In the introductory optics class I took in college, one day the professor said "Let's measure the speed of light!" and pulled out a ruler.
The class laughed.
He then set the ruler on the table. The ruler was one of those where the tick marks are raised, not merely printed on. The ruler was metal and reflected light well.
He then shone a laser at the ruler, so that the light bounced off and hit the blackboard. The lines on the ruler acted as a diffraction grating and a diffraction pattern was visible on the blackboard.
He marked the peaks with chalk, then went back to the ruler and used the ruler to measure the distance from where it had been to the blackboard. He then used the ruler to measure the distance between the marks he had made for the diffraction peaks.
From those distances, and the separation between the lines on the ruler, and the frequency of the laser he was using, it was a simple calculation to get the speed of light.
Or course, in a sense this is cheating, as you have to know the frequency of the light source, so he had to use that as a magic constant in his calculation.
Yeah, there are many ways of doing it with wave interference phenomena, but that requires you to know the wavelength. Doing it entirely based on speed of propagation is much more tricky, because it comes down to measuring small time differences.
I've done the direct propagation measurement. Took about 20 hours (design, build, runs, analysis, report) in a four-person team, to obtain a value of .97 c. Laser, beam restrictor, beamsplitter, rotating mirror, and a 40 meter hallway with a mirror at the end. As the photons are traveling from the rotating mirror down the hall and back the mirror rotates slightly. Measuring the angular displacement of the beam with respect to the rotation speed gives you c. We used a low-res linear CCD array and oscilliscope, but you could probably do it at home... maybe with a dSLR sensor with suitably high response. You'd need a measurement of the CCD pixel density, but that wouldn't be too hard to find online. Then just handling the time sync issues.
You can actually do it with a pulsed laser (hook up a laser diode to a function generator), a stationary mirror, and a photovoltaic cell. Hook up the function generator and the photovoltaic cell to an oscilloscope, mount the mirror a suitably long distance away, and you can actually see the timing difference between laser pulse and detection at the photovoltaic cell. Vary the distance and you can subtract out the delays in detection and such.
I did this as an experiment in a junior physics lab last semester. It felt like cheating. All you needed was twenty feet of space.
We just measured the distance with a microscope, a 4 meter setup with a mirror to double the angle. It took about 2 hours and the only electronics were the rotating mirror. Our error was within 1%.
You can do the same thing with a 1000RPM mirror and about 50 feet with a caliper and get with 3% I suppose, as long as you are lined up good with the rotating mirror.
Starting with something like a GNU Radio board (http://gnuradio.org/) and a commercial antenna, you could put together a basic CW or ICW radar in a weekend without too much trouble. A little bit of care is required to not break any local laws or piss people off.
Simply, you would send out a radio signal, bounce it off a target and measure the time between when you sent the signal and when it was received. That delay is inversely proportional to the speed of light. Take a bunch of samples to integrate away short term clock inaccuracies (but don't integrate too long, because some types of clock noise will make your answer worse and not better) and you'll get a pretty good estimate of c.
Another GNU Radio based experiment would be to attempt to pick up multipath reflections of TV or radio broadcasts off large geographical features or buildings. Basically, you would capture two signals - a direct version of the broadcast and a delayed version. The errors would be large, but you would be able to get fairly close to a reasonable estimate of c (in air).
Before doing either of these experiments, mocking them up with a speaker and microphone or two ultrasound transceivers is a good idea and will save you a bunch of time. 40kHz is easier to work with than 2.4Ghz for sure.
I've done it with a microwave and some marshmallows (I taught this lab to some first year college students long ago when I spent a term as a college physics instructor).
It's similar to tzs' method below, in that you have to know the frequency of the microwave's radiation, so it's not entirely satisfactory.
But, given that, it's a really nice demonstration of standing waves with a cool result to calculate.
The method is to cut a bunch of marshmallows in to small chunks (or just buy mini-marshmallows), spread them on a tray in a microwave and turn it on. After a while, you'll see that the marshmallows are bubbling up in some spots, and not cooking very much at all in others. Measuring the distance between either the lows or the highs gives you the wavelength of the standing wave.
Given that wavelength and the frequency of the microwave radiation, you can calculate the speed of light.
I'm going to punt on it and leave the calculation up to the reader, mostly because I haven't thought about this in 15 years or so and I'm sure I'd miss a factor of 2 somewhere:).
Also, this will not work unless you can get a microwave where you can turn the turntable (the rotating plate thingy) off. Most microwaves didn't have a turntable in the early 90s, but this isn't true any more.
Interesting answers there. I remember doing the capacitor experiment in a first-year physics course in university. Though we were measuring mu sub 0, the permeability of free space. The formula is just reversed though.
It should be an interesting and cheap way to measure the speed of light.
Not really, no. The speed of light in air is very nearly identical to the speed of light in a vacuum. Wikipedia gives the refractive index of air as 1.0003, which is the ratio between the speed of light in a vacuum and the speed of light in air.
The use of air as a medium rather than a vacuum is unlikely to be a significant source of error in an amateur measurement of c.
The class laughed.
He then set the ruler on the table. The ruler was one of those where the tick marks are raised, not merely printed on. The ruler was metal and reflected light well.
He then shone a laser at the ruler, so that the light bounced off and hit the blackboard. The lines on the ruler acted as a diffraction grating and a diffraction pattern was visible on the blackboard.
He marked the peaks with chalk, then went back to the ruler and used the ruler to measure the distance from where it had been to the blackboard. He then used the ruler to measure the distance between the marks he had made for the diffraction peaks.
From those distances, and the separation between the lines on the ruler, and the frequency of the laser he was using, it was a simple calculation to get the speed of light.
Or course, in a sense this is cheating, as you have to know the frequency of the light source, so he had to use that as a magic constant in his calculation.