Pre-Lab Assignment:
Speed of Light in an Optical Fiber

This assignment should take approximately 30–45 minutes to complete. You will do this work independently. When you arrive at lab, you will compare your responses with your lab partners and record the outcome of that discussion in your shared lab notebook before beginning the experiment.

Section 1: Context — The Speed of Light and the World It Built

The speed of light is one of the most fundamental constants in physics — and one of the hardest won. It took humanity centuries of ingenious experimentation to pin it down, and the story of how we got there is one of the great narratives in science.

Galileo (1638) was among the first to try. He and an assistant stood on hilltops miles apart, uncovering lanterns and trying to measure the time for light to travel between them. The experiment failed — not because Galileo was careless, but because light is simply too fast for human reaction time to capture over such short distances. He concluded, incorrectly, that light travels instantaneously. The failure was instructive: it told future scientists they would need much larger distances or much faster clocks.

Fizeau (1849) succeeded where Galileo could not. Using a rotating cogwheel with 720 teeth and a mirror 5.39 miles away, he measured the speed of light as 194,000 miles per second — not perfect, but remarkably close given the tools available. The key insight was using the cogwheel as a mechanical shutter to create precisely timed light pulses.

Michelson (1926) refined the measurement further, replacing the cogwheel with an eight-sided rotating mirror and extending the measurement distance to 44 miles. His result — 299,796 km/s — stood as the most precise measurement for decades.

Today the speed of light in a vacuum is defined exactly as 299,792,458 m/s. We no longer measure it — we define it, and use it to define the meter.

From measurement to application: The same physics that drove centuries of curiosity about the speed of light now underpins the infrastructure of the modern world. Optical fibers — hair-thin strands of glass or plastic — carry light pulses that encode the data traffic of the internet, phone calls, and financial transactions across continents and ocean floors. The speed of light in fiber (slower than in vacuum because light travels slower through a medium) determines how quickly information can travel and how engineers design networks to account for signal delay.

In today’s experiment you will measure the speed of light in a plastic optical fiber using a technique that would have been unimaginable to Galileo — two pulses of light, a fiber optic cable, and an oscilloscope that can resolve time differences of billionths of a second.

As you read, think about which of these stories you might want to tell: the centuries-long quest to measure something no one could see or touch, the physics of light slowing down when it enters matter, the invisible fiber optic network that connects the modern world, or something else related to this experiment. You will have the opportunity to communicate this experiment to a non-scientist audience — your choice of angle will shape how you tell that story.

Answer the following questions:

1. Fizeau’s cogwheel and your oscilloscope both solve the same fundamental problem. What is that problem, and how does each instrument solve it?
2. Light travels at 3.00 × 10⁸ m/s in a vacuum but slows down in a medium. Why does this matter for the design of fiber optic telecommunications networks? What would an engineer need to know about the speed of light in fiber to design a long-distance network?
3. Of the storytelling angles described above, which appeals to you most and why? You do not need to commit to this yet, but start thinking about what story you want to tell.

Section 2: Instrument Preview — The Oscilloscope and Triggering

In the oscilloscope lab you learned how to display a signal using the vertical scale and timebase. Today you will use the oscilloscope differently — instead of displaying one signal and measuring its properties, you will display two signals simultaneously and measure the time difference between them.

To do this reliably, you need the oscilloscope display to be stable — the same waveform appearing in the same position on the screen each time. If the display is not stable, the two pulses will appear to drift or jump, making it impossible to measure the time between them. This is where triggering becomes essential.

What triggering does: The oscilloscope does not draw continuously — it takes a snapshot of the signal and draws it on the screen, then waits and takes another snapshot. Without triggering, each snapshot starts at a random moment in time, so the waveform appears in a different position each time. The display looks like it is jumping or scrolling. Triggering tells the oscilloscope exactly when to start each snapshot — for example, “start drawing when the voltage on Channel 1 rises through 1 volt.” Because each snapshot starts at the same moment in the signal, the waveform appears stable and stationary on the screen.

Why Channel 1 is the trigger source: In this experiment, Channel 1 carries the reference pulse — a direct tap from the circuit that generates the light pulses. Channel 2 carries the delayed pulse — the signal that has traveled through 20 meters of fiber. By triggering on Channel 1, you ensure that every snapshot starts at the same point in the reference pulse. The delayed pulse on Channel 2 then appears shifted to the right by exactly the travel time through the fiber.

Why this matters: If you triggered on Channel 2 instead, or used no trigger, the two pulses would not appear in a stable, consistent relationship on screen — and you could not measure the time between them reliably.

Now answer the following questions:

1. In your own words, explain what triggering does and why it is necessary for this experiment. Do not copy the explanation above — use your own words and your own analogy if that helps.
2. The oscilloscope has two trigger modes: Normal and Auto.
   • In Normal mode, the oscilloscope waits indefinitely for the trigger condition to be met before drawing a snapshot.
   • In Auto mode, the oscilloscope has a finite patience — if the trigger condition is not met within a certain time, it draws anyway.
   • Which mode do you think is more appropriate for this experiment, where the signal is a continuous stream of pulses at over 500,000 per second? Why?
3. The trigger level is the voltage threshold that starts the snapshot. If the trigger level is set too high — above the peak of the reference pulse — what will happen? What will you see on screen?
4. The trigger slope determines whether the oscilloscope triggers on a rising or falling voltage. For a pulse that rises sharply and then falls, why might triggering on the rising edge give a more consistent result than triggering on the falling edge?
5. What is the minimum timebase setting available on the TBS 1102B-EDU? The time delay you will be measuring is expected to be around 100 nanoseconds — is the oscilloscope capable of resolving this time difference? Show your work. Note: if you kept good notes from the oscilloscope lab, you should already have this information and will not need to look it up again.

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Section 3: Physics Recall and Protocol Design

Part A: The physics

In Physics 2 you learned about the index of refraction — the ratio that describes how much light slows down when it enters a medium. Before you can design a measurement protocol, you need to connect that concept to what you will actually measure today.

1. Write the definition of the index of refraction n as an equation. Define every symbol you use.
2. The plastic optical fiber in this experiment has an index of refraction of n = 1.49. Using your equation from question 1, calculate the speed of light in the fiber. Show your work.
3. You will measure the time t it takes for a light pulse to travel through a fiber of known length l. Starting from the definition of index of refraction, derive an equation that lets you calculate the speed of light in a vacuum c from the quantities n, l, and t. Show every step — do not look this up. You will compare your derivation with your partners when you arrive at lab.
4. What are the units of your answer? Does your equation give a result in the correct units for speed? Check this explicitly.

Part B: Protocol design

5. Write a rough step-by-step protocol for how you will measure the time delay between the reference pulse and the delayed pulse. Your protocol should address:
   • How you will set up the oscilloscope (channels, timebase, trigger source)
   • What you will connect to each channel
   • How you will identify the reference pulse and the delayed pulse on screen
   • How you will measure the time difference between them

Your protocol should be clear enough that your lab partner could follow your logic. You do not need to know every button — focus on the sequence of steps and the reasoning behind each one.

Section 4: Predictions

1. Sketch what you expect the oscilloscope display to look like when both the reference pulse (Channel 1) and the delayed pulse (Channel 2) are displayed simultaneously. Label each pulse, indicate which is delayed and by how much, and mark the time axis with approximate values based on your calculations.
2. Using your equation from Section 3 and the fiber length of 20 meters, calculate the expected time delay between the reference pulse and the delayed pulse. The index of refraction of the fiber is n = 1.49. Show your work and report your answer with appropriate units.
3. The manufacturer states the expected delay is between 90 and 110 nanoseconds. Is your calculated value consistent with this range? What does this range tell you about the precision of the measurement?
4. When you arrive at lab and make your measurement, you will compare it to your prediction. If your measured delay differs significantly from your prediction, what are the most likely sources of that discrepancy — in the measurement, in the apparatus, or in your calculation?

When you arrive at lab, compare your responses with your lab partners. Pay particular attention to your equation derivations in Section 3 — if your equations differ, work through the physics together and agree on the correct form before beginning the experiment. Record the outcome of your comparison in your shared lab notebook. Then begin the experiment.

Learning Objective Alignment

Use this table when building your grade proposal to identify which parts of this assignment provide evidence for each learning objective.

Section / Question	Learning Objectives
Section 1, Questions 1–2	1, 2
Section 1, Question 3	7
Section 2, Questions 1–4	2, 4
Section 2, Question 5	2, 5
Section 3, Part A, Questions 1–4	1, 5
Section 3, Part B, Question 5	3
Section 4, Questions 1-2	3, 6
Section 4, Questions 3-4	3, 6