1. The document describes an experiment where lasers of different colors were shone through single and double slits to observe the resulting interference patterns of light. Calculations were done to determine the wavelengths of red and green lasers based on the interference patterns. 2. The key results were that the calculated wavelengths from the interference patterns matched closely with the actual wavelengths of the lasers, within low percentage errors. This provided evidence that light behaves as waves and interference occurs as predicted by the wave theory of light. 3. The double slit patterns were more distinct with uniform bright bands, while the single slit patterns had a blurrier central bright region that faded at the ends, demonstrating the different effects of single and double slit interference

1. Kaitlyn Greiner
Formal Lab Report:
Interference of Light
Date Performed: July 30th, 2014
Lab Partners: Erin Phlegar and Stephen Few
Physics 102 L, Section: 02
Professor Teklu
Abstract:
We set out to study the interference patterns of light that passed through single and
double slit slides. This interference proves that light behaves like a wave. We calculated the
wavelengths of red and green lasers shining through double and single slit slides. We observed
the patterns they made after passing through the slits. We found constructive and destructive
interference in the patterns. This shows that the interaction, called interference, took place, which
shows that light behaves like a wave.

2. Introduction:
In this experiment, our goal was to study the interference patterns of light through a
single and double-slit using a laser of two different colors. From Thomas Young’s work, we
know that light behaves like a wave because it forms interference patterns when shown through a
double slit. Since we know that light behaves like a wave, we can measure the wavelengths of
colors of light. Light rays interact if more than one passes through the same place (slits) at the
same time. This experiment will focus on the interference of light. After the light rays have
passed beyond the slit(s), the electric and magnetic fields oscillate and result in the sum of the
waves. This is an interaction called interference. Interference can be constructive or destructive.
Constructive interference means that two waves are in phase with each other and create a wave
with higher amplitude. This means that one wave has to be a whole number of wavelengths past
the other wave so that they are in phase. This “path difference” can be calculated with the
formula, dsinΘ, in a double slit experiment. Destructive interference means that two waves are
out of phase with each other and result in a cancellation of the two waves.
In a single slit experiment, we will focus more heavily on this destructive interference.
We expect to find a bright central band during a single slit experiment. The band shows light that
has passed without interference. We expect this pattern to be very spread out and for the bright
spots to quickly diminish from the bright center. We are expecting to see a finer pattern and that
appears more uniformly bright in the double slit experiment.
Description of Apparatus:
We set up a laser (red or green) behind a single or double slit slide on a mount and placed
a piece of paper further away after the slide. We taped our piece of paper on some boxes to stand
it up. Our patterns were projected here on this sheet of paper. We measured the distance, L, from
our slit slide to our piece of paper. Sometimes, we had to change this distance in order to see our
pattern more clearly. To do this, we slid the laser and slide to various locations on the mount. We
found our values for Y by measuring parts of the pattern projected on the sheet of paper. The
parts that we measured for Y varied for the double slit and single slit experiments. We used these
values to calculate our angle, Θ, between the beam path and the pattern. In the double slit
experiment, we were given our slit spacing, d, on the slide. In the single slit experiment, we were
given our width of the slit, a, on the slide. This description is depicted in the sketches below:

3. Procedure:
We set up a laser behind a single or double slit slide and then placed a piece of paper
after the slide. For the double slit experiment, we used a red laser and then a green laser and
determined the wavelength of each color. We chose the distance, d, between the two slits on our
double slit slide to be .5mm. After getting our red laser set up behind the double slit slide, we
measured the distance, L, from this slide to the paper on which the pattern was being projected.
Next, we found Y by observing the pattern on our sheet of paper. We measured the length of our
entire central, bright pattern then counted the bright fringes within this pattern. We divided its
length by the number of bright fringes counted. We calculated the angle between the beam path
and the pattern by using the equation, tanΘ=Y/L. Since the zeroth order band is in the center of
the interference pattern, our value for m is one. After we found the angle, we were able to plug
everything into the equation, mλ=dsinθB, and solve for the wavelength of the red laser. We
compared our result to the actual value of 650nm and calculated our percent error.
We repeated this same process for the green laser. We kept our distance, d, between the
two slits the same but we changed our length, L, in order to see our pattern more clearly. Our
value for the order of the interference band, m, remained one. We calculated using the first order
band throughout this experiment. We solved for the wavelength of the green laser and compared
our result to the actual value of 532nm. We calculated a percent error.
For the single slit experiment, we used a red laser and a green laser and determined the
wavelength of each. We replaced our double slit slide with the single slit slide. We chose a
width, a, on our single slit slide to be .04mm. We measured the length, L, in the same way from
the single slit slide to the piece of paper. We found Y measuring the distance from the middle of
the dark space above our main pattern to the middle of the dark space below our main pattern
and dividing this value by two. We divided by two because the value of y1 is actually from the
middle of our main pattern to the middle of the next dark space. By measuring from the middle
of a dark space to the next middle of a dark space, we were actually finding 2y1. We, then,
calculated our angle using our Y and L. The value of the order of the interference band, m, is still
one. We then plugged all of these values into the equation, mλ=asinθD, to calculate the
wavelengths for the red and green lasers. Again, we changed the length, L, slightly for the green
laser in order to see the pattern more clearly. We compared the calculated wavelength value for
the red laser to 650 nm and calculated our percent error. We compared the calculated wavelength
value for the green laser to 532nm and calculated our percent error.
Results:
Double Slit-
mλ=dsinθB
Red laser:
D=.5mm or .5x10^-3m
L=166cm or 1.66m
Y=5.1cm/23 bright fringes
Y=.222 cm or .00222m
tanΘ=.00222/1.66
Θ=.077

4. M=1
Mλ=dsinθB
(1)λ=(.5x10^-3)sin.077
λred=6.68x10^-7m or 667.9 nm
actual: 650 nm
% Error:
((650-667.9)/650)x100%
=2.75%
Green Laser:
D=.5mm or 5x10^-3m
L=205cm or 2.05m
Y=5.1cm/24 bright fringes
Y=.2125cm or .002125m
tanΘ= .002125/2.05
Θ=.059
M=1
(1)λ=(.5x10^-3)sin.059
λ=5.18x10^-7m or 518.3 nm
actual: 532 nm
% Error:
((532-518.3)/532)x100%
=2.58%
Single Slit-
mλ=asinθD
Red Laser:
w=.04x10^-3m
L=127.2 cm or 1.272m
Middle of dark to middle of dark=4.5cm
4.5/2=2.25cm or .0225m
Y=.0225m

5. tanΘ=.0225/1.272
Θ=1.01
(1)λ=(.04x10^-3)sin1.01
λ=7.07x10^-7m or 707.4 nm
actual: 650nm
% error:
((650-707.4)/650)x100%
=8.83%
Green Laser:
w=.04mm or .04x10^-3m
L=140.5 cm or 1.405m
Middle of dark to middle of dark=4.1cm
4.1/2=2.05cm or .0205m
Y=.0205m
tanΘ=.0205/1.405
Θ=.836
(1)λ=(.04x10^-3)sin.836
λ=5.84x10^-7m or 583.6 nm
actual: 532nm
% Error:
((532-583.6)/532)x100%
=9.70%
Data Table:
Double Slit
(calculated)
Double Slit (%
Error)
Single Slit
(calculated)
Single Slit (%
Error)
Red Laser 667.9 nm 2.75% 707.4 nm 8.83%
Green Laser 518.3 nm 2.58% 583.6 nm 9.70%
Conclusions:
This experiment proved the wave theory of light, that light behaves like a wave. We
proved this by calculating the wavelengths of the two different colored lasers by observing their
patterns. After comparing our calculations to the actual values of the wavelengths, we found that
we had very low percent errors. This shows that our formulas are very effective in finding
wavelengths of light. Our patterns showed the interaction of the light waves. There was not a
large difference in the patterns between the different colors. We did find that double and single
slits generate slightly different patterns of light. The double slit pattern has very distinct bright
and dark bands of light and does not fade at the ends. The single slit pattern has a bright central

6. pattern that is less distinct and blurrier. This pattern faded at the ends. Both patterns had dark and
bright bands. Constructive interference creates a wave with higher amplitude and is shown in the
experiment as the bright bands of light in the patterns. This means that the waves arrived at the
sheet of paper in phase with each other. The dark bands that appeared in this experiment show
destructive interference, meaning the waves arrived at the sheet of paper out of phase with each
other. They cancelled each other out and no light resulted in these places. These observed
interactions show that the interference of light took place.