Speed of Light: Modulated Laser

Ken Cheney

February 25, 2006

Abstract

The speed of light is measured by 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 calculate the speed of light.

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!

Hints

Distance: The time difference isjust barely measurable with out 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 into 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 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.

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 independent as possible, find the mean and standard deviation of the mean, and compare this with your difference from the defined value of c.

Most important: CONCLUDE SOMETHING!!!