Measuring the Speed of Light

Being asked to measure the speed of light with such a small number of materials can at first seem daunting, but luckily only a simple circuit is required to achieve the task.  At the outset, we know that when a signal is sent down a line, if that line has no break in it, the pulse is sent back to it's source, much like a reflected wave.  Since we are using a 1000 meter co-axial cable it takes some time for the signal to travel.  All we need to do is find out exactly how much time that actually takes.  The circuit below is what we used to achieve this process:

The RC circuit at the front-end of the coaxial cable creates voltage pulses of roughly 100 ns.    The pulses are sent down the inner conductor of the cable where they appeared on the oscilloscope through channel one.  To get the best oscilloscope reading, we set the scope to trigger externally using a splitter at channel one.  The pulses then travel down the rest of the coaxial cable and reflect off the open end.  After traveling back the full length of the cable (for a total trip of 2000 feet), the scope detects the reflected  pulse through channel 1.

Click for a sample scope reading of  this phenomenon

We know that the reflected pulse travels 1000 ft or 608 m after reflecting off the open end of the coaxial cable. We also know, from the oscilloscope reading, that it took    3.16 µs for the pulse to travel this distance.  Therefore, we calculate the pulse speed to be 1.92 x 10⁸ m/s.  

Obviously, the pulse is not traveling at the speed of light. This decrease in speed can be attributed to the dialectric material inside the cable. The traveling pulse creates magnetic fields which cause positive and negative charges to cluster in the dialectric. These two poles rapidly oscillate inside the dialectric, thus retarding the motion of the pulse.         

From our Electromagnetism text, we know the relationship between the velocity of the pulse and the speed of light. 

We also know that e _r=2.26, m _r=1 for the polyethelyne dialectric. Therefore, we can experimentally measure the speed of light to be 2.88 x 10⁸ m/s. Compared to the known value of c, this equates to a percent error of 4%. 

Introduction | Cable Info | Lab Procedure and Results | Conclusions