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Introduction

Although it may not appear to be so, the speed of light is not infinitely fast but a measurable quantity. It is an amazing fact that under suitable conditions every one in the Universe would measure the same value for the speed of light c. That this is so has profound implications and you will see some of these implications when you when you learn about special relativity in lecture. For now, we will perform a simple measurement and measure the speed of light in an electrical cable.

When we speak of the ”speed of light”, it is important to understand that what we mean by light encompasses much more than what call “light” when we look at, say, a light bulb. Light is a so-called electromagnetic wave that means, first of all, that it is wave-like in nature and secondly, that it is composed of an oscillating electric field and a magnetic field wave. It turns out that these two waves oscillate at right angles to one another as they travel through space. It is also the case that both waves are synchronized in the sense that the crests of the electric field wave occur at the same time as the crests of the magnetic filed wave and similarly for the troughs. The distance between successive crests of either the electric field wave or the magnetic field wave is the wavelength of the light wave. The speed of light is simply the amount of time it takes for the crests of the light wave to travel a distance equal to a wavelength.

We will measure the speed of light using a very low frequency radio wave. We will launch this wave down two cables of a particular geometry. The cables are identical except for their length. The radio wave will travel down the length of the shorter cable in a shorter period of time than it takes to traverse the longer cable. By measuring the transit time difference for the two cables and knowing the cable length difference, we will be able to measure allow the speed of light in a cable. It will turn out for reasons that are not important now, that this speed is somewhat smaller than the speed of light in air (or vacuum).

Procedure

  1. Connect one end of a cable to the waveform generator in channel 1. Connect the other end of the same cable to the channel 1 input of the oscilloscope.

  2. Connect one end of another cable to the waveform generator in channel 2. Connect the other end of the same cable to channel 2 of the oscilloscope.

  3. Adjust the frequency of the waveform generator until you see a 10 kHz square wave for both channel 1 and channel 2. Adjust the time sweep until you can see the width of the "turn-on" (the time it takes for the voltage to go from the minimum to maximum value).

  4. Are both waveforms aligned? if not fix the offset by following the instructions here on page 57: https://web.archive.org/web/20241002144852/https://beyondmeasure.rigoltech.com/acton/attachment/1579/f-050a/1/-/-/-/-/MSO1000Z%26DS1000Z_UserGuide.pdf

How long does it take for the voltage to reach its maximum value for channel 1?

- Answer here

How long does it take for the voltage to reach its maximum value for channel 2?

- Answer here

What is the time difference between channel 1 and channel 2 (try to measure this at the same point in the two waveforms)? Include an uncertainty on this value. You can take the uncertainty as half the turn-on time (this is a rough approximation; if we had more time, we would try to decrease the turn-on time and not take measurements by eye).

- Answer here
  1. Now, replace one cable (channel 2) with a long cable and measure the time difference between channel 1 and 2 (including an uncertainty). 
- Answer here

Assuming \Delta t = c(\Delta L), where \Delta L is the difference in length between the two cables, what is the speed of light in the cable (with uncertainty)?

  1. You will need to measure the length of the long cables too! Find out the best way to measure the length
- Answer here
  1. Now, add another long cable to channel 2 (using a connecter). Repeat the process above to get the speed of light.

What measurement do you get for the speed of light in the cable (with uncertainty)?

- Answer here
  1. Now, add another long cable to channel 2. Repeat the process above to get the speed of light.

What measurement do you get for the speed of light in the cable (with uncertainty)?

- Answer here

Are your measurements consistent with each other (within uncertainties)? Which measurement gives the most precise value?

- Answer here

Are the uncertainties on the 3 measurements correlated, or do you think you might be systematically over- or under-estimating the speed? Why or why not?

- Answer here

Make a plot of the time difference as read from the ocsilloscope and the various lengths measured. Attach the plot here