Home experiments to derive the speed of light?

Question

Are there any experiments I can do to derive the speed of light with only common household tools?

Answer 1

I don't know if it qualify as home experiment, but you can use the internet to get access to thousands of kilometres of optical fibres for free. It allows you to measure a lower bound for the speed of light in the fibres, which is $c/n$, where $n$ is the refractive index of glass, typically around 1.5. This corresponds to $2\times 10^8 \text{m/s}$. Using ping, you measure a round trip time, that is it should correspond to 100 km/ms of round trip.

From Paris, I ping the website of Columbia, in New-York, I have

fred@sanduleak2:~$ ping www.columbia.edu
PING www.columbia.akadns.net (128.59.48.24) 56(84) bytes of data.
64 bytes from www-csm.cc.columbia.edu (128.59.48.24): icmp_req=1 ttl=113 time=125 ms
64 bytes from www-csm.cc.columbia.edu (128.59.48.24): icmp_req=2 ttl=113 time=116 ms
....
64 bytes from www-csm.cc.columbia.edu (128.59.48.24): icmp_req=16 ttl=113 time=112 ms
^C
--- www.columbia.akadns.net ping statistics ---
17 packets transmitted, 16 received, 5% packet loss, time 16023ms
rtt min/avg/max/mdev = 108.585/118.151/132.156/7.728 ms

The minimum round trip time is 108 ms, which would correspond to 10,800 km instead of 5839 km. Off by a factor of 2, but the correct order of magnitude, due to delays in switches etc., which is why we said this is a lower bound.

If one looks more precisely the trajectory of my packets to New York with tracepath

fred@sanduleak2:~$ tracepath www.columbia.edu

 1:  sanduleak2                                            0.266ms pmtu 1500
 ....  
 3:  pioneer.ens-cachan.fr                                 1.072ms 
 ....
 6:  vl172-orsay-rtr-021.noc.renater.fr                   28.747ms asymm  9 
 7:  te0-1-0-5-paris1-rtr-001.noc.renater.fr              20.931ms 
 8:  renater.rt1.par.fr.geant2.net                        30.307ms asymm  9 
 9:  so-3-0-0.rt1.lon.uk.geant2.net                       33.780ms asymm 10 
10:  so-2-0-0.rt1.ams.nl.geant2.net                       36.570ms asymm 11 
11:  xe-2-3-0.102.rtr.newy32aoa.net.internet2.edu        127.394ms asymm 12  
12:  nyc-7600-internet2-newy.nysernet.net                128.238ms 
13:  columbia.nyc-7600.nysernet.net                      135.948ms 
14:  ....

We see that the packets travel around (Paris, London, Amsterdam) and cross the Atlantic between Amsterdam (10) and New-York (11) in 127-37=90 ms (roundtrip). This still gives us a 9000 km distance, way too long. I don't know if it is due to the cable trajectory, electronic delays, to small sampling by tracepath or an error on my calculation.

Related to this ping delay, you have the funny 500 miles bug.

Another in-the-lab experiment using cheap material and computers is in the arXiv paper speed of light measurement using ping. However, their measurement is indirect (they measure the propagation inside CAT5 cables), but it should also be doable with optical fibres.

Edited to add: My idea of using tracepath probably comes from Measuring the Earth with Traceroute. In this paper they are more lucky than I was (only 20% slower, instead of 100% !)

Answer 2

There is a trick I have heard about before but never tried. The basic idea is to put a mars bar in a microwave oven for a short amount of time. First you remove the turntable, so the chocolate bar stays stationary. Then you turn the microwave on just long enough for the chocolate to start to melt. It should melt at the nodes of the standing field. You simply measure the distance between the nodes, and multiply by the frequency of the microwave oven to obtain the speed of light. There is a YouTube demonstration (by a kid) here.

Answer 3

You could find a capacitor and read of its capacitance, alternately build one and measure it, and measure its dimensions. Now you can get a good estimate on the permitivity of vacuum, epsilon.

There are possibly other intricate ways to measure this number.

The speed of light is then given by a relation involving another number, the vacuum permeability, µ , which needs no measuring as it is defined.

This relation can be derived from Maxwell's equations.

$c=\frac{1}{\sqrt{\varepsilonµ}}$

Answer 4

You might also want to try the rotating mirror method, of Léon Foucault. It is detailed here and here. The only difficult part is the rotating mirror, but it could probably be done with a drill.

Answer 5

I can't think of a way to do it with "common household tools" but if you have an oscilloscope, a laser diode, a couple of photo-sensors, a beam splitter, you can do it. All of these things are readily available from science supply/hobby stores online, but not usually in most homes.

Set up the laser diode to hit the beam splitter and be split into two beams. Set up the two beams so that they hit two photo-sensors, but make one of the photo-sensors exactly twice the distance from the beam splitter as the other. This will create two separate paths for the light, one twice as long as the other. Run the output of the photo-diodes into two channels of the oscilloscope. Switch on the laser diode, and you should see two pulses on the o-scope, one from each of the two laser diodes. The difference between them is the time it takes the light beam to travel the distance of the difference in the two paths.

The reason to do it this way is accuracy - if you only had one beam, and your photo-diode took, say, 1 microsecond longer to turn on than what was in the documentation, or your laser were slow to turn on, then you would get very inaccurate results. But with two beams, those errors cancel each other out, and so all you're left with is the time of the light.

Answer 6

With a clock and a telescope you could repeat Rømer's determination of the speed of light.

Answer 7

I think the simplest would be to use an RF oscillator, a receiver to determine its frequency and Lecher wires (i.e. a pair of parallel wires) where the nodes of the standing wave are determined using an RF voltmeter. See http://en.wikipedia.org/wiki/Lecher_lines .

This was one of the experiments in an electronics kit which I had in my youth. The length of the Lecher line was about 5m and the frequency of the oscillator was about 100Mhz using just one transistor in a common base circuit.

As a variation it is also possible to change the frequency and measure how much the nodes have moved.

Answer 8

Those laser tape-measures operate in an interesting way, that relies on the speed of light to determine distance. So conversely, if you have a known distance, then with the same equipment you should be able to estimate c.

What the tape measures do is modulate the intensity of the outgoing laser according to the intensity of the reflected light. It's basically an oscillator whose frequency depends on the optical propagation delay. The commercial products use the resulting frequency to determine a distance to display.

If you can get at the oscillator output, and set up to measure a known distance, you should be able to estimate c as the frequency in Hz times the round-trip distance in meters.

Answer 9

Perhaps a Fizeau inteferometer:

http://en.wikipedia.org/wiki/Fizeau_interferometer

Most of that should be in range of a keen amateur but I'm not sure what you use as a beam splitter without just buying one though.

Answer 10

What about a doppler shift method? A doppler speed radar or lidar gun might have all the necessary components, for its logic to be reversed. Here's one for instance, ready for disassembly. http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=300374815766&rvr_id=169891150704&crlp=1_263602_304642&UA=M*S%3F&GUID=0537e92612c0a06456359f45ffd1174f&itemid=300374815766&ff4=263602_304642#ht_2332wt_979

Answer 11

Didn't the amateur radio guys (Hams) once launch a ballon like reflecting satellite? Is it still in orbit? Even at a few hundred kms, the delay would be in the ms. Maybe the ISS is partly reflective.

Answer 12

Has anybody a pointer to the Kinect patent?? the device of the XBox measures distance using reflection of infrared light, so for sure it depends on a finite lightspeed to work.