26/03/2025
KOÇ UNIVERSITY
COLLEGE OF SCIENCES
PHYS 206: GENERAL PHYSICS IV
Michelson Interferometer Experiment
Lab Report #3 (27.04.2025)
Instructor Name/Surname: Alper Kiraz
Lab Coordinator: Nazmi Yılmaz
Student Name: Ali Aral Eren
Student ID: 79405
PHYS 206 Spring 2025
Lab Report 3
Contents
Introduction of the Experiment................................................................ 3
Theory ..................................................................................................... 3
Experimental Setup ................................................................................. 4
Data Analysis .......................................................................................... 6
Questions ................................................................................................ 6
1. Calculate the Wavelength of the laser. ............................................... 6
2. Calculate the percentage error ............................................................ 6
Conclusion .............................................................................................. 7
References ............................................................................................... 7
Appendix ................................................................................................. 7
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Introduction of the Experiment
In this lab, the participants conducted an experiment called “Michelson Interferometers”. The
experiment was based on the concept of interference among two beams of light that meet in
space. Taking on a wave model perspective, the wave’s maxima values collide with the other
wave, it creates bright or dark spots when visualized on a screen.
When there is a phase different, the device that is used is helpful in calculating the interference of
these waves. The device – Michelson Interferometer- was developed in 1881 by A.A. Michelson.
The device operates by dividing a beam 50-50%, reflecting them via mirrors, and recombining
them to visualize their interference patterns.
Hence, throughout this experiment, the objective was to align and operate a Michelson
Interferometer to observe interference patterns, and utilize the displacement of the movable
mirror to calculate the wavelength of the laser beam. For the experiment, the participant
postulated the following hypothesis:
If a Michelson interferometer is used to observe self-interference patterns, the shift in the mirror
will cause fringe movements on the screen, which will be used to calculate the lasers wavelength
accurately.
Theory
The Michelson Interferometer operates on the concept of lighr interference, in which a single
beam is split into two paths using a beam-splitter. Each beam reflects of a mirror and returns to
the same splitter, where they recombine and interfere with each other, creating fringe pairs,
consisting of constructive and destructive interferences. The diagram of a Michelson
Interferometer is shown in Figure 1.
Figure 1: Diagram of a Michelson Interferometer
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Below are formulas for constructive and destructive interferences basing on the movement of the
mirror:
Constructive:
∆L = mλ
Destructive:
∆L = (m + 0.5)λ
For a Michelson Interferometer, the movable mirror allows control over the trajectory of the laser
beam, and since the mirror oscillates along the optical axis, the path is 2d, where d is the
displacement of the mirror. Hence, when the number of fringes that pass as the mirror moves is
known, the wavelength of the original laser is found with the following formula:
𝜆=
2𝑑
𝑚
Where d is the displacement of the mirror,
m is the observed number of fringes.
Figure 2 is a representative of the interference pattern aforementioned.
Figure 2: Interference Pattern
Experimental Setup
The experiment was conducted using the following equipment:
• Interferometer base with built-in micrometer and leveling feet
• Movable mirror
• Beam splitter
• Three-point adjustable fixed mirror
• Beam expanding lens with component holder
• Fitted case
• Laser Source. (A low power laser that operates in the visible range)
The equipment was used to form the setup is shown in Figure 3.
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Figure 3: Experimental Setup
The following specifies the procedure for the experiment:
1. Align the laser and interferometer as described in the preceding section, so an interference
pattern of circular fringes is visible on your viewing screen.
2. Adjust the micrometer knob so the lever arm is approximately parallel with the edge of the
interferometer base. In this position the relationship between knob rotation and mirror movement
is most nearly linear.
3. Turn the micrometer knob one full turn counterclockwise. Continue turning counterclockwise
until the zero on the knob is aligned with the index mark.
NOTE: Whenever you reverse the direction in which you turn the micrometer knob, there is a
small amount of give before the mirror begins to move. This is called mechanical backlash, 6
10− and is present in any mechanical system involving reversals in direction of movement. You
can eliminate backlash in your measurement by beginning with a full counterclockwise turn and
then turning only counterclockwise when counting fringes.
4.If you are using a blank piece of paper as your viewing screen, make a reference mark on the
paper between two of the fringes. You will find it easier to count the fringes if the reference mark
is one or two fringes out from the center of the pattern.
5. Rotate the micrometer knob slowly counterclockwise. Count the fringes as they pass your
reference mark. Continue until a predetermined number of fringes has passed your reference
mark (count at least 20 fringes). As you finish your count, the fringes should be in the same
position to your reference mark as they were when you started to count.
6. Record the distance that the movable mirror moved toward the beam-splitter as you turned the
micrometer knob. Remember, each division on the micrometer knob corresponds to one micron
of mirror movement.
7. Record m, the number of fringes that crossed your reference mark.
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PHYS 206 Spring 2025
Lab Report 3
Data Analysis
Throughout this section of this lab report, the participant will provide a Table of experimental
data collected in the experiment, including the values found in the 6 th and 7th step of the
experiment.
dm (nm)
m
6400
20
Table 1: Accumulated Data
Observe in Table 1 that when the mirror displaced a total of 6400 nm, there were 20 fringes
observed.
Questions
1. Calculate the Wavelength of the laser.
According to the formula provided in the theory section:
2𝑑
𝜆=
𝑚
The following calculation was made:
6400 𝑛𝑚
𝜆 =2∗
= 640 𝑛𝑚
20
Hence, the calculated wavelength of the laser is 640 nm, red color.
2. Calculate the percentage error
Knowing that the original laser had the wavelength od 632.8 nm, the calculation of the
percentage error is as follows:
640 − 632.8
∗ 100 = 1.14%
632.8
These calculations provide us with the fact that the experiment was completed with high
accuracy. For the miscalculation, there is only one small mistake that prevented the
participant from correctly calculating the actual value. Firstly, since the formula for the
wavelength only depends on the number of fringes and the displacement of the mirror, the
error results from the miscalculation of one of these. Since the number of fringe pairs is
actually an integer value, if the actual number were 19 or 21, the error would be even
higher when calculated. (The participant calculated the error, and it is 6.46% and 3.69%)
Hence, the number of fringes was not miscalculated. However, since the displacement of
the mirror is calculated with high insensitivity, the number 6400 nm is too rounded, since
the observation was done using the human eye with the rotation. It is not possible to find
6328 nm of mirror movement with only the human eye. Hence, the only source of error in
this experiment is the sensitivity of measurement.
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Conclusion
In this experiment, the participant used the Michelson Interferometer to observe interference
patterns and determine the wavelength of a laser source. By aligning the setup and counting 20
fringe shifts while the movable mirror was displaced by 6400 nm, the wavelength was calculated
to be 640 nm.
This result closely matched the original laser beam with a percentage error of 1.14%, indicating
high accuracy. The experiment successfully showed that the interferometer's capability to
measure extremely small displacements and calculating a light source’s wavelength. However,
there was an error caused by the participants, in measuring the displacement.
Overall, the lab helped the participant to understand key concepts in wave optics, particularly
interference and coherence.
References
[1] Lab Manual for the Third Experiment
Appendix
dm (nm)
6400
7
m
20