Interference and

Diffraction
1 GOAL
If you are wondering what experimental evidence exists for the claim “light is a
wave”, you do not need to look no further. In this lab you will directly observe
interference patterns and diffraction patterns of light. These patterns are
hallmarks of wave phenomena. The patterns are familiar from other systems that
exhibit wave behavior, such as water waves.
Interference and diffraction patterns, which appear when light encounters small
apertures or obstructions, cannot be explained with the ray model; the wave
nature of light must be explicitly taken into account in order to understand them.
This lab provides an opportunity to directly observe these hallmark wave
phenomena and to further your conceptual understanding of interference and
diffraction.
You will conduct your own precision measurement, one to determine the
diameter of a thin wire or strand of hair, using light interference. Parts A and B, in
which you observe light having passed through two narrow closely-spaced slits
and through a single narrow slit, respectively, will prepare you for this precision
measurement in Part C.

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2 THEORY
A. Double slit interference
A single light source, the red light of a laser, will be used throughout this lab. We
will consider this light be monochromatic; that is, consisting of a single wavelength.
To conduct the precision measurement in Part C you will need to know the
particular wavelength of light being emitted by this laser. The wavelength will not
be given to you. You will measure it in this first activity.
In this experiment the red laser light will be aimed at a pair of narrow closely
spaced slits. It is often referred to as a Young’s Double Slit apparatus. The pattern
of light on a distant view screen will be observed and analyzed. Features of the
pattern depend on the light wavelength and therefore a careful analysis of the
pattern will make possible a calculation of it.

Figure 1. Double slit interference geometry

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 2 THEORY
A top down diagram of the system geometry is shown below in Figure 1. The slit
separation d is much less than the view screen distance D. A point on the view
screen, such a P1, can be identified either by the angle θ made with respect to
the central axis or by the length y as shown in the diagram.
The two slits can be modeled as two coherent in-phase point sources of light. The
“light waves” emanating from these two sources combine to form an interference
pattern. At the view screen total constructive interference occurs at points where
the two combining waves are in phase. This occurs where the path lengths from
slits to screen are identical, in this geometry at the point marked P0, or where the

path lengths differ by a distance equal to an integer number (1, 2 , 3, ...) of

wavelengths. Using these conditions and the geometry of the system it can be
shown that the angles at which total constructive interference occur are:
d sin m  m m = 0, ±1, ±2, ±3, … (1)

In this equation λ is the light wavelength and m is an integer index that can take
on the values 0, ±1, ±2, ±3, … The positive and negative values refer to maxima,
symmetrically positioned, on one side or the other of the central axis. In words, for
example, one would say that 𝜃 3identifies the angle at which the third order (m =
3) maximum of the interference pattern occurs.

B. Single slit interference

In Part A you determined the laser’s wavelength by analyzing the two-slit interference
pattern, but this was only possible because you were given the manufacturer’s reported
value for the slit width. In Part B you will see how this process can be reversed. Now that
you know the laser’s wavelength, you can analyze an interference pattern to determine
the size of the aperture or obstruction that the light encounters.

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 2 THEORY
In this experiment, instead of two slits, the light will encounter a single narrow slit.
The so-called single slit diffraction pattern will be observed on the screen. The
exact nature of the pattern depends on both the light wavelength λ and the slit
width a. The goal of this activity is to determine the slit width. The geometry of the
experiment is shown in Figure 2.

Figure 2 Diffraction pattern of a Single slit

The intensity at any point depends on the phase relation between the various
waves emanating from these points when they arrive at a single point on the view
screen. If all the waves arrive in phase, the light intensity at the point on the screen
will be a maximum; otherwise, not. And it may seem a surprising coincidence, for
so many combining waves, but there are points where the phase relationships of
all the waves are just right to produce zero intensity. These are the minima that
you have marked on the screen. It can be shown that these points of complete
destructive interference occur at angles that satisfy the condition,
a sin m  m l m= ±1, ±2, ±3, … (2)

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3 SET-UP AND PROCEDURE

Figure 3 Experimental setup.

aperture disk

Figure 4(a) The combination of Linear Position and High Sensitivity Light Sensor, (b)
aperture disk of the light sensor, and (c) light sensor sensitivity mode.

Figure 5 Slit assembly.

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 3 SET-UP AND PROCEDURE

A. Double slit interference

a. Place the dynamics track on a level surface. Use of adjustable feet for the

track is convenient, but optional.

b. Attach the combination of Linear Position and High Sensitivity Light

Sensor(Figure 4(a)) to the track. Slide the light sensor to approximately the center
of the position sensor.

c. Set the entrance aperture disk of the light sensor to the 0.3 mm setting but you
should rotate the disk in order to get precise data, and set the light sensor
sensitivity to the middle, 10 μW, setting.(Figure 4 (b)&(c))

d. Attach the Slit assembly to the track, with the label and silver reflective side

toward a laser source. A starting position is at the 20 cm mark on the track. You
can change the distance in order to get precise data.

e. Move the bar of the Multiple Slit Set(Figure 5)so as to center the double

slit(select the three different slit width or a slit separation and repeat below steps.)

f. Attach the Red Diffraction Laser to the track, facing the slit assembly. A starting
position is at the 5 cm mark. You can also change the distance in order to get
precise data.

g. Secure the Multiple Slit apparatus far from the top entrance aperture of the

light sensor(screen). The slits-to-view screen distance D is an important parameter.

Distance, D should be at least 900 mm.

h. Turn on the laser and confirm that you see red light striking the Slit assembly.

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 3 SET-UP AND PROCEDURE

i. Adjust the vertical and horizontal direction of the laser using the two

thumbscrews on the back of the laser, so that the beam passes through the
double slit and falls on the light sensor front plate as shown in Figure 6. Roughly
center the diffraction pattern on the top entrance aperture of the light sensor.

j. Connect the sensors to an interface, and open the data collection software
(Logger Pro). Move the position sensor to the far right as viewed from the light
sensor side.

k. Set samplings rate to 100 samples/sec and collection time to 60 sec in the ‘Data

Collection( )’ of the menu. Before taking the data, zero the values by clicking at .
Start the data collection( ).

l. Grasp the position sensor, and slowly and smoothly move the light sensor across
the full width of the stage as shown in Figure 6. Take enough time to perform the
motion. If you move too quickly, the light sensor will not have time to respond to
variations in the intensity pattern.

m. The pattern you observe on the view screen should be a horizontal line of

alternating bright and dark spots, or maxima and minima, something like that
shown in Figure 7.

Figure 6 Diffraction pattern on the screen

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 3 SET-UP AND PROCEDURE

Figure 7 Double slit interference pattern, showing locations of the first three maxima.

n. Compare the bright red spot with the highest intensity position at the very

center of the pattern of your results like Figure 7. This is the central m = 0 maximum
for which the angle and position are zero (𝜃 0= 0, y 0 =0). Measure and record the
locations of all the marked maxima with respect to the central maximum. (y1, y2,
y3)

o. What feature appears to arise from the double slit? Make a sketch of intensity
vs. position on the graph. As before we’ll say the intensity at the center of the
screen, the brightest point, is 100. Add the new calculated column to convert the
maximum value of the intensity to 100(%). The max function can be used and
written as follow :
max("intensity")

p. Derive an equation to calculate the wavelength of the laser source using the
equation (1). Compare your results with the theoretical value.
How does the slit spacing d and the slit width a affect the double-slit pattern?
Discuss what you expect to happen to the double-slit pattern based on
equation you derived.
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 3 SET-UP AND PROCEDURE

B. Single slit interference

a. Follow steps from a to k in experiment A.
b. Change from double slit to single slit set. Move the bar of the Multiple Slit Set

so as to center the single slit(select the three different slit width (0.04, 0.08, 0.16
mm) and repeat below steps.)

c. The pattern you observe on the view screen should be a horizontal line of

alternating bright and dark spots something like that shown in Figure 2 and 8.

d. You can notice that the maxima in this pattern are much broader than in the
double slit pattern from Part A. In fact, because they are so broad, marking the
positions of the maxima is an imprecise process. To analyze the pattern with
precision it is better to mark the minima. (Note that the minima, especially the first,
might not appear perfectly dark. Check any point where the intensity drops and
then rises again.)

Figure 8 Single slit diffraction pattern, showing locations of three minima.

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 3 SET-UP AND PROCEDURE

e. Move the position sensor to the far right as viewed from the light sensor side.
h. Start data collection. Grasp the position sensor, and slowly and smoothly move
the light sensor across the full width of the stage. Take enough time as you did in
previous experiment.

i. Measure and record the distance ∆2y between the symmetric pairs of minima

on either side of the central maxima as shown in the graph of Intensity vs position
about single slit. We’ll label the minima with an integer index m= ±1, ±2, ±3 ... (The
center of the screen is bright, so there is no m = 0 minimum.)

j. What feature of the pattern appears to arise from the single slit? Make a sketch
of intensity vs. position on the graph. As before we’ll say the intensity at the center
of the screen, the brightest point, is 100. As you did in the experiment A, add the
new calculated column to convert the maximum value of the intensity to 100(%).

k. Derive an equation to calculate the wavelength of the laser source using the
equation (2). Compare your results with the theoretical value.
How does the slit width affect the diffraction pattern? Discuss the tendency of
your results which you got changing the slit width based on the equation you drive
for the wavelength of it?
How is the single-slit pattern different, from the double-slit pattern? Also, what
causes the difference in the pattern?

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 3 SET-UP AND PROCEDURE

C. Diffraction by an obstruction
a. Design an experiment to measure the diameter of a strand of your hair (or a

thin line in your slit). Scissors are available. Follow step a in experiment B.

b. Remove the bar of the Multiple Slit Set from slit assembly and attach a strand
of your hair using scotch tape.

c. Follow steps from c to j in experiment B.

d. Diffraction from a thin obstruction like a strand of hair, which can be thought
of as the negative of a narrow slit, is very similar to the diffraction pattern you
observed in experiment B. In fact, the minima in the pattern occur at angles that
satisfy Equation (2). After carrying out the experiment, record your measurements
and calculate the diameter of your hair. (laser wavelength = 635nm)

e. If we redid these experiments with a blue laser instead of red, what changes
would you have needed to make?

f. What would happen to the diffraction pattern if the track width was smaller?

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