon laser that you are using, the
wavelength of the light is
 = 632.8 ± 0.1 nm.
Lasers
You will use a laser to produce the light for this experiment.
"Laser" is actually an acronym for Light Amplification by
Stimulated Emission of Radiation. Basically, a laser works
by exciting atoms and collecting the light produced when
the atoms lose their excess energy. The key to the
process is that the light emitted by one atom can stimulate
another atom to emit light. Mirrors on either end of the
laser reflect the light, so that it passes through the laser
many times, stimulating more light emission and thus
amplifying the light.
The light from a laser is
monochromatic. Its wavelength is determined by the
atoms involved in the laser and by the length of the laser.
The light is also coherent, meaning that all of the waves
are in phase with one another. The coherence of laser
light produces its great intensity compared with "ordinary"
Use Equations 2, 3, and 4 to calculate b or d for each of
the sets of slits, and compare your results with the
manufacturer values. There is a computer spreadsheet to
help you with the calculations.
Use the method outlined in Chapter 4 of Squires to derive
the error equations for b or d in each case. Compute the
uncertainties and compare them to the difference between
the two values of b or d for each case. Comment on your
results: Are the values consistent within the expected
uncertainty?
Laser Diffraction
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Laser Diffraction
3