Measuring the speed of light

Introduction

With modern inexpensive apparatus this previously almost impossible experiment can now be carried out to a good degree of accuracy in the school laboratory.

The experiment described here measures the speed of light through a polymer fibre optic cable using the timing capabilities of a fast PC-based oscilloscope

Equipment required

• A PC with PicoScope installed
• A PicoScope PC based oscilloscope with 50 MHz or more bandwidth
• A fibre optic transmitter and receiver unit with a method of high frequency square modulation in the region of 250 kHz to 1 MHz.
• Suitable leads and connectors.
• Ready-made fibre optics apparatus is manufactured by Lascells Ltd and is available as product 280-216 from: Technology Supplies Ltd. Phoenix House, Tern Hill, Market Drayton, Shropshire UK. Tel.  +44 1630 637300

This apparatus contains the transmitter and receiver with internal modulator together with monitoring sockets for the oscilloscope. Also included are a 5 m and 20 m fibre optic cable.

Background theory

A solid state, square wave oscillator running at 1 MHz will produce a signal with a 1 µs period and a square pulse lasting 0.5 µs. If this signal is used to modulate a light beam which passes along a fiber optic cable we get a pulse of light lasting 0.5 µs. A phototransistor can detect the pulse at the other end of the cable and convert it back into a pulse of electricity. The two electrical pulses (the original and the received one) can then be displayed on an oscilloscope screen. Since the light takes a finite amount of time to reach the receiver the second signal will be delayed in time (dt) and the received pulse will be shifted along the timebase axis. If we measure this shift it will tell us how long the light pulse took to travel the length of the fiber optic cable and hence the speed of the light can be calculated if the cable length is known.

Practical considerations

1. Since light travels at about 300 million metres per second in air, so if our fiber optic cable is 30 m long we would be looking for a time delay of 0.1 µs. A 50 MHz (or better) oscilloscope is required.
2. When we monitor the electrical pulses we are measuring the delay between transmitted and received electrical signals not the light pulses. If there is any time required for the conversion of light to electricity or vice versa then this would introduce errors into the calculation.
3. At high frequencies “square waves” become rounded due to stray capacitances and non-linear responses of the converters. The precise edge of the pulses is often lost.

Experiment setup

Arrange the fiber optic system to transmit a high frequency modulated light beam along the cable which should be about 5 m or so in length. Couple the receiver unit to the cable. Monitor the transmitted pulse at Channel A on the Pico ADC and the received pulse at Channel B.

The photograph shows the Lascells equipment connected as described and the results given later were taken from this apparatus.

The PC oscilloscope settings are typically:

• Timebase 200 ns/div
• Channel A and B input +5 V DC
• Trigger single shot, rising to capture a pulse when GO is selected. Use a sensitivity of 400 mV or so at various pre-trigger values.

Carrying out the experiment

Switch on both the transmitter and receiver and select GO on the oscilloscope screen. Adjust the amount of pre-trigger and reselect GO until a trace is obtained which shows the “square” transmitted pulse and the received, much more rounded, pulse shifted to the right. When you are familiar with the pulse shapes, reset the timebase to as short a time possible to display the two leading edges of the pulses or the two trailing edges. Save and print out the screen image.

Switch off both units and replace the 5 m cable with a 2 0m cable. Switch on again and repeat the experiment making timebase adjustments as required. Save and print again. You should find that the second print-out, with the longer cable, has a larger delay between the two pulses. (PicoScope rulers or automated measurements can be used here to help with the time measurement).

Calculations and theory

If there are time delays in any part of the electronics then these delays should be the same for both experiments with the 5 m and 20 m cables. The only difference between the two experiments is that the light had to travel a further 15 m in the second case. If we measure dt from each print-out then subtracting one from the other should give the amount of time taken to travel the extra 15 m.

From the print-outs given using leading edges we get:
0.55 µs (-0.02) for the 5 m dt
0.64 µs (-0.01) for the 20 m dt
i.e. 0.57 and 0.65

The difference between these two values is 0.08 µs which is the time taken for the light to travel 15 m.

The speed of the light is distance/time which is 15/0.08 x 10^–6 which gives 1.9 x 10⁸ m·s^–1

Questions and discussion of results

How does this result compare with the speed of light in air?

Investigate the definition of the term refractive index and see whether you can calculate an approximate value for the expected speed of light along the fiber optic cable. (The refractive index of the polymer used is about 1.6)

Further study

How do the results compare when trailing edges are used in the calculation?

No mention has been made of errors in the measurements. Estimate the errors in all measurements and establish the estimated accuracy of the final result.