Speed of Light: Modulated Laser
Ken Cheney
March 16, 2006
Abstract
The speed of light is determined by amplitude modulating a laser at a high
frequency, then splitting the beam into parts that travel different distances,
the phase of the returning beams are compared to find the time difference
and the speed of light is calculated.
Disclaimer
c 2.99792458  108 m/s is properly regarded as the defined ratio between
meters and seconds. Since this is defined we are actually not measuring the
speed of light (any more than we would measure the conversion factors
between feet and inches or seconds and minutes) but we are measuring a
ratio. However generally those not doing relativity ignore this fine point and
talk of measuring the speed of light!
GEOMETRY
Photocells
Laser beams
Lenses
Mirror
Laser
Beam Splitter
B
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a
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Hints
Distance: The time difference is just barely measurable with our
equipment. Make the path difference as large as possible. Use some
ingenuity!!
It is possible (barely) to send the beam across the room four times using
three mirrors. If you can manage this you will double your accuracy at the
cost of two mirrors. We last doubled our accuracy at the cost of $3,000
oscilloscopes! 
Photocells: The photocells are quite fussy. Get a signal on the oscilloscope
first with a small path difference so it is relatively easy to align the beams
with the photocells.
The beams need to be well focused (that’s why you use lenses just before the
photocells).
The beams need to be directed almost straight into the photocells.
Experiment with the geometry to achieve this.
Magnetic mounts: Once you do have everything aligned you don’t want it
to move. Use the metal base plate and magnetic lens holders so everything
will stay put. Perhaps tape down anything non magnetic!
Phase (time) difference: This can be measured two ways:
 The digital oscilloscopes can automatically measure the phase
difference!
 Also measure the phase difference “by hand”.
Be sure to center the oscilloscope traces vertically (ground and
center) and measure the time between the zero crossings, not the time
between maximums.
Adjust the time base to make the difference between the zero
crossings fill as much of the screen as possible.
If possible use the cursers on the oscilloscope to measure the time
difference.
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CONNECTIONS
CONNECTIO
NNSNS
Oscilloscope
Ch 1 Ch 2 Trigger
Synchronize
Synchronize
Modulate Laser
Channel 1
Channel 2
Two
wires
each
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Do your results mean anything???? Two checks:
 Estimate your measurement errors, use propagation of errors, and
compare the estimated error in the speed of light with your actual
error.
 Take several measurements, as independently as possible, find the
mean and standard deviation of the mean, and compare this with your
difference from the defined value of c.
 Find the class average and standard deviation of the mean, comment!
 Recall that you need the standard deviation of the mean, not the
standard deviation that Excel gives you!
Standard Deviation of the Mean   m 
Most important: CONCLUDE SOMETHING!!!
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