PHYS 3650L - Modern Physics
Laboratory
Laboratory Advanced Sheet
Speed of
Light
1. Objectives. The objective of this laboratory is to
use the Foucault method to measure the speed of light.
2. Theory. The Foucault method.
Figure 1. Diagram of the Foucault method.
A method we will be using today was developed by Foucault
in 1862. The diagram of the experimental setup is shown in Figure 1.
Imagine the rotating mirror MR stationary. Parallel beam of light
from the laser is focused at point s by lens L1. Lens
L2 is positioned so that the image point at s is reflected
from the rotating mirror MR and is focused onto the fixed spherical
mirror MF. Mirror MF reflects the light back along the
same path to again focus the image at point s. In order that the
reflected point image can be viewed through the microscope, a beam splitter is
placed in the optical path, so a reflected image of the returning light is
also formed at point s'. Now, suppose that MR is rotated
slightly so that the reflected beam strikes MF at a different
point. Since the fixed mirror has spherical shape, the beam will still be
reflected directly back toward MR. The return image of the source
point will still be formed at points s and s'. The only
significant difference in rotating MR by a slight amount is that
the point of reflection on MF changes. Now imagine that
MR is rotating continuously at a very high speed. In this case, the
return image of the source point will no longer be formed at points s
and s'. This is because, with MR rotating, a
light pulse traveling from MR to MF and back finds
MR at a different angle when it returns when it was first
reflected. Measuring the displacement of the image point caused by rotation of
MR, the speed of light can be determined. Detailed analysis shows
that the speed of light can be calculated by using the following
formula:
 |
(1) |
where
c is the speed of light,
w is the rotational speed of the
rotating mirror
A is the distance between lens L2 and
lens L1, minus the focal length of lens L1,
B is the distance
between lens L2 and rotating mirror MR,
D is the distance between the rotating mirror
MR and fixed mirror MF, and
Ds' is the displacement of the
image point when rotating mirror is rotating relative to the position
of the image point when the rotating mirror is stationary, as viewed through
the microscope.
By rotating the mirror first in one direction
and then in the opposite direction, the total beam deflection is doubled,
thereby doubling the accuracy of the measurement. Under these conditions, the
equation (1) becomes
 |
(2) |
where wCW and wCCW are expressed in revolutions per
second.
3. Apparatus and experimental procedures.
a. Equipment.
1) High speed rotating mirror assembly.
2) Fixed mirror.
3) Measuring microscope.
4) He-Ne laser.
5) Optics bench.
6) Laser alignment bench with bench couplers.
7) 48 and 252 mm lenses.
8) Calibrated polarizers (2).
9) Component holders (3).
10) Alignment jigs (2).
11) Measuring tape.
b. Experimental setup. To be provided by the
student.
c. Capabilities.
To be provided by the student.
d. Procedures. Detailed instructions are provided in
paragraph 4 below.
4. Requirements.
a. In the laboratory.
1) Your instructor will introduce you to the
equipment to be used in the experiment and help you to set up and align the
equipment.
2) Record the position of rotating mirror and
lenses on the optics bench.
3) Measure the distance between rotating and
fixed mirrors.
4) Switch the rotating mirror power supply to
CW, turn the motor on and let it warm up at about 600 rev/s for at
least 3 minutes.
5) Bring the speed of rotation to about 1000
rev/s and use the microscope to measure the deflection. Record the speed at
which the motor is running and micrometer reading. Turn off the motor and
let it cool off for about a minute.
6) Switch the direction of rotation to
CCW. Turn the motor on and repeat your measurements in step
5.
7) Repeat the measurements in steps 5 and 6
two more times.
b. After the laboratory. The items listed below
will be turned in at the beginning of the next laboratory period. A complete
laboratory report is not required for this
experiment.
Para 3. Apparatus and experimental
procedures.
1) Provide a figure of the experimental
apparatus (para 3b).
2) Provide descriptions of the capabilities
of equipment used in the experiment (para 3c).
Para 4. Data. Data tables are
included at Annex A for recording measurements taken in the laboratory. A copy
of these tables must be included with the lab report. Provide the items listed
below in your report in the form a Microsoft ExcelTM spreadsheet
showing data, calculations and graphs. The spreadsheet will
include:
1) Recorded positions of rotating mirror and
two lenses.
2) Focal lengths of two lenses.
3) Measured value of the distance between
fixed and rotating mirrors.
4) Calculation of the parameters A and
B.
5) Table which includes the speeds of
rotation for both clockwise and counterclockwise directions with
corresponding deflections.
6) Calculation of the speed of
light.
7) Calculation of the percent discrepancy in
the speed of light. Your instructor will provide the actual
value.
Para 5. Results and
Conclusions.
5. Results and
Conclusions.
a. Results.
1) A statement of the measured value for the
speed of light.
2) A statement of the percent
discrepancy in the speed of light.
b. Conclusions.
1) Assess the accuracy of your
experiment.
2) Describe the sources of error in the
experiment.
Annex
A
Data
1. Position of Lens 1.
L1 = _________________________________ m
2. Position of Lens 2.
L2 = _________________________________ m
3. Position of Rotating Mirror.
MR = _________________________________ m
4. Distance between Rotating and Fixed
Mirrors.
D = _________________________________ m
5. Deflection Measurements.
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Trial |
wcw
(rev/s) |
s'cw (m) |
wccw
(rev/s) |
s'ccw (m) |
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1 |
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2 |
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3 |
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Last update:
September 08, 2008