Diffraction and Interference
Mitch Musgrove, Edgar Valle, Ahmed Abuzant
Department of Physics and Astronomy, Augustana College, Rock Island, IL 61201
Abstract: This experiment had the purpose of looking at diffraction and interference of
light waves and validating our calculated data against an accepted theoretical curve.
Along the way we also calculated the wavelength of the red laser we were using as a light
source. The accepted value of wavelength of the laser was 650nm, and our calculated
values ranged from642.909 nm +/- 80.73nm to 689.553nm +/- 89.21nm. Both values
containing 650nm within their error. Also our intensity vs. angle curves in figures 10
through 13 also match fairly well with the theoretical curves for each.
I. Introduction
The main purpose of this lab was to take data relating light intensity from a laser diffracted through both a
single then double slit, this data was then compared with a theoretical curve of the a diffraction pattern. We
also calculated the wavelength of our laser with the taken data. A single slit will cause light passing through
it to be diffracted causing patterns of dark and bright spots on a screen. This is due to light from different
parts of the slit having to travel different distance to the screen. Once 2 or more slits are introduced the
pattern projected on to the screen is complicated with an interference pattern caused by light from different
slits interfering. Both the interference and diffraction patterns are caused by the different path lengths light
must travel from different locations within a single slit and from other slits. To take data we used a light
intensity sensor and a motion sensor in conjunction with data studio to determine the location of the bright
and dark spots in each pattern. The equation used to calculate the wave length was 𝑚𝜆 = 𝑎𝑠𝑖 𝑛(𝜃), a= slit
width, 𝜃 =the angle with which a peak is located from the central bright spot, m = the number of bright
spots away from the central bright spot.
II. Experimental Setup
Motion
Sensor
Light Sensor
Figure 1 – Experimental setup
The setup of this lab was very simple including little equipment as seen in figure 1. The physical setup
included a red laser pointed a diffraction slit. Distance L is the length between the slits and viewing screen,
𝜃 is the angle between the central bright spot and a bright spot located a distance, d, to the left or the right
on the viewing screen. The light sensor was used in conjunction with the position sensor located on a track
to determine the distance, d, with which each bright spot was located from the central bright spot. The data
from these sensors was put together in data studio. To take data we had to manually move the light sensor
along its track with the motion sensors measuring how far along the track we had moved. As we moved the
light and motion sensor setup along their track, Data Studio created a light intensity vs. time (figure 2)
graph and a distance vs. time (figure 3) graph. With these 2 graphs we then used the equation 𝑚𝜆 = 𝑑𝑠𝑖𝑛𝜃
to calculate the angle with which each bright spot was diffracted from the central bright spot. When taking
data the room had to be completely dark so the light sensor didn’t pick up any stray light rays. Also to
acquire smooth graphs of our data we had to move the sensors very slow and smoothly across the track.
After we calculated our angles and wavelengths we use our intensity values from the 5 peaks of our single
slit and the 11 peaks for the double slit and determine our percentage of the max intensity for each bright
spot. These values along with our angle values can be plotted on a graph to show a wave function (figure)
that should look similar to that of our intensity vs. time graphs (figure 3). We used the equation
I  I0
sin 2 α
cos 2 δ
α2
to calculate a theoretical curve for our intensity vs. angle graphs.
III. Results
We made two runs for both single and double slit to gather data using Data Studio. Data studio took the
data from both sensors and created two graphs as seen in figures 2 through 5.
Figure 2 - Intensity vs. Time graphs of single slit runs.
Figure 3 - Position vs. Time graphs of single slit runs.
Run 2 took more time as seen on both graphs. This was because after completing run 1 we noticed some of
the peaks on each side of the central peak were hard to distinguish. We found that moving the sensors
slower in run 2 that this spread all the peaks out and made them easier to see.
Figure 4 - Intensity vs. Time graphs of double slit runs
Figure 5 - Position vs. Time graphs of double slit runs.
When taking data for the double slit pattern we had to move the sensors much slower, as can be seen in the
graphs. This was due to double slit causing 11 peaks rather than 5 as with single slit so we had to go slower
to spread all 11 peaks out so that they were distinguishable between each other. Even then some of the
peaks were so small that we had to zoom in on the graph to view them. Below are the tables created with
our data to calculate the wavelength of the laser and also the intensity of the peaks as a function of θ.
Light Intensity, Ch A, Run #1
Position, Ch 1&2, Run #1
Time ( s ) Light Intensity Intensity (% max) Time ( s ) Position d ( m ) Error (m)
4.7
0
0
4.7
-0.061
0.0005
5.6
0
0
5.6
-0.073
0.0005
6.7
0
0
6.7
-0.088
0.0005
8.2
0
0
8.2
-0.118
0.0005
9
0
0
9
-0.133
0.0005
9.7
0
0
9.7
-0.145
0.0005
Angle (⁰)
0.048238
0.034469
0.01724
0.01724
0.034469
0.048238
Figure 6 - Single slit diffraction data run #1 (5 peaks).
Error (⁰) Wavelength (m)
0.000574
6.42929E-07
0.000574
6.89246E-07
0.000575
6.89553E-07
0.000575
6.89553E-07
0.000574
6.89246E-07
0.000574
6.42929E-07
Error
8.07E-08
8.69E-08
8.92E-08
8.92E-08
8.69E-08
8.07E-08
Light Intensity, Ch A, Run #2
Position, Ch 1&2, Run #2
Time ( s ) Light Intensity Intensity (% max) Time ( s ) Position ( m )
Error Angle (⁰)
11.8
0.1
0.006493506
11.8
-0.065
0.0005 0.033321
13.2
0.1
0.006493506
13.2
-0.079
0.0005 0.01724
16.5
0
0
16.5
-0.109
0.0005 0.01724
18.3
0
0
18.3
-0.123
0.0005 0.033321
19.8
0.1
0.006493506
19.8
-0.137
0.0005 0.049385
Figure 7 - Single slit diffraction data run #2 (5 peaks)
Light Intensity, Ch A, Run #1
Position, Ch 1&2, Run #5
Time ( s ) Light Intensity Intensity (% max) Time ( s ) Position ( m )
34.1
1.8
0.033395176
34.1
-0.079
36
2.1
0.038961039
36
-0.084
41.7
3.9
0.072356215
41.7
-0.094
43.7
20.2
0.374768089
43.7
-0.099
46.2
43.9
0.814471243
46.2
-0.104
48
53.9
1
48
-0.109
50.3
44.1
0.818181818
50.3
-0.114
52.2
20.8
0.385899814
52.2
-0.119
54.1
3.8
0.070500928
54.1
-0.124
58.1
2.3
0.042671614
58.1
-0.134
59.4
2
0.037105751
59.4
-0.139
Error
0.000574
0.000575
0.000575
0.000574
0.000574
Wavelength
6.66297E-07
6.89553E-07
6.89553E-07
6.66297E-07
6.582E-07
Error
8.41E-08
8.92E-08
8.92E-08
8.41E-08
8.26E-08
Error
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
Angle
0.034469
0.028728
0.01724
0.011494
0.005747
0
0.005747
0.011494
0.01724
0.028728
0.034469
Error
0.000574
0.000574
0.000575
0.000575
0.000575
0.000575
0.000575
0.000575
0.000575
0.000574
0.000574
Error
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
Angle
0.034469
0.029876
0.01724
0.011494
0.005747
0
0.004598
0.011494
0.01724
0.029876
0.034469
Error
0.000574
0.000574
0.000575
0.000575
0.000575
0.000575
0.000575
0.000575
0.000575
0.000574
0.000574
Figure 8- Double slit diffraction data run #1 (11peaks)
Light Intensity, Ch A, Run #6
Position, Ch 1&2, Run #6
Time ( s ) Light Intensity Intensity (% max) Time ( s ) Position ( m )
30.1
1.8
0.032374101
30.1
-0.079
32.8
2.1
0.037769784
32.8
-0.083
36.5
3.9
0.070143885
36.5
-0.094
38
20.2
0.363309353
38
-0.099
40
44.3
0.79676259
40
-0.104
42.1
55.6
1
42.1
-0.109
43.4
44.5
0.800359712
43.4
-0.113
45.8
20.3
0.365107914
45.8
-0.119
47.2
3.9
0.070143885
47.2
-0.124
51
2.2
0.039568345
51
-0.135
52.4
2.1
0.037769784
52.4
-0.139
Figure 9 - Double slit diffraction data run #2 (11 peaks)
The wavelength values in the single slit data that we calculated came out to be close to the actual laser
wavelength value of 650nm. Our calculated wavelength values ranged from 642.909 nm +/- 80.73nm to
689.553nm +/- 89.21nm. Our error was propagated using the equation on pg 75 of source [1]. All of our
values had the accepted value within their error. Our Intensity vs. Angle graphs were the last thing we
created to compare with a theoretical curve.
Single Slit Diffraction (Run #1)
1.0
Intensity (Max %)
0.8
0.6
0.4
0.2
0.0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Angle From Central Peak (Degrees)
Figure 10 - Intensity (max %) vs. Angle from Central Peak graph of single slit diffraction (Run #1) with theoretical curve plotted
along with data points.
.
Single Slit Diffraction (Run #2)
1.0
Intensity (Max %)
0.8
0.6
0.4
0.2
0.0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Angle From Central Peak (Degrees)
Figure 11 - Intensity (max %) vs. Angle from Central Peak graph of single slit diffraction (Run #2) with theoretical curve plotted
along with data points.
.
Figure 12 - Intensity (max %) vs. Angle from Central Peak graph of double slit diffraction (Run #1) with theoretical curve plotted
along with data points.
Figure 13 - Intensity (max %) vs. Angle from Central Peak graph of double slit diffraction (Run #1) with theoretical curve plotted
along with data points.
IV. Discussion
The calculations we made for the wavelength of the laser all had the accepted value of 650nm within their
error which show promising results. Our calculated wavelengths varied from 642.909 nm +/- 80.73nm to
689.553nm +/- 89.21nm. Figures 10 through 13 show fraction of max intensity vs. angle θ. The calculated
fit line in all 4 plots was created using the equation below.
I  I0
sin 2 α
cos 2 δ
α2
Our theoretical line for both single slit runs match very well with our calculated points showing our data
was good. The theoretical curve for the double slit plots however did not match our calculated data as well.
Although the two curves did not match as well as single slit the double slit curves still strongly resembled
the shape of the theoretical curve showing our data may have had a larger amount of error but should still
be acceptable.
References
[1] Taylor, John R. An Introduction to Error Analysis: The Study of Uncertainties in Physical
Measurements. Sausalito, CA: University Science, 1997. Print.
[2] Vogal, Cecilia. Diffraction and Interference. Augustana College Moodle. 22 Mar. 2012. Web. 22 Mar.
2012. <http://helios.augustana.edu/~cv/351/>.