Speed of Light in an Optical Fiber

Before you begin: retrieve your pre-lab from D2L and compare your responses with your lab partners. Pay particular attention to your equation derivations — if your equations differ, work through the physics together and agree on the correct form before touching the apparatus. Record the outcome of your comparison in your shared lab notebook. Then begin the experiment.

Your Task Today

Centuries of scientific curiosity culminated in a precise, agreed-upon value for the speed of light. Today you will measure it yourself — not across miles of open air with mirrors and cogwheels, but through 20 meters of plastic fiber with an oscilloscope that resolves time differences of billionths of a second. The physics is the same. The tools are more powerful.

Your measurement will connect a number on your oscilloscope screen to one of the most fundamental constants in nature. It will also connect to something more immediate: the fiber optic cables that carry the world’s data traffic move information at exactly this speed. Understanding it is not just historical curiosity — it is the physics of the infrastructure that connects the modern world.

By the end of today’s lab session you will have:

Set up and calibrated the Speed of Light Apparatus
Measured the time delay for light to travel through 20 meters of plastic fiber
Calculated the speed of light in the fiber and in vacuum
Propagated your uncertainty through the calculation
Reflected on the story you want to tell about this experiment

Record everything in your shared lab notebook — what you do, what you observe, what surprises you, and how you reason through problems.

Section 1: Getting to Know the Apparatus

At your bench you will find the Speed of Light Apparatus, two fiber optic cables (one 15 cm, one 20 m), the oscilloscope, and two probes.

Take a moment to examine the apparatus before connecting anything. You will see:

A yellow LED on the board — this lights up when the apparatus is powered
A blue fiber optic housing labeled D3 — this is the LED that emits the light pulses into the fiber
A black fiber optic housing labeled D8 — this is the detector that receives the pulses
Two blue test points labeled Reference and Delay — these are where you connect your oscilloscope probes
Two white test points labeled GND — these are the ground connections for your probes
A knob labeled Calibration Delay — you will use this during calibration

Before powering on, look at the fiber optic ends on the 15 cm and 20 m cables. Are they clean, flat, and polished? If an end looks cloudy, chipped, or scratched it may need to be repolished — ask your instructor before proceeding.
The apparatus generates over 500,000 light pulses per second from the red LED (D3). The Reference test point taps the electrical signal that drives those pulses directly — before the light travels anywhere. The Delay test point carries the signal detected at D8 — after the light has traveled through the fiber. In your own words, explain why connecting these two signals to your oscilloscope allows you to measure the travel time of light through the fiber.

Section 2: Setting Up the Oscilloscope

You will be using the oscilloscope differently from the oscilloscope lab. Instead of displaying one signal, you will display two signals simultaneously on the same screen and measure the time between them. The oscilloscope settings below are specific to this experiment — follow them carefully before connecting to the apparatus or powering it on.

Make the following settings on the oscilloscope:

Trigger mode: Auto
Trigger source: Channel 1
Trigger slope: Positive (rising edge)
Channel 1 vertical scale: 1 V/div
Channel 2 vertical scale: 0.5 V/div
Input coupling: AC on both channels
Timebase: 50 ns/div
Vertical display mode: ALT (alternating — shows both channels)

Now connect the probes:
- Channel 1 probe tip → blue Reference test point
- Channel 1 ground lead → white GND test point directly below Reference
- Channel 2 probe tip → blue Delay test point
- Channel 2 ground lead white GND test point directly below Delay

Before powering the apparatus, move Channel 2’s input selector to the Ground position. This keeps Channel 2 oﬀ the screen temporarily so you can see Channel 1 clearly during setup.
Why do you think it is important to use the ground leads on the probes for this experiment? What might happen to the signal quality if you skipped this step?

Section 3: Calibration

Calibration is the most important step in this experiment. Its purpose is to account for any electronic delay in the apparatus itself — delay that exists even before light travels through any fiber. By calibrating with the 15 cm fiber (whose travel time is less than 1 ns and is negligible), you set the apparatus so that zero fiber distance corresponds to zero time difference on the oscilloscope. Any delay you measure with the 20 m fiber will then reflect only the travel time through that fiber.

Why this matters: Miscalibration introduces a systematic error into your measurement — your result will be consistently off in one direction. Unlike random error, you cannot average your way out of a systematic error. Getting the calibration right is essential before making any measurement.

Installing the 15 cm fiber

Turn the Calibration Delay knob to the 12 o’clock (straight up) position.
Loosen the fiber cinch nuts on D3 (LED) and D8 (detector).
Insert one end of the 15 cm fiber into D3 until it seats, then lightly tighten the cinch nut.
Insert the other end into D8 and tighten the cinch nut.
Plug in the power adapter. The yellow LED should light up. If it does not, check the power connection and alert your instructor.

Viewing the reference pulse

You should now see a pulse on Channel 1 — the reference pulse. It should be approximately 3.5 V in amplitude and 35 ns wide (measured at half its peak height). Sketch what you see and record the amplitude and approximate width in your lab notebook. Does it match your pre-lab prediction?
If you see no pulse, work through the following before changing anything:
- Is the trigger level set correctly? Could it be above the peak of the pulse?
- Is the timebase appropriate to show a pulse of this width?
- Is the apparatus powered on?

Diagnose before adjusting.

Adding Channel 2 and calibrating

Switch Channel 2’s input selector from Ground to AC coupling. A second pulse should now appear — the signal received through the 15 cm fiber. It should be approximately 1 to 1.5 V in amplitude and 75 ns wide. Record its appearance in your lab notebook.
Using the vertical positioning knobs, align the baseline (the flat part before the pulse) of both Channel 1 and Channel 2 traces with the second grid line from the bottom of the screen. Both baselines should sit on the same horizontal line.
Using the horizontal positioning knob, align the peak of the Channel 1 (Reference) pulse with the second vertical grid line from the left of the screen.
Rotate the Calibration Delay knob on the apparatus until the peak of the Channel 2 pulse coincides with the peak of the Channel 1 pulse — the two pulses should overlap as closely as possible.
Switch the timebase to 20 ns/div. At this finer scale you can see the alignment more precisely. Fine-tune the Calibration Delay knob until the two peaks overlap as well as possible. Record what you observe.
When the calibration looks good, carefully loosen the cinch nuts on D3 and D8 and remove the 15 cm fiber. Do not disturb the Calibration Delay knob or any oscilloscope settings after this point.
Why is it important not to touch the Calibration Delay knob after calibration is complete? What would happen to your measurement if you accidentally bumped it?

Section 4: Measurement

The apparatus is now calibrated. You are ready to make your measurement.

Installing the 20 m fiber

Insert one end of the 20 m fiber gently but firmly into D3 until it seats. Lightly finger-tighten the cinch nut.
Insert the other end into D8 and lightly tighten the cinch nut.

Observing the delay

Observe the oscilloscope screen. The Channel 2 pulse should now have shifted to the right of the Channel 1 pulse, and its amplitude should have decreased to approximately 50% of what it was during calibration. Sketch what you see. Does it match your pre-lab prediction?
If the Channel 2 pulse has not shifted to the right, or if you see no Channel 2 pulse, work through the following:
- Is the 20 m fiber fully seated in both D3 and D8?
- Is the Channel 2 input still set to AC coupling?
- Is the trigger still stable?

Diagnose before adjusting.

Measuring the time delay

Measure the time delay between the reference pulse and the delayed pulse. Measure from the second vertical grid line from the left (where the Channel 1 peak was anchored during calibration) to the peak of the Channel 2 pulse. Count the number of horizontal divisions and multiply by the timebase setting (20 ns/div). Record your measurement.
What is the ILE of this time measurement? The ILE is determined by how precisely you can read the position of the pulse peak on the screen. At 20 ns/div, what is the smallest time increment you can reliably read? Record your ILE and explain your reasoning.
Take three independent readings of the time delay — have each group member make the measurement independently without looking at each other’s values. Record all three values. Then compare your results with at least one other group:
- Do your three readings agree within your stated ILE?
- Does the other group’s ILE agree with yours? If your ILEs diﬀer, discuss how each group arrived at their estimate. Who has the stronger justification?
- Do your measured time delay values agree with the other group’s values within the combined uncertainties?
- If any of these comparisons reveal a disagreement, what might explain it?
- Record the outcome of this comparison in your shared lab notebook
Use your three readings to calculate a best estimate of the time delay. How do you decide which value to report as your best estimate?

Section 5: Calculating the Speed of Light

You now have a measured time delay and its uncertainty. Use your derived equation from the pre-lab to calculate the speed of light.

Record the fiber length l = 20 m. Before using this value, think about its uncertainty. The fiber was cut to length during manufacturing — how precisely do you think it was cut? Estimate a reasonable uncertainty ∆l for the fiber length and justify your estimate.
Using your equation for the speed of light with n = 1.49, calculate the speed of light in vacuum from your measured time delay. Show all steps.
Now propagate your uncertainty through the calculation. You have two sources of uncertainty: ∆t (from your time measurement) and ∆l (from your estimate of the fiber length uncertainty). Use the propagation rules from the error analysis activity to find ∆c. Which source of uncertainty has the greater impact on your result?
Report your result in correct form: (c ± ∆c) with appropriate units.
The accepted value for the speed of light in vacuum is c = 2.998 × 10⁸ m/s. Does your result agree with the accepted value within your stated uncertainty? Apply the comparison rule from the error analysis activity and show your work.
The manual for this apparatus gives n = 1.5 for the fiber, but we have been using n = 1.49. Recalculate c using n = 1.5. How much does your result change? What does this tell you about the sensitivity of your measurement to the assumed value of the index of refraction?

Section 6: Reflecting on the Experiment

Before you leave, take a few minutes to reflect. Record your responses in your shared lab notebook.

Compare your measured time delay to your pre-lab prediction. Do they agree? If not, what is the most likely explanation?
You identified two sources of uncertainty in your calculation — the time measurement and the fiber length. Which dominated? Was this what you expected from your pre-lab analysis?
What sources of systematic error might affect this measurement? Think about the calibration step, the fiber connections, and the index of refraction value. For each source you identify, state whether it would make your measured value of c too high or too low.
This experiment connects a measurement you made on a lab bench to one of the fundamental constants of nature — and to the fiber optic cables that carry the world’s data. You will soon communicate this experiment to a non-scientist audience. Think about the storytelling angle you chose in your pre-lab. Has working through the experiment changed which angle appeals to you, or reinforced your original choice? What is the most surprising or compelling thing you could tell a non-scientist about what you did today?

A note on your upcoming communication assignment: you will produce a one-page public-facing written piece about this experiment, and some of you will also give a short oral presentation. Both are for a non-scientist audience. Your lab notebook reflections from today — especially question 37 — are a good starting point. Start thinking now about what story you want to tell and who you are telling it to.

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, Question 2	1, 2
Section 2, Question 5	2
Section 3, Questions 6–17	3, 4
Section 3, Question 19	2, 5
Section 4, Questions 20–21	3, 4
Section 4, Questions 22–25	5, 6
Section 5, Questions 26–31	5, 6
Section 5, Question 32	2, 6
Section 6, Questions 33–35	2, 4, 5
Section 6, Question 36	1, 7