Determination of Speed of Light using the Foucault Method
Raghuveer Dodda, Physics 425
The Foucault Method consists of a beam of light emitted from a source incident on a
rotating mirror that is rotating at a constant angular velocity. This mirror reflects the
beam towards a fixed mirror a few meters away, placed at an angle from the axis
between the source and rotating mirror. The fixed mirror reflects the beam back to the
rotating mirror, and the beam travels back to the source. The returning beam shifts by a
small distance along the direction perpendicular to propagation of light. The fixed
distances and this shift are measured. One can calculate the Speed of light from these
measurements by using the laws of Optics.
INTRODUCTION
The Speed of Light is an important
physical constant, and several people
like Galileo, Römer, and Fizeau
attempted to measure it accurately
before the 19th century. Foucault
developed the method used in this
experiment in 1862. When Michelson
used Foucault’s method, he measured
the speed of light to be 2.99774 x 108
m/s. The presently accepted value is
2.99792458 x 108 m/s (Lee, 1999).
MATERIALS AND METHODS
Figure 1 - Schematic diagram for the Foucault
Method
The apparatus consisted of a laser
generator that acted as the source of
light. The laser beam traveled the
distance of 860mm to reach the rotating
mirror (which is not rotating initially).
The laser generator and the rotating
mirror were adjusted to be at the same
height and were placed on a bench so as
not to alter their positions during the
experiment.
The fixed mirror was
placed at a distance of 5000mm from the
rotating mirror. The line joining the two
mirrors made an angle of 12o with the
longer axis of the bench, as shown in
Fig1.
The position of the laser bema generator
was adjusted very carefully to ensure
that the laser incident on the rotating
mirror retraces it path to the laser
generator (alignment jigs were used for
this purpose). The rotating mirror was
rotated a very small amount towards the
fixed mirror so that the light from the
laser generator reached the fixed mirror.
The fixed mirror is then adjusted (using
the adjustment knobs that are behind the
mirror) to ensure that the laser retraces
its path back to the rotating mirror and
eventually to the laser generator.
Two lenses and a microscope (which
contains the beam splitter) were placed
on the bench as shown in Fig1. The
microscope was obviously necessary to
look, at the returning beam, from the top
to measure the expected shift. The
lenses served the purpose of ensuring
that the laser beam was focused when it
reached the rotating mirror (laser tends
to spread out when traveling long
distances). It is very important to note
that the lenses and the microscope were
placed before the adjusting the beam
position on the fixed mirror. Once this
set-up was in place, we could see the
returning beam spot through the
microscope.
The rotating mirror was then rotated at a
fixed angular velocity and the shift in the
beam spot was observed through the
microscope. The process is repeated, by
rotating the mirror in the opposite
direction.
position S will find that the rotating
mirror has changed its position by the
time this pulse has traversed the distance
between the mirrors. This pulse will not
retrace its initial path but instead will
make a different angle with the rotating
mirror. Incidentally, the result is the
same if we assume that the rotating
mirror is stationary but that a pulse
incident on the fixed mirror at S return
from the position S1. The ray diagram
presented in Figure 2 utilizes this notion
because the problem then can be solved
the principles of thin lens optics. Since, a
beam is a continuous stream of pulses,
everything we discussed about the pulse
also holds for the beam (Lee, 1999).
RESULTS AND DISCUSSION
The following measurements were
made:
1. ω = 2 π (1015.00 ± 0.005)
radians/sec is the rotational
velocity of the rotating mirror.
2. Δs’ = Δs = 0.16 ± 0.005 mm (the
average of 0.15 ± 0.005 mm in
CCW and 0.17 ± 0.005 mm in
CW) is the shift in the beam spot
of the laser due to the rotation.
3. A = 388. ± 0.5 mm is the
distance between the lens L2 and
the source.
4. B = 472. ± 0.5 mm is the
distance between the lens L2 and
the rotating mirror.
5. D = 5000 ± 0.5 mm is the
distance between the fixed mirror
and the rotating mirror.
Figure 2 depicts the case when the
rotating mirror is in motion. A pulse of
light incident on the fixed mirror at
Figure 2 - Various measured distances
The shift S1 – S = ΔS can be related to
the angle of the rotation (during the time
the pulse of light travels between the two
mirrors), Δθ, using the properties of an
arc as follows:
From thin lens theory, we know that an
object of height ΔS in the focal plane of
L2 will be focused in the plane of point s
(s is the image formed after the returning
beam does through the beam splitter).
Therefore, the following equation holds:
From EQ1 and EQ2,
Also,
From EQ3 and EQ4, it follows that
b
Rewriting EQ5 yields an equation to
calculate the speed of light:
The following is the calculated speed of
light in air:
c = (2826.185 ± 513.656) x 1011 mm/s .
or
c = (2.862185 ± 0.513656) x 108 m/s.
LITERATURE CITED
Lee, Bruce 1999. The Foucault Method. The
PASCO scientific 012-07135A Speed of Light
Apparatus manual, Dave Griffith. Roseville,
California: PASCO scientific, 1999.
Lee, Bruce 1999. Measuring the Velocity of
Light: History. The PASCO scientific 01207135A Speed of Light Apparatus manual, Dave
Griffith.
Roseville,
California:
PASCO
scientific, 1999.