# Measuring the speed of light

This project must be done by individuals.

We know that the speed of light is very fast -- so fast, it's difficult to measure. Let's think about how one might measure the speed of light. What sort of precision is possible with simple tools?

#### Part I: Galileo

Galileo tried to measure c, the speed of light, way back in the 1600s. His idea was similar to the method he used to measure the speed of sound:

• at night, send an assistant to stand a measured distance D (about one kilometer) away, holding a lantern with a shutter
• event 1: Galileo notes the time, then uncovers his own lamp
• when the assistant sees the flash of Galileo's lantern, he opens his shutter
• event 2: when Galileo sees the flash of the assistant's lantern, he notes the time again

Galileo can then use the events 1 and 2, and the distance D, to compute the speed of light.

Your job is to make reasonable estimates of the uncertainties in Galileo's measurements, and use them to estimate the uncertainty in Galileo's computed value of c.

1. how would Galileo measure the distance D?
2. Galileo's measured value of D was (very roughly) 1000 m. What is a reasonable guess for the uncertainty in D?
3. how would Galileo measure the time of events 1 and 2?
4. what is a reasonable guess for the uncertainty in each of these measurements of time?
5. Galileo's measured time difference (t2 - t1) was (very very roughly) 0.5 seconds
6. what was Galileo's computed value for c, the speed of light?
7. use the equation

total uncertainty in time  =   (uncert in t1) + (uncert in t2)

to compute the total uncertainty in time
8. use the equation

total uncertainty in c       uncert in time       uncert in distance
----------------------  =   ---------------- +   ------------------
Galileo's value of c            time                distance

to compute the uncertainty in Galileo's estimate of the speed of light

To be fair to Galileo, he knew very well that his measurement was uncertain. He concluded that the best he could do was to state that the speed of light was at least ten times faster than the speed of sound. That's certainly correct. Good job, Mr. G.!

#### Part II: You

We live hundreds of years after Galileo, of course, so we have much better measuring tools. Well, our special laboratories do, but what about ordinary people, like you? Imagine that you and a friend decide to measure the speed of light, using the same method as Galileo.

Instead of lanterns, though, you use flashlights, or some similar cheap and simple light source. You can't afford to fly to exotic locations, and have a total budget of just \$50. In addition, you have only 3 days to perform the experiment, so you'll have to make do with nearby locations and equipment you can purchase easily and quickly (or which you already own).

1. How far away can you and your friend stand and still see each other? Estimate a realistic distance D, and tell me where you would do this experiment.
2. How would you measure D?
3. What is a reasonable estimate for the uncertainty in D?
4. What sort of clock will you use to measure the times t1 and t2?
5. How will you start and stop the clock?
6. Estimate the uncertainty in each measurement of t1 and t2. You may need to find reasonable values for human reaction times, or other relevant effects.
7. Using the known speed of light, and reasonable estimates for all relevant experimental effects, roughly what time difference will you measure?
8. Estimate the uncertainty in your time measurements, using the same equation shown above for Galileo's experiment.
9. Estimate the uncertainty in your value for the speed of light, using the same equation shown above for Galileo's experiment.

How much more precise would your value be than Galileo's?